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University of Miami
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2011-04-18
A Model Describing the Effects of Equipment,Instruction and Director and Student Attributes on
Wind-Band IntonationBrian C. WuttkeUniversity of Miami , [email protected]
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Recommended Citation Wuttke, Brian C., "A Model Describing the Effects of Equipment, Instruction and Director and Student Attributes on Wind-BandIntonation" (2011). Open Access Dissertations. Paper 564.http://scholarlyrepository.miami.edu/oa_dissertations/564
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UNIVERSITY OF MIAMI
A MODEL DESCRIBING THE EFFECTS OF EQUIPMENT, INSTRUCTION AND
DIRECTOR AND STUDENT ATTRIBUTES ON WIND-BAND INTONATION
By
Brian C. Wuttke
A DISSERTATION
Submitted to the Facultyof the University of Miami
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Coral Gables, Florida
May 2011
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© 2011Brian C. Wuttke
All Rights Reserved
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UNIVERSITY OF MIAMI
A dissertation submitted in partial fulfillment of
the requirements for the degree of Doctor of Philosophy
A MODEL DESCRIBING THE EFFECTS OF EQUIPMENT, INSTRUCTION AND
DIRECTOR AND STUDENT ATTRIBUTES ON WIND-BAND INTONATION
Brian C. Wuttke
Approved:
___________________________ ___________________________
Stephen F. Zdzinski, Ph.D. Terri A. Scandura, Ph.D.
Associate Professor of Music Education Dean of the Graduate SchoolAnd Music Therapy
___________________________ ___________________________ Edward P. Asmus, Ph.D. Nicholas J. DeCarbo, Ph.D.
Associate Dean of Graduate Studies Professor of Music Education and
Professor of Music Education and Music Therapy
Music Therapy
___________________________ ___________________________
Gary Green, M.M. Marilyn Neff, Ed.D.
Professor of Instrumental Performance Assistant Professor of Education
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WUTTKE, BRIAN C. (Ph.D., Music Education)
A Model Describing the Effects of Equipment, (May 2011)
Instruction and Director and Student Attributeson Wind-Band Intonation
Abstract of a dissertation at the University of Miami.
Dissertation supervised by Professor Stephen F. Zdzinski.
Number of pages in text. (194)
The purpose of this study was to test a hypothesized model of wind-band intonation,
using equipment, instruction and director and student attributes as components. Band
directors ( N = 5) and their students ( N = 200) were given a combination of published and
researcher designed tests to measure equipment quality, experience, knowledge of
instrument pitch tendencies and aural discrimination skills. In addition, each band was
video recorded to observe their warm-up, tuning and rehearsal procedures and activities.
Spectrum analysis using Praat phonetic analysis software (Boersma & Weenik, 2010)
was used to measure wind-band intonation. Structural equation modeling (SEM) using
AMOS (Arbuckle, 2008) was the method chosen to analyze and interpret the data.
Although the hypothesized model could not be estimated, a model generating approach
resulted in a three-factor model describing the effects of instruction and student attributes
on wind-band intonation. Model fit was good (χ 2
= 3.486, df = 7, p = .837, GFI = .994,
CFI = 1.00, RMSEA = .000). The respecified model indicated that instruction and
student attributes explain 99.3% of the variance in the dependent variable wind-band
intonation. For each SD increase in the latent instruction variable, wind-band intonation
increases by .95 a SD. Activities involving aural-based tuning strategies, tuning intervals
and chords evidenced higher intonation scores. For each SD increase in the latent student
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attributes variable, wind-band intonation increases by .16 a SD. This suggests that
instrument quality, experience in band and private lessons, and aural acuity combine to
affect intonation scores, but these student attributes are less influential than instruction.
A supplementary finding revealed that 72.5% of the students (n = 145) made at least one
error ( M = 4.05, SD = 3.76) on the test measuring knowledge of their instrument’s pitch
tendencies.
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iii
ACKNOWLEDGEMENTS
Jerry and Annette Wuttke, my parents, for their support and encouragement.
Lucy Wuttke, my wife, for her faith and devotion.
Gabrielle, Alexandria and Sophia, my daughters, for their patience.
Dr. Stephen Zdzinski, my advisor, for his eternal optimism and guidance.
Drs. Nicholas DeCarbo and Joyce Jordan, my mentors, for demonstrating how structureand dedication to teaching can impact learning.
Dr. Edward Asmus, for suggesting that intonation could be scientifically measuredthrough spectrum analysis.
Dr. Peter Miksza, for recommending the spectrum analysis software Praat.
Mr. Gary Green whose superb musicianship serves as a constant reminder of music’s
priceless value.
Dr. Charles Ciorba, for promoting the idea of pursuing a graduate degree in music
education.
The bands participating in the 2001 All Japan Band Competition for demonstrating that
superb intonation from middle and high school aged students is humanly possible.
The band directors and students in the Miami-Dade County school system who
participated in the study.
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TABLE OF CONTENTS
Page
LIST OF FIGURES ..................................................................................................... viii
LIST OF TABLES....................................................................................................... x
CHAPTER ONE
Introduction............................................................................................................ 1
Need for the Study ................................................................................................. 2
Purpose .............................................................................................................. 4
Model Components................................................................................................ 6
Wind-band intonation ...................................................................................... 6
Equipment........................................................................................................ 7
Instruction ........................................................................................................ 8
Director attributes ............................................................................................ 10
Student attributes ............................................................................................. 10
Other Influences..................................................................................................... 12
CHAPTER TWO
Review of Literature .............................................................................................. 14
Wind-band Intonation ............................................................................................ 14
Pitch .............................................................................................................. 15
Tuning standard ............................................................................................... 17
Temperature and dynamics .............................................................................. 19
Harmonic series ............................................................................................... 20
Temperament ................................................................................................... 22
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Equipment .............................................................................................................. 23
Instruction ............................................................................................................. 25
Curricular scope and sequence......................................................................... 25
Warm-up and tuning strategies ........................................................................ 30
Director Attributes ................................................................................................. 32
Student Attributes .................................................................................................. 35
Perception ........................................................................................................ 35
Experience........................................................................................................ 37
Knowledge of instrument pitch tendencies...................................................... 38
Summary ............................................................................................................. 39
CHAPTER THREE
Method .............................................................................................................. 41
Participants............................................................................................................. 41
Measures ............................................................................................................. 42
The dependent latent variable: wind-band intonation .................................... 44
Spectrum analysis ...................................................................................... 44
The latent variable: equipment......................................................................... 48
Quality........................................................................................................ 49
Band instrumentation................................................................................. 49
The latent variable: instruction ........................................................................ 51
Warm-up, tuning and rehearsal.................................................................. 51
The latent variable: director attributes ............................................................. 52
Director experience.................................................................................... 52
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Director aural acuity .................................................................................. 52
The latent variable: student attributes.............................................................. 53
Student experience ..................................................................................... 54
Student pitch acuity.................................................................................... 54
Instrument tuning skill ............................................................................... 55
Procedure .............................................................................................................. 56
Data analysis .......................................................................................................... 58
CHAPTER FOUR
Analysis of Data..................................................................................................... 62
Descriptive Statistics.............................................................................................. 63
Wind-band intonation ................................................................................... 63
Equipment ...................................................................................................... 64
Instruction ..................................................................................................... 67
Director attributes ......................................................................................... 68
Student attributes .......................................................................................... 69
Interrelationships between the Observed Variables ............................................ 72
Model Estimation ................................................................................................ 76
Model Respecification ........................................................................................ 77
Revised four-factor model ............................................................................... 80
Three-factor model........................................................................................... 82
Three-factor covariate model........................................................................... 83
Three-factor adjusted model ............................................................................ 84
Discussion ........................................................................................................... 87
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CHAPTER FIVE
Conclusion ............................................................................................................. 91
Implications............................................................................................................ 94
Future Research ..................................................................................................... 96
APPENDICES
Appendix A: Research Announcement ................................................................. 100
Appendix B: Informed Consent Forms .............................................................. 101
Appendix C: Band Director Inventory .............................................................. 107
Appendix D: Chorale in B
b
Major .................................................................... 110
Appendix E: Testing Instructions ..................................................................... 111
Appendix F: Student Test Packets .................................................................... 113
Appendix G: Supplementary Testing Materials .................................................... 144
Appendix H: Video Observation Forms ........................................................... 148
Appendix I: Spectrum Analysis Results ................................................................ 155
REFERENCES
References ......................................................................................................... 186
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viii
LIST OF FIGURES
Page
Figure 1. A hypothesized latent trait model describing the effects of equipment,instruction and director and student attributes on wind-band intonation.... 5
Figure 2. The general effect of observed dynamics on pitch deviation byInstrument type according to Kohut (1996)................................................ 13
Figure 3. The visual representation of a sine wave.................................................... 16
Figure 4. Visual representation of constructive and destructive interference of
two sine waves at 60 Hz and 66 Hz ............................................................ 17
Figure 5. The harmonic series in A with a fundamental of 55 Hz to the8th
harmonic of A = 440 Hz ........................................................................ 21
Figure 6. This formant depicts split peak variance around the expected
frequency of 175.47 Hz. In Praat, positioning the cursor over each
peak provides the exact frequency (Hz) and amplitude (dB). Thisinformation is used to calculate mean deviations from the
expected frequency ..................................................................................... 46
Figure 7. A latent variable structural equation model describing the effects
of equipment, instruction and director and student attributes onwind-band intonation .................................................................................. 61
Figure 8. This graph depicts mean differences of instrument quality between bands ........................................................................................................... 65
Figure 9. This graph depicts mean differences of musical experience between
bands ........................................................................................................... 70
Figure 10. Distribution of student test scores on the PTM ......................................... 72
Figure 11. Revised four-factor model of wind-band intonation ................................. 81
Figure 12. Three-factor model of wind-band intonation ............................................ 82
Figure 13. Three-factor covariate model of wind-band intonation............................. 83
Figure 14. Distribution of student test scores on the PTM with adjustment............... 86
Figure 15. Three-factor adjusted model of wind-band intonation .............................. 87
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Figure 16. A model describing the effects of instruction and student attributeson wind-band intonation ............................................................................ 92
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x
LIST OF TABLES
Page
Table 1. Proposed Sequence for Teaching Intonation to StudentWind Instrumentalists .................................................................................. 29
Table 2. Defining Model Components for Latent and Observed Indicator Variables, Measure Names and Abbreviations............................................ 43
Table 3. Chord Calculator Depicting the Intonation Score for a High School Band. 48
Table 4. Ideal Wind-Band Instrumentation and Voice Group Assignments
for Octaves in F............................................................................................ 50
Table 5. Spectrum Analysis Scores of Sample Extractions from Five BandPerformances Listed by Final Score in Ascending Order............................ 64
Table 6. Instrument Part Assignments by Voice and BIM Score Comparisons........ 66
Table 7. Video Observation Scores from Five Bands for Observed VariablesDescribing Instruction.................................................................................. 68
Table 8. Observed Variables of Model Components Comparing Disaggregated (D)and Aggregated (A) Correlation Coefficients.............................................. 74
Table 9. Standardized Residual Covariances for a Three-factor Correlation
Model of Wind-Band Intonation.................................................................. 85
Table 10. Correlations, Mean Scores and Standard Deviations for a Model
Describing the Effects of Instruction and Student Attributes
on Wind-Band Intonation ( N = 200)............................................................ 93
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CHAPTER ONE
Introduction
For high school band directors, teaching students to perform in tune is probably
their most difficult task. Michael Smith (2004) said “a band is wickedly difficult to tune
[and that] the only thing harder to tune is a chorus of piccolos playing upper-register
discords.” Percy Grainger (1939) urged band directors performing “Rufford Park
Poachers” in Lincolnshire Posy to overlook intonation problems inherent in the soprano
saxophone with this comparison: “But are the B [ sic] clarinets ever heard in tune? Never
by me. Yet I readily admit that they are un-do-withoutable.” William Revelli (1938) was
more eloquent stating, “It is safe to presume that intonation represents one of the most
important and difficult phases which directors of school music have to teach.” Donald
Wilcox (as cited in Casey, 1993) was probably the most succinct stating, “Intonation is
everything.” Similar beliefs are supported by a variety of authors who note the abundant
quantity of articles pertaining to wind-band intonation appearing throughout music
education publications (Graves, 1963; Latten, 2005; Millsap, 1999; Nichols, 1987; Pottle,
1961). In addition to all of the literature on the subject, music education conventions
regularly program clinics and workshops dealing with band tuning strategies. This
practice supports the idea that directors have a continued interest in discovering new
methods that will help them teach wind-band intonation more effectively.
Why are band directors still so interested in this subject? One answer suggests
that performance ratings at evaluations and festivals are strongly related to the band’s
ability to perform in tune. Findings from a study investigating conductor expressivity
inadvertently found that judges’ comments at band festivals cited intonation as the most
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common concern (Price, 2006). In a study where music majors were asked to evaluate
wind band performances, Johnson and Geringer (2007) noted that “lower ratings of less
experienced groups were related to deficiencies in intonation and tone.” Ratings aside,
these findings suggest that good intonation is an important characteristic for many
listeners. Although impeccable intonation is not required for appreciating a performance,
it “is characteristic of a musically sensitive performance” (Morrison & Fyk, 2002). Even
a beautifully shaped phrase will be marred by divergent tones and unfocused pitches. If
refined intonation is such an important ingredient for accomplishing meaningful
expression, it would seem that a unified and sequential approach to solving wind-band
intonation problems would have been adopted by band directors long ago. This
assumption would be false (Latten, 2005).
Need for the Study
Although wind-band intonation is a group endeavor, research studies that deal
with the topic are typically designed to measure the tuning skills of individual wind
instrumentalists (Dalby, 1992; Duke, 1985; Karrick, 1998; Kopiez, 2003; Morrison,
2000; Swaffield, 1974; Swift, 2003; Worthy, 2000; Yarbrough, Morrison, & Karrick
1997). This design relies on the assumption that instrumentalists tune the same way
individually as they would when performing in an ensemble. Few research studies
attempt to analyze tuning in group settings. “A major drawback to tuning research is that
most investigations have been conducted with only one subject at a time, and in many
cases, removed from any actual musical context” (Karrick, 1998). This is likely due to
technological limitations involved with gathering accurate pitch readings from
instrumentalists performing in an ensemble. Electronic tuners work best when used by
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one instrumentalist at a time in a quiet setting. They do not operate reliably in the
presence of more than one sound and should not be used to measure the tuning accuracy
of winds in consort.
Millsap (1999) states, “while there is an abundance of resources devoted to
intonation and tone production, a review of the current body of literature suggested
that…ensemble intonation and tone quality has not been examined in a research-based
setting.” To clarify, this is not to say there is a lack of scientific studies involving the
tuning practices of wind instrumentalists; rather there is a lack of research involving
tuning in the ensemble setting. Stoffer and Leukel (2004) recognized the necessity for
measuring intonation in different harmonic contexts and devised a study to measure
tuning ability using the SpectraPro spectrum analysis program. Although the study only
had four flautists performing in two pairs, this design suggests that spectrum analysis can
be used to measure pitch deviations from more than one source simultaneously. Another
important outcome of this study was confirmation that pure tuning may be preferred.
Judging from literature pertaining to the subject, wind-band tuning pedagogy
relies heavily upon theory rather than empirical evidence. It is astonishing to think that
many ensemble teaching practices currently employed by band directors are based upon
what band directors have shared for generations. According to Schleuter (1996),
Most instrumental music teachers teach the way they were taught as children; they
seldom examine or question traditional methods and techniques of instruction
with regard to current theories and knowledge about music learning. Good, bad,
and inefficient methods and techniques of teaching music persist through
unquestioned adherence to tradition.
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If ever there was a subject ripe for empirical study, then wind-band intonation is that
subject.
Purpose
The purpose of this study is to propose a theoretical model of wind-band
intonation. In order to realize the model, the following research questions will be
investigated:
1. What are the descriptive statistical characteristics of the observed variables?
2. What are the interrelationships among the observed variables?
3.
Can a model of wind-band intonation be estimated? If so, what do post hoc
tests suggest about model fit?
4. Are there alternative models that also fit the data?
The idea for developing a model describing wind-band intonation was inspired by Otaki’s
(2001) one-year approach to band fundamentals, DeCarbo’s (1984, 1986) research in
error detection, conventional wisdom (Casey, 1993) and personal teaching experience
(Wuttke, 2007). A hypothesized latent trait model (Figure 1) describes how wind-band
intonation is directly affected by equipment, instruction and director and student
attributes. The model was constructed using Analysis of Moment Structures (AMOS)
software (Arbuckle, 2008).
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Figure 1. A hypothesized latent trait model describing the effects of equipment,
instruction and director and student attributes on wind-band intonation.
Due to the intangible nature of pitch, skeptics would argue that wind-band
intonation cannot be measured without an unwieldy number of variables. Therefore,
structural equation modeling (SEM) will be the method used to test the hypothesized
latent trait model. While other statistical techniques are limited to measuring a few
variables simultaneously, SEM provides an adaptable theory that can transform as new
evidence is discovered. More importantly, when directional paths are specified a priori,
SEM coefficients can imply a causal relationship and provide insight into what
components can be controlled to impact student learning. According to Casey (1993),
“some teachers feel that intonation is too hard to teach…as a result teaching intonation
can be frustrating for even the best teachers.” Using SEM to define a locus of control can
help band directors’ focus on obtaining equipment that will improve overall wind-band
intonation without incurring expensive cost overruns, implement more effective warm-up
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and tuning techniques, and provide sequential instruction to students in order to improve
wind-band intonation. By increasing teaching efficacy, band directors will have more
time to shape musical expression. Helping students create beauty through musical
expression is perhaps the ultimate goal.
Model Components
Quantifying properties associated with measuring wind-band intonation is much
more complex than this parsimonious model suggests (Figure 1). According to Asmus
and Radocy (2006), “many variables in music education are difficult to measure.”
Tuning epitomizes this belief because it comprises “an amalgam of several sub-skills
including pitch discrimination, pitch matching, and instrument tuning” (Morrison & Fyk,
2002). A myriad of external influences on intonation include: air temperature, equipment
quality, ensemble instrumentation and instructional content. More exist. The oval
structures depicted in Figure 1 represent latent variable constructs. They will consist of
indicator variables that will be operationally defined by preexisting and researcher
designed tests. Describing these latent constructs in terms of their composition and
relationship to each other is an important first step towards estimating the hypothesized
model.
Wind-band intonation. The Merriam-Webster (2010) dictionary defines
intonation as “the ability to play or sing notes in tune.” This sounds simple but band
directors often struggle when trying to explain it to their students. They often rely on
analogous comparisons to describe tuning. Before the age of digital television, Laycock
(1966) described the process of tuning the wind-band as, “[it] is not unlike tuning a TV
set; one must be tuned to the correct channel before the fine tuning adjustment can be of
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any help.” Therein lies the problem; “pitch is intangible making it a challenge for
directors to explain to student performers” (Welsh, 1954). Essentially, pitch can be
defined in two ways: 1) in acoustical terms as a physical manifestation, and 2) in
psychological terms as a perceptual neurological phenomenon. In this study, wind-band
intonation will be defined in acoustical terms and measured through spectrum analysis.
Equipment. Although there may be agreement that equipment exerts a direct
effect on wind-band intonation, there is debate about the direction and magnitude of this
influence. DeRoche (1987) states, “Problems of intonation, tone, range and technique are
all affected by the quality and condition of the performer’s equipment.” Although
intuition suggests that wind-band intonation will improve proportionately with wind
instrument quality, there actually may be little difference. Instrument manufacturers and
performers “claim to detect clear and consistent tonal differences between otherwise
similar instruments made from different materials, but physical analysis suggests that
these claims may be illusory” (Fletcher & Rossing, 1998). Just how much of a difference
does instrument quality affect wind-band intonation? If the only difference between two
bands of like instrumentation is whether the clarinets are constructed with wood or
plastic, yet wind-band intonation is equally palatable, this finding could have a profound
financial impact upon school band programs. If musical instruments manufactured with
less expensive materials can produce equally desirable results, it might serve to dispel the
myth that poor wind-band intonation is in some way attributed to instrument design
rather than instruction or student attributes.
Another aspect of equipment involves instrumentation. Historically, wind-band
instrumentation has varied considerably (Fennell, 1954). The goal of establishing an
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internationally recognized instrumentation standard was first addressed at the American
Bandmasters Association convention in 1930 with implementation by music publishers in
1932 (Manfredo, 2006). High school band directors generally abide by these standards
when determining their ensemble’s instrumentation but may not understand how their
choices affect ensemble intonation.
When the winds perform in consort, intonation can be affected by the availability
and distribution of instrumentalists assigned to the soprano, alto, tenor and bass voices.
In chordal harmony, instruments assigned to the bass voice typically perform the
fundamental, thereby establishing an overtone series to which the upper voices must
conform. A common problem for many school bands is a disproportionate number of
upper voices to the bass voice –too many flutes, trumpets and saxophones, and not
enough bassoons, bass clarinets and tubas. This imbalance inhibits the upper voice
performer’s ability to hear the overtones produced by the lower instruments. To
compensate for this disparity, directors sometimes rely on the idea suggesting that
unbalanced instrumentation can be rectified by teaching a “pyramid of balance” where
performers on the upper voices perform proportionately softer than those on the lower
voices. However, this often produces a contrived sound and does little to solve poor
intonation and often creates more problems than it solves. In the hypothesized model,
equipment will be defined by quality and instrumentation.
Instruction. A recent survey described a hypothetical band program and asked
high school band directors ( N = 134) to report the number of years of high school
teaching experience and to estimate how many weeks and minutes per rehearsal it would
take to “get their band to perform the chorale Awake, My Heart, Sing Gladly by Nicolaus
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Selneccer in tune” (Wuttke, 2008). A full score of the chorale was provided to guide
their judgment. A statistical analysis found a very small non-significant correlation
(r = .06, p = .50) between teaching experience and the estimated number of weeks for
achieving in-tuneness. There was also a very small negative correlation (r = -.04, p =
.63) between teaching experience and estimated minutes per rehearsal for achieving in-
tuneness. A small, non-significant negative correlation was found between the estimated
number of weeks and minutes (r = -.13, p = .15). One participant in the survey
responded: “By in tune I think you mean about 80%” (Wuttke, 2008). This disparity
suggests that high school band directors exhibit exceptional incongruity conceptualizing
scope and sequence when implementing curriculum designed to improve wind-band
intonation.
Much of what occurs in rehearsal is controlled by the band director, yet there is
little research on instructional content in regards to teaching intonation. Nichols (1987)
theorized that band directors could “…effect considerable improvement in their students’
intonational performance by carefully planned intonation instruction presented in an
organized and consistent manner.” Instead, many high school band directors rely on a
trial and error approach to problem solving by attempting to correct performance errors
as they occur rather than by careful planning. Paynter (as cited in Neidig, 1979) laments,
“But correcting is really not the most efficient way to rehearse…guiding the performer so
the mistake is not made in the first place…is more efficient.” And perhaps in language
that most band directors can relate to; “the easier way to teach is to wing it” (Casey,
1993). Despite all of the articles and workshops devoted to helping directors correct
wind-band intonation through a unified approach, it is not unlikely to observe different
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bands warming-up and tuning using completely different strategies. Therefore,
instruction will be defined by the content and quality of warm-up, tuning and rehearsal
strategies.
Director attributes. A frustrating dilemma arises when band directors realize in
the middle of conducting a rehearsal or performance that they cannot directly control
intonation. Of course, they can stop and provide verbal explanations or provide a
reference tuning note for students, but even the best conducting gestures cannot fix pitch
problems in real time. David Hans (as cited in Casey, 1993) recollects telling his
students, “You can play in tune, but I cannot conduct you in tune.” Donald Hunsberger
(as cited in Casey, 1993) states, “I believe there is only one person responsible for each
individual’s intonation and that person is behind the mouthpiece.” But band directors do
play an important role in developing good wind-band intonation by providing meaningful
feedback, creating balanced instrumentation, designing a sequential curriculum, and
implementing effective lessons. Essentially, band directors are where learning begins
because their musical skills, educational background and experience are the basis for
making logistical and curricular decisions. This belief rests on the assumption that band
directors hear intonation problems; therefore, director attributes will be defined by
experience and aural acuity.
Student attributes. In this model, wind-band intonation is directly influenced by
student attributes. In spite of this obvious assertion, conventional wisdom and results
from perceptual studies sometimes clash. It is extraordinarily unusual to find articles
describing how to improve wind-band intonation without mentioning the importance of
developing student listening skills. Miller (1997) writes,
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For student wind players the most difficult and often unmastered aspect of
playing seems to be hearing the entire ensemble. Those who can’t hear are unable
to play in tune or achieve good balance and blend because they have not acquired
the necessary hearing skills.
However, performing in-tune on a wind instrument goes beyond perceiving out-of-
tuneness. Ely (1992) found virtually no correlation (r = .07) between perceiving pitch
deviations and performing in tune. Pfordreshor and Brown (2007) found that poor pitch
singing occurs with poor integration of production, memory, and/or sensorimotor skills as
opposed to perceptual shortcomings. Performing on a wind instrument likely involves
the same kind of skill integration. According to Goolsby (as cited in Latten, 2005) “…as
soon as a piece of machinery is placed in the mouth, the psychomotor skills developed
over the years are bound to prevail over the perceptual task.” Certainly, perceptual skills
are required to detect the need for tuning adjustments, but it is more important to identify
exactly what kind of perceptual skills are required to make these adjustments in terms of
their relevancy to the physical aspect of the tuning task.
Experience is another student attribute, and it can be described in terms of the
length of time participating in music. Wind instrumentalists hoping to improve their
ability to perform in tune need time to develop neuromuscular skills. Exactly how much
time is needed to produce acceptable results is not clearly delineated. Research suggests
that expert musicians appear to have invested about “10,000 hours of dedicated practice
over ten or more years” (Altenmueller and McPherson, 2008). However, school bands
often produce acceptable results in much less time. Otaki (2001) prescribes a one-year
approach; “In Japan, most band clubs are independent, self-feeding entities which depend
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upon rapid assimilation of beginners into often highly advanced ensembles.” Private
lessons are also beneficial. A study designed to measure the tuning performances of high
school wind instrumentalists found that students receiving private instruction tended to be
the most accurate tuners (Yarbrough, Morrison & Karrick, 1997).
Another area of interest regarding wind-band intonation concerns student
comprehension of instrument pitch tendencies. Again, conventional wisdom prevails;
“Be sure students learn all of the pitch tendencies on their instruments by working
individually with a tuner outside of class” (Heath, 1980). Miller (1997) states
emphatically, “Each player must be taught the intonation deficiencies of his particular
instrument.” Experienced wind instrumentalists realize that certain notes require
adjustments such as alternate fingerings or embouchure adjustments in order to conform
to the tonal center of the wind-band. Mutes, instrument carriage, pad height and slide
adjustments are all responsible for pitch deviations on wind instruments. Consequently,
student attributes can be defined by perceptual skills, instrumental experience and
knowledge of instrument pitch tendencies.
Other Influences
Factors not depicted in the hypothesized model can also influence wind-band
intonation. For example, air temperature directly impacts wind-band intonation. Modern
wind instruments are manufactured to a standard where A=440 Hz at 72° Fahrenheit.
Extreme deviations from this standard will produce intonation problems. As air
temperature increases, pitch rises. The amount of sharpness due to an increase in air
temperature is also dependent upon the size and material composition of the wind
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instrument (Kent, 1959). A study by DeCarbo and Fiese (1989) found that larger wind
instruments needed to be re-tuned more frequently if kept idle for more than two minutes.
Dynamic extremes also cause pitch discrepancies. According to Kohut (1996),
most wind instruments tend to go sharp in loud passages and flat in soft passages. The
single reed instruments are the exception as they respond opposite sounding flat in loud
passages and sharp in soft passages (Figure 2). This explains the tendency of school
bands to perform within mezzo dynamic ranges. Straying too far from this dynamic
center can cause divergent pitch problems. Since the effects of air temperature and
extreme dynamics are well documented they will act as control variables in order to focus
on measuring the hypothesized model components.
Figure 2. The general effect of observed dynamics on pitch deviation by instrument typeaccording to Kohut (1996).
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CHAPTER TWO
Review of Literature
In 2001, the 120-member Saitama Sakae High School Symphonic Band traveled
from Tokyo, Japan to perform at the Florida Music Educators Association Clinic and
Conference. In the general opening session, band members sat quietly on stage for over
45-minutes while speeches were made and awards distributed. Then, without warming-
up or tuning to a reference pitch, the band performed a transcription of Wagner’s Prelude
to Act III from Lohengrin. The performance defied logic; despite sitting idle for so long,
the students created a beautiful sonority with superb intonation. Furthermore, many of
the students in the ensemble had been performing on their instrument for less than one
year (Otaki, 2001). This seemed to contradict pedagogy describing the need for warm-up
and tuning procedures and prompted much discussion among conference attendees
leading the author on a quest to discover the means for recreating this sound. The
following review of literature represents the scholarly component of what pedagogues,
researchers, band directors and musicians believe are important theories, findings and
approaches to achieving ideal wind-band intonation.
Wind-band Intonation
Theoretically, tuning is an absolute; either the pitches match or they don’t. In
reality however, conditions exist where imperfect intonation is accepted as musicians
make an important distinction between the process of tuning and the product of
intonation. Kopiez (2003) refers to intonation as “the skillful ability of playing in tune.”
Karrick (1998) states, “Intonation is a term that can be used to describe, qualitatively, the
result of tuning or the degree to which musicians achieve in-tuneness.” Because music is
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a temporal art, tuning the wind-band is an ongoing process where musicians are
constantly working to adjust their pitch to each other. “The fact is that many musicians
perform as a part of a larger ensemble where performers are constantly listening and
adjusting to one another” (Karrick, 1998).
Garofalo (1996) describes 6 factors that cause poor wind-band intonation: 1)
condition and quality of the instrument and accessories, 2) fundamental performance
procedures, 3) insufficient warm-up, 4) deviating from standard tuning frequency of
A = 440 Hz, 5) psychological or perceptual issues, and 6) pitch ten dencies of instruments
and performers. Garofalo’s classification not only helps identify the causes of poor wind-
band intonation, he provides a concise description of the subject with specific corrective
recommendations. The opposite extreme occurs when authors of articles and methods try
to explain tuning based on analogous comparisons. Phrases like “play to the bottom of
the sound” or “play golden, oval tones” may be derived from some theoretical principle,
but they don’t always provide an explanation to students without prior intervention.
Colwell (1969) writes, “A little knowledge is a dangerous thing, and pitch is an area
where many only have a little knowledge.” The concept of wind-band intonation is broad
in scope but is frequently described by authors in terms of: 1) pitch, 2) tuning standard, 3)
temperature and dynamics, 4) the harmonic series, and 5) temperament.
Pitch. In music, pitch can be described as the fundamental frequency of sound.
According to Helmholtz (1954), “For musical tones…we anticipate a regular motion of
the air…” He is referring to the periodic vibration of air molecules that are measured in
cycles per second—the number of wave crests that occur in one second. The visual
representation of air molecules is generally depicted as a sine wave (Figure 3).
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Helmholtz was so influential in describing the nature of sound that the abbreviation for
frequency (Hz) is based on the first and last letters of his last name.
Figure 3. The visual representation of a sine wave.
For wind instrumentalists, a substantial portion of tuning skill relies on matching
pitch. Performers will often compare their pitch with the target pitch. If the pitches are
not the same, the performer will attempt to determine whether their pitch is higher or
lower than the target pitch. This level of aural discrimination provides the instrumentalist
with the information needed to make a physical adjustment—whether on the instrument
or embouchure—to raise or lower their pitch as needed. This is not the only way that
instrumentalists perceive pitch differences.
According to Miles (1972), beats are pulsations of sound heard when two tones of
slightly different frequencies, such as 440 Hz and 442 Hz, occur at the same time.” This
phenomenon is described by the beat theorem (Helmholtz, 1954). When two sine waves
vibrate at frequencies ( f 1 and f 2 ) that are very close, we experience a phenomenon
called beating. As a moving pitch ( f 1) approaches a fixed pitch ( f 2), the rate of beating
decreases. As a moving pitch ( f 1) departs from a fixed pitch ( f 2), the rate of beating
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increases. When sine waves overlap, the amplitude is periodically enhanced and
diminished through constructive and destructive interference (Figure 4). Thus, beating
may also be described as a periodic variation in amplitude that occurs at a rate ( f 1 – f 2)
with a frequency shift ( f 1 + f 2 / 2). In practicality, instrumentalists seek to improve
wind-band intonation through beat elimination and by manipulating their fundamental
pitch.
Figure 4. Visual representation of constructive and destructive interference of two sine
waves at 60 Hz and 66 Hz.
Tuning standard. While most instrumental music teachers realize that tuning to
a predetermined pitch—usually B b
or A—is an important process for checking intonation
consistency, it is often taken for granted how much these tuning pitches have fluctuated
over time. Throughout history the concert pitch A has often been used as the tuning
standard. Some pipe organs manufactured in 1500 A.D. are centered at A = 505.8 Hz.
From the late 16th
through 17th
centuries, this tuning standard gradually decreased to
A = 393.2 Hz in order to accommodate other representative instruments of that time.
However, from the early 18th
century, pitch tended to increase, varying from
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A = 415-429 Hz. According to Kent (1959), “this tuning level represented the classical
pitch of music.”
In the 19th
century, the orchestra assumed greater importance and wind
instruments were improved through a variety of technological advances. One method for
producing exciting effects was accomplished by raising the pitch. By the end of the
century, some wind bands were performing at a tuning frequency of A = 457 Hz.
Although a preliminary attempt to fix A = 440 Hz at 72° F was proposed by the Congress
of Physicists held at Stuttgart in 1834, this standard was not internationally recognized
until 1939. Modern orchestras generally tune at A = 440-442 Hz. The Boston Symphony
Orchestra purportedly tunes at A = 445 Hz (Long, 1977). The problem with performing
at a pitch standard higher than A = 442 Hz is that it can wreak havoc on wind instruments
that are manufactured to A = 440 Hz at 72° F. Up until “the first years of the twentieth
century manufacturers produced both low-pitched instruments at A = 440 Hz and high
pitched instruments at A = 457 Hz (Kent, 1959). According to Kent (1959), “At times
both types of instruments were inadvertently used in the same band with rather peculiar
results.”
Instrument manufacturers and musicians have long realized that the first step in
establishing pitch uniformity in the ensemble was recognizing a set tuning standard. A
standard of tuning is essential in order to circumvent tuning complications that would
occur in the ensemble if instruments manufactured to different standards were used. For
example, a clarinet manufactured to A = 440 Hz at 72° F will have its barrel pulled
slightly at 72° F whereas a clarinet manufactured to A = 442 Hz at 72° F will have its
barrel pulled significantly to tune-down to the pitch of the clarinet manufactured at
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A = 440 Hz. The clarinet manufactured at A = 440 Hz at 72° F would likely never be
able to push in far enough to meet the pitch level of the clarinet manufactured at A = 442
Hz at 72° F. Even greater discrepancies, especially for throat tones, will arise as tradition
dictates that clarinets are often tuned completely closed to concert B b
or A (Kent, 1959).
Temperature and dynamics. In spite of recognizing a set tuning standard, other
factors such as temperature and dynamic extremes can cause diametrically opposed pitch
discrepancies in wind instruments. As a general rule, pitch tends to rise incrementally in
wind instruments as a direct result of increases in room air temperature and the player’s
breath. Pottle (1961) describes this difference as follows:
Whatever the outside temperature, the air inside an instrument at the mouthpiece
end will soon be raised to about 90° F (since the player’s breath is 98.6° F), so
that if we assume the temperature outside the instrument is 70° F, the mean
temperature in the instrument is something between 90° F at the mouthpiece and
70° F at the bell, or say 90° + 70°/2 = 80° F.
This increase is not the same among different wind instruments which vary due to
instrument size and composition—wood and metal retain heat differently and smaller
instruments warm faster than larger instruments. Therefore, idle non-playing time
adversely effects wind-band intonation. “Directors need to recognize that excessive time
expended on individual tuning procedures, while the remainder of the ensemble remains
idle, may contribute to poor intonation” (Decarbo & Fiese, 1989).
Kent (1959) found that in “temperatures less than 80° F, fifteen to twenty minutes
of playing a brass bass has been necessary in order to stabilize intonation.” In addition,
“During a long rest in the performance, any wind instrument should be warmed by
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blowing the breath through the instrument to avoid flatness when playing is resumed”
(Kent, 1959). Another problem arises when performing in an environment when the air
temperature is above 80° F. To compensate for discrepancies of pitch at extreme high
temperatures, the director could raise the tuning standard A = 442 Hz at higher
temperatures above 80° F, but then must accept the discrepancies between wind and non-
wind instruments (Kent, 1959; Pottle, 1961). Therefore it is advisable to maintain the
tuning standard of A = 440 Hz whenever possible (Garofalo, 1996).
Perhaps the most perplexing problem facing wind instrumentalists is maintaining
pitch uniformity at extreme dynamic levels. Not understanding these tendencies can
confound an instrumental music teacher trying to solve tuning problems in varying
degrees of loudness. In general, tones from single reed instruments fall flat as loudness
increases whereas brass instruments and flutes sound increasingly sharp when played
louder, with flute pitch deviations being most noticeable. In some cases, deviations due
to dynamic change can be as much as 25 cents (Pottle, 1961).
Harmonic series. A basic concept of sound is described by the acoustical
phenomenon known as the harmonic series, which was purportedly discovered by the
Greek philosopher Pythagoras (c. 570-595 BCE). When a pitch is sounded, it consists of
the fundamental pitch and several higher pitches known as overtones (Figure 5). The
pitches are all related by a series of whole number ratios of 2:1, 3:1, 4:1, continuing
infinitely. The concept of tuning pitches according to these perfect ratios is referred to as
just intonation. According to Helmholtz (1954), “This relation of whole numbers to
musical consonances was from all time looked upon as a wonderful mystery of deep
significance.”
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“The harmonic series directly affects tone quality, intonation, and ensemble
blend” (Kohut, 1996). When instrumentalists create sounds they are, in a sense,
manipulating the amplitude of the fundamental and overtones in the harmonic series. For
example, a bright tone reinforces the upper harmonics, diminishing the amplitude of the
fundamental and lower harmonics. A dark tone reinforces the fundamental and lower
harmonics, while a characteristic tone represents a balance between the fundamental and
harmonics that define the distinctive timbre of the instrument or voice. Ultimately, tone
quality is a factor affecting both the perception and performance of pitch. Results from
studies measuring the effect of tone color indicate that musicians associate bright tone
with sharp and dark with flat intonation (Geringer & Worthy, 1999; Worthy, 2000). Of
course, as any tuner will reveal, pitch is acoustically unaltered if the fundamental
frequency remains unchanged.
Intonation is the degree to which an instrumentalist conforms to the harmonic
series. When tuning the wind-band, intonation is often conceptualized from the bottom-
up. “The overtones of the large instruments are in the range of the fundamental notes of
the upper instruments, and therefore must be kept down in tune” (Miller, 1996). In other
(Hz) 55 110 165 220 275 330 385 440
1 2 3 4 5 6 7 8
Figure 5. The harmonic series in A with a fundamental of 55 Hz to the 8th
harmonic
of A = 440 Hz.
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words, the lower instruments need to conform to A = 440 Hz because rising above this
pitch standard will cause the listener to perceive the upper winds as flat. In order to
accomplish just-tuned octaves in the wind-band, the upper winds must match the
overtones produced by the fundamental produced in the lowest instruments. This
scaffold-like approach to tuning is also the basis for harmony. Hoshina (2005) explains,
“You can build a major triad by using the notes up to the sixth harmonic. You can also
create a dominant seventh chord with notes up to the seventh harmonic.”
Temperament. The idea of temperament arose in the 15th
and 16th
centuries in
order to create instruments—primarily keyboard instruments as they were fixed pitch and
could not make minute adjustments in real time—that would stray the least from the
perfect ratios described by just intonation (Duffin, 2007). The assumption that the
modern tuning system of equal temperament is the best because of its widespread
acceptance is misleading. Intonation practices, like style and dynamic interpretation, are
based upon periodic trends. The present system of equal temperament has gained wide
acceptance as a musical pitch standard only recently. Although piano tuners knew of the
concept of equal temperament as early as the late Renaissance period, J.S. Bach actually
preferred an extended meantone system for tuning keyboards. This system still allowed
for some pure thirds and fifths in certain keys. Therefore, contrary to popular belief,
Bach’s music for “The Well-Tempered Clavier” is not synonymous with equal
temperament (Duffin, 2007). For consistency, manufacturers strive to create wind
instruments that conform to the equal tempered scale. Due to inconsistencies between the
pure ratios of just intonation and the contrived metrics of equal temperament they can
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never truly succeed, but they “come close enough so that a sensitive wind player can
learn to adjust [the] instrument” (Long, 1977).
Karrick (1998) noted that advanced high school and collegiate wind
instrumentalists ( N = 16) tend to deviate less from equal temperament than Pythagorean
and just-diatonic systems when performing melodic and harmonic intervals with recorded
excerpts. He found the greatest deviations in pitch occur with the intervals of thirds and
sixths rather than fourths, fifths and octaves. Kopiez (2003) found no significant
differences in pitch deviations for intervals performed in just intonation and equal
temperament by professional trumpet players ( N = 2). Pitch adjustments, when made,
were manipulated by embouchure changes and not alternate valve combinations.
In modern wind performance, a flexible approach incorporating a variety of
intonation systems should be realized. Colnott (2002) suggests that music containing
notes longer in duration than one second and in the absence of keyboard percussion
instruments, just intonation should be used. In other words, tuning all of the pitches and
intervals until the combined sound is beatless. When keyboard instruments are present,
he recommends the performers listen and adjust to the equal-tempered system of tuning
present in the fixed pitch instruments.
Equipment
Describing instrument quality represents dichotomous beliefs about design
specifications and the materials used in construction. Wind instrument intonation is the
direct result of the air temperature inside the instrument. Although certain materials,
such as grenadilla wood for clarinets and silver-plated brass instruments can impact tone
quality, the materials chosen to manufacture the instrument are irrelevant to improving
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intonation (Fletcher & Rossing, 1998). This may surprise band directors who believe that
purchasing more expensive instruments will produce better ensemble intonation.
According to Colwell (1969), “Another wrong track is to buy good intonation…It is
impossible to buy instruments that will play in tune. Only the performer can do that.” In
a survey of instrument quality in relation to intonation Hindlsey (1971) found “the
students’ own first-line instruments proved entirely capable of being played in tune when
kept with the proper adjustment.” The problem with instrument manufacturing occurs
when inexpensive instruments are mass produced with poor quality control in regard to
design specifications. This can lead to inaccurate placement of tone-holes and
inconsistencies in tube length which can drastically alter pitch consistency. Another
problem occurs as the result of poor care and maintenance. “A carelessly replaced pad on
a saxophone can turn a half-step into a quarter tone” (Long, 1977).
The quality of woodwind reeds, brass mouthpieces and brass instrument bells can
impact tone quality and intonation and perception task measurements supporting the idea
that bright tone is often perceived sharp, while dark is perceived flat (Worthy, 2000).
Maxey (2003) notes the following pitch tendencies on the clarinet: reed strengths under
2½ may cause the pitch to drop, more open-faced mouthpieces generate a higher pitch
than closed-faced mouthpieces, clarinets go flat on crescendos while most other
instruments go sharp, and keys that open too far will produce unusually sharp notes.
Wehner (1970) describes the effects of oboe reed profiles on pitch tendency and makes
recommendations based upon student embouchure development. He concludes, “The
music educator should experiment with various oboe reed profiles in order to find the
types that enable each of his students play in tune.”
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Instruction
The idea that intonation can be improved through training seems logical.
Common practice suggests techniques such as teaching students beat elimination,
vocalization techniques and working with tuners can improve musician tuning skills.
Elliot (1974) found regular practice during band class resulted in improved pitch
discrimination and tonal memory abilities. Graves (1963) found that aural, visual and
conventional tuning methods improve intonation equally well. The aural method
consisted of: (1) practicing while using an electronic pitch reference, (2) comparing
played tones with reference tones, and (3) perception and performance using the beat
elimination method. The visual method used a strobe tuner to detect intonation tendencies
indicating needed correction to student performers. The conventional method presented
concepts related to good intonation, which allowed for student and instructor to identify
pitch deficiencies in performance. All three methods were conducted through private, not
group instruction. Of the three methods, teaching tuning skills through the process of
beat elimination is an important area of focus. Miles (1972) found that beginning
students can then be trained how to eliminate beats from mismatched pitches.
Furthermore, most beginning wind students can use this strategy to match unison and
harmonized pitches on their instruments to achieve correct intonation.
Curricular scope and sequence. Tuning is a long-term goal. A common
mistake occurs when band directors attempt to solve ensemble intonation problems
minutes before an important performance instead of developing and implementing a daily
tuning routine. “The least effective thing I witnessed was directors running all over a
stage with a tuner just before a concert” (Barnes, 2010). Producing a characteristic
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sustained tone on a wind instrument is paramount to playing in tune and should precede
intonation studies. In a comprehensive review of literature dealing with band tuning
practices, Millsap (1999) describes how incorporating long tone exercises in daily warm-
up procedures can improve ensemble intonation. According to Altenmueller and
McPherson (2008) “…the more complex a task is, the shorter the practice time should be
scheduled in one session and the longer the breaks should be planned.” Despite detailed
sequential tonal and rhythm theories of instruction (Schleuter, 1996), “There is a need for
an instructional method designed to enhance tuning awareness and intonation skills as
part of regularly scheduled instrumental lessons” (Pasqua, 2001).
Perhaps the first condition deals with awareness. Bloomquist (1981) claims, “The
student must know when he is out of tune in order to be able to play in tune.” Criswell
(2008a) advocates using cards that are the same color but in slightly different shades to
visually demonstrate slight pitch differences. “Oral and written feedback helps students
become self-corrective as they pursue goals” (Bowman, 2007). After students have
experience producing a sound, the concept of tuning is introduced. “Teaching students
how to tune their instrument to one or two tuning notes, although important, does not
necessarily enable students to play in tune within a musical context” (Ely, 1992). Heath
(1980) suggests that teachers “Let the students correct fine pitch differences with their
embouchures before you instruct them to adjust their instruments.” Winkler (1996)
recommends “Playing along with students will give them the sensation of two
instruments playing in tune, even if the teacher is doing all the work. Later, encourage
the student to make the adjustments.”
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When students gain skill supporting a steady tone, other strategies have been
shown to help improve intonation. Garofalo (1996) believes that every student should
chart the intonation deficiencies on their instrument by performing a variety of scales
while using an electronic tuner. He cautions, “you should not look at the scope or meter
while playing because this is likely to effect [sic] the accuracy of the charting.” Instead,
he suggests that students work in pairs with one student recording pitch deviations while
the other student performs. Another strategy that has been shown to be effective (Miles,
1972) is the process of beat elimination. Garofalo (1996) describes the beat elimination
method as follows:
Once beats are heard, you must determine if you are sharp or flat to the other
player(s). If you are not sure, slowly start adjusting the pitch upward or
downward using a physical and/or mechanical technique that is appropriate for
your instrument and the note being played. If the beats begin to get faster, you are
going in the wrong direction, reverse the adjustment. As soon as the sound
becomes clear or resonant (beatless), you are in tune.
Another recent area of research deals with computer assisted instruction (CAI). Swift
(2003) reported a significant interaction ( F (1,38) = 4.52, p = .04) between the treatment
group that practiced tuning using Coda Music Technology’s Intonation Trainer and the
control group. However there were problems with the study due to small sample size
( N = 41) and sampling technique—students were participants in the top level band at the
researcher’s school and randomly divided into two groups instead of assigned by ability.
Few studies other than Milsap’s (1999) long-tone study have embarked upon
organizing tuning strategies into a meaningful, sequential curriculum. This is surprising
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because when motivating students to perform better in tune, the director “has direct
control of the musical materials selected for the learning task and the teaching strategies
applied within it” (Asmus, 1995). Pasqua (2001) implemented ten sequential tuning
activities in a cooperative learning tuning activities group (CLTA). Activities included:
adjusting when flat, adjusting when sharp, and tuning intervals. At the conclusion of the
study, the CLTA group evidenced a statistically significant ( p < .001) improvement in
mean tuning scores. Latten (2005) provides the most recent investigations into curricular
development for improving wind-band intonation.
According to Latten (2005), the “three conditions…necessary as a foundation for
successful development of intonation…[are] use of good quality instruments whose
tuning most closely matches equal temperament, constant striving for excellence in tone
quality, and development of the ability to audiate.” Working under that assumption he
asked high school and collegiate wind-band conductors, collegiate studio faculty,
intonation researchers, authors and wind-band experts ( N = 41) to provide up to three
descriptions for each of nine skill statements that, in their experience, result in successful
intonation. Participants were then asked to rank the skill statements from the most
fundamental to advanced. High reliability reported among the subgroups and aggregate
panel were very high ranging from r = .86 to r = .98. Statistical significance for the
sequence was not indicated due to a lack of significant differences between four pairs of
skills. The findings depicted in Table 1 do seem to support a sequential order that
corroborates intonation sequences described by Kohut (1973) and Shuler (as cited in
Casey, 1993).
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Table 1
Proposed Sequence for Teaching Intonation to Student Wind Instrumentalists
Latten, 2005 Shuler, 1993 Kohut, 1973a
1. Students demonstrate bysinging or humming, the ability to
match pitches (in context of tonal patterns and isolated pitches).
1. Students sing or hum pitchesstarting with familiar songs.
b
2. Students operate purely
mechanical intonation
adjustments on the their
instrument
2. Teacher provides model of in-
tune and out-of-tune sounds on
instrument against fixed reference
pitch to demonstrate acoustical beats.
1. The students are instructed
where to adjust the tuning
mechanism(s) on their instrument
as soon as they produce their firsttones.
3. Students recognize the absence
or presence of acoustical beating
(out-of-tuneness).
3. Students adjust pitch on their
instrument with tuning slides.
2. Students are taught to
recognize acoustical beats as soon
as they can produce a steady tone.
4. Students adjust pitch oninstrument with embouchure or
airstream without adversely
affected tone quality.
4. Students adjust their embouchures in combination with
slower or faster airstream to
manipulate pitch
3. Students are taught how toaurally tune the mechanism(s) on
their instrument.
5. Students demonstrate
knowledge of pitch tendencies on
instrument including the direction
of out-of-tuneness.
4. Students are taught to identify
pitch tendencies and adjust
intonation on these notes with the
embouchure and alternatefingerings when their playing
range exceeds an octave.
6. Students demonstrate
knowledge of the effects of
dynamics, temperature, use of mutes on their instrument’s pitch
tendencies.
c
7. Students demonstrate ability to
adjust chord tones to beatlesstuning in ensemble settings.
8. Students aurally identify chordtones within chords.
9. Students demonstrate cognitive
understanding of the pitch
deviations between justintonation and equal
temperament. Note: Entries are paraphrased from each author’s publication. aKohut first published Instrumental Music
Pedagogy in 1973; however, it is listed in the references with the second edition in 1996. bAlthough Kohutdoes not list singing in his intonation sequence, he does advocate singing with solfege in chapter 2. cKohut
describes the effects of dynamics and temperature on wind instrument intonation in chapter 3.
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Warm-up and tuning strategies. Kohut (1996) describes how tuning must not
precede an adequate warm-up and that successful tuning practices should emphasize the
aural aspects of adjusting pitch. As previously described, the warm-up process is
important in order to physically bring the air temperature inside the instrument up to the
tuning standard of A = 440 Hz at 72° F. Another aspect of the warm-up is to develop
fundamental performance skills. “Virtually all trained instrumentalists recognize the
importance of daily long tone studies yet few directors—and perhaps fewer students—
seem to budget the rehearsal time needed to adequately implement these exercises”
(Wuttke, 2010). Long tone studies also aid in embouchure development, breath support,
and can improve tone quality. Rather than investing in the long term benefits provided
by these studies, directors and students attempt to circumvent them altogether by trying to
fix intonation by tuning. This may be due to the fact that much has been written on the
subject.
Tuning the wind-band should be a cyclical process which constantly shifts back
and forth between the individual to the group. “Tuning that isolates problems and
identifies individuals who are in error is mandatory if tuning is to be meaningful”
(Bloomquist, 1981). According to Heath (1980), “Many novice band directors
immediately attempt to tune their groups to the quality level of the college band from
which they recently graduated. This expectation can cause rehearsals to lose
momentum…” Bloomquist (1981) states, “Ensemble tuning can take from a few minutes
to a few hours, and many musicians have probably observed a rehearsal where every
moment was used for tuning.” This should not imply that tuning shouldn’t take long if
warranted; rather it behooves directors to teach ensemble members the tuning strategy
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that they can implement as a group. “Teach ensemble players to discriminate between
pitches played in tune and out of tune. Avoid the temptation simply to tell them to push
and pull slides and joints…this mindless process does not ask students to make the tuning
decisions of which they are capable” (Byo, 1990). Otaki (2001) supports this assertion,
“Successful tuning depends on how well [the] ensemble has learned [the] tuning process
and each individual’s responsibility to listen to [the] appropriate voices.”
A great deal of controversy surrounds the practice of providing a reference pitch
for the ensemble. According to Long (1977), “The tradition of using the oboist is
questionable, since so many oboists, particularly among amateur players, do not produce
a consistent A = 440 Hz. Long advocates using an electronic reference pitch for students
and amateur ensembles because the pitch is reliable in all environmental conditions.
Smith (2004) does not advocate using an electronic tuning note because it is not an
“engaging sound.” Yet the idea of using an electronic source is apparently not new.
“Leopold Stokowski, during his tenure as conductor of the Philadelphia Orchestra, used a
mechanical tuning device with the orchestra at the Curtis Institute as early as
1938…Stokowski used A = 438 Hz” (Long, 1977).
Using the tuba in the wind-band as a reference for tuning all other instruments is a
recent trend. Although the bass instruments provide overtones to which the upper wind
must conform in the context of performing harmony, this does not provide an overt
indication of in-tuneness to the student performer when matching pitches in like registers.
A two-way ANOVA with repeated measures measuring the effects of stimulus octave
and timbre on tuning accuracy found a significant difference ( F (3,207) = 6.28, p < .001)
by the flute, oboe, clarinet and tuba stimuli, with the greatest pitch deviations from the
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tuba stimulus (Byo, Schlegel & Clark, 2011). This study supports the idea of increasing
tuning accuracy by providing reference pitches in like registers to the groups that are
making tuning adjustments on their instruments. The study also raises the question of
whether “tuning up” to reference pitch at the beginning of a rehearsal or performance is
really tuning.
Some conductors discard the notion of tuning to one note all together. “Tuning to
one note on a tuner divorces the ear from the tuning process and reinforces the mistaken
notion that there is one correct frequency for each note” (Boone, 2004). Several
pedagogues advocate using multiple notes or portions of a scale to provide a context with
which to compare the performed pitch with the reference pitch (Garofalo, 1996; Kohut,
1996; Pottle, 1962; Wuttke, 2010). Tuning is based on perception and response, “The use
of a digital tuner tends to draw a student’s attention away from the aural aspect of playing
music” (Boone, 2004).
Director Attributes
The band director is usually the initial source of instructional feedback inasmuch
as intonation is concerned. “He must evaluate pitch, be able to state the direction of the
pitch change, and reverse a decision if he’s called it wrong” (Bloomquist, 1981). Barnes
(2010) is more direct saying, “Music Teachers who can’t tell if students are playing sharp
or flat should find a different line of work.” Certainly, much of what occurs in rehearsal
is the result of the director’s perceptual skills. According to Stauffer (1954) “We can
study and theorize to the solution of an intonation problem, but if it is rejected by the ear,
it is not acceptable musically, at least to the person making the judgment.” A video had
two independent observers (r = .86) code 40 rehearsals taught by 10 teachers and found
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that error correction accounted for 49% of band rehearsal time with band directors citing
intonation as the most frequently observed error type, but spending the least amount of
time correcting the problem (Cavitt, 2003).
Purists in the profession might attribute the ability to perceive intonation errors on
the podium with their chosen instrument of study. DeCarbo (1984) found no significant
relationship between the instrumental music teachers’ major performance instrument and
their error detection ability. Tuning the wind-band, and maintaining good intonation does
require coordination between perception and motor skills. Long (1977) describes his
experience at a state music educators’ convention where:
There was on display a model of the Johnson Intonation Trainer. This is an
electronic, three-octave keyboard instrument, each note of which has an
adjustable pitch for the purpose of making minute, but controlled changes in
tuning. The gentleman demonstrating asked many curious band directors to try
their skill at tuning a perfect fifth. Towards the end of the day he lamented that
only two out of every five of the directors were able to tune the fifth accurately.
In addition to perception, the director is likely responsible for overseeing other aspects
related to intonation. Where tuning is concerned, Smith (2004) lists seven
responsibilities for the conductor: 1) ensure performers come to rehearsals and
performances with instruments in tune and teaching them if needed, 2) provide a reliable,
stable, preferably non-electronic tuning sound, 3) establish and enforce the rules of the
tuning ritual, 4) be alert and responsive to tuning during the rehearsal or concert, 5) teach
the performers how to listen for tuning if needed, 6) understand the physics and acoustics
of the instruments, and 7) constantly refine personal tuning discrimination skills.
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Experience also seems to be a factor that influences perception. “The director’s
constant analysis of tuning and his willingness to realize that there is always something to
learn about the subject is essential for the growth and effectiveness of both the conductor
and his ensemble” (Bloomquist, 1981). It does seem logical that more experienced
directors would perceive intonation differently then teachers with less podium time.
According to DeCarbo (1986), instrumental teachers with at least eleven years teaching
experience identified errors significantly better ( p < .05) than teachers with five years or
less. Fundamentally, “neophyte instrumental music teachers must have error detection
skills to be effective teachers.” Bencriscutto (1965) concurs, “It would seem that, for the
teacher of music, the first and single most important requirement should be the ability to
hear correctly the relationship of pitches within the octave. It is ironic that a college
curriculum for music majors does not require a course in intonation…”
The idea of training pre-service teachers to increase perceptual skills is sometimes
confused with tuning skills. Fogarty, Buttsworth, & Gearing (1996) found that a battery
of six intonation tests consisting of melodic and harmonic tone differences administered
to college students ( N = 87) enrolled in an aural training program “appear to tap an ability
that is not significantly modified by training and is more or less the same across different
instrument families. But tuning skills are not necessarily related to aural discrimination
skills. Dalby (1992) devised a computer intonation training and testing program
consisting of drill-and-practice exercises using intervals, triads, and brief chorales. After
a 9-week training period, a two-way ANOVA revealed a difference in favor of the
experimental group, ( F (1,34) = 9.25, p = .005). This study seems to suggest that
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intonation and tuning is a skill where training can be beneficial for college undergraduate
music majors.
Student Attributes
Students are an essential component of this model because their perceptual ability
to discriminate pitch differences, experience, and knowledge of instrument pitch
tendencies can directly influence wind-band intonation. Bloomquist (1981) writes,
“Almost everyone can learn to play in tune and recognize pitch variance.” Tuning an
instrument involves perceiving the interactions between a reference pitch and the pitch
being performed. It is an intricate dance of perception, process and production.
Perception. According to Wolbers (2002), “The Music Man was correct in
suggesting that students should “think” the sound they wish to produce before they play
it.” Many articles have been published that advocate teaching intonation using the beat-
elimination method (Byo, 1990; Colnot, 2002; Dalby, 1992; Garolfalo, 1996; Graves,
1963; Latten, 2005; Laycock, 1966; Nichols, 1987; Swift, 2003). When considering
perceptual tasks, Miles (1972) found that virtually all student performers can learn how to
recognize and eliminate beats caused when two slightly different pitches are performed
simultaneously. Smith (2004) states, “I have never encountered anyone with a normal
hearing range who could not distinguish beats. That includes people who are said to be
tone-deaf.” Cognitive amusia, the scientific term for tone-deafness, afflicts a very small
portion of the population. Scientific studies suggest that only 4-5% of the population are
afflicted with some form of amusia (Fry, 1948; Kalmus & Fry, 1980; Pfordresher &
Brown, 2007). These findings are generally accepted even though the early study by Fry
(1948) lacked data analysis and the later study by Kalmus & Fry (1980) used a single
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measure of musical ability suggesting questionable validity and reliability. Pfordresher &
Brown (2007) distributed a questionnaire distributed to university students ( N = 1105) in
2005 and estimated that although 59% claimed they could not fluently imitate melodies
by singing, only 4-11% would satisfy the requirements for amusia.
Ely (1992) tested undergraduate and graduate instrumental music majors from
Ohio State University ( N = 27) and found a very low correlation (r = .07) between
subjects’ abilities to play in tune and their abilities to detect intonation problems. This
study supports the idea that student perceptual skills are similar. This may not be true for
other facets of aural stimuli. Swaffield (1974) tested select undergraduate music students
( N = 25) and found significant differences ( p < .001) between contextually melodic fine
tuning accuracy skill and the following four factors: timbre, intensity (amplitude),
duration, and pitch. The interactions between pitch and timbre ( F (6, 2699) = 8.849, p <
.001), and pitch and duration ( F (4, 2699) = 8.849, p < .001) were significant. The
interaction between pitch and intensity ( F (4, 2699) = 1.712, p = .10) was not statistically
significant.
Teachers who want to increase their students’ ability to discriminate differences
in pitch should be aware of the apparent influence of tone quality on pitch perception.
Geringer and Worthy (1999) tested timbre perception using paired instrument tones as a
measurement of intonation with high school, college music majors, and college non-
music majors ( N = 116) and found a significant difference ( F (10,565) = 7.75, p < .01)
between inexperienced instrumentalists who rated brighter tone quality as sharp and
darker tone quality as flat. Timbre was either the same or different in the paired
instrument tones, frequency was not altered. As one would imagine, the non-music major
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ratings were more extreme than experienced instrumentalists. Timbre has also been
found to significantly affect woodwind students’ abilities to detect intonational deviations
in listening tasks, and these students are significantly better at detecting intonation
deviations involving unlike timbral combinations than they are in duets involving like
timbral combinations (Ely, 1992).
The effect of the interaction between timbre and pitch perception on tuning skill is
not known. Ely (1992) reported that timbre was found to have a significant effect
( p < .001) on subjects’ abilities to detect intonation problems, but not on their abilities to
play in tune. He states, “…musicians can have the ability to perceive correct intonation
without being able to reproduce it on a musical instrument. Something is lost in the
perceptual/performance transfer.” Although important, preference for timbre and tone
quality should not subsume good intonation. Madsen and Geringer (1976) found that
undergraduate and graduate music students ( N = 50) listed intonation in relation to tone
quality preferences as follows: subjects preferred sharp and in-tune accompaniment
significantly more ( p < .001) than flat, and good intonation as opposed to good tone
quality in every comparison.
Experience. Tuning a wind instrument is the result of neuro-muscular skills that
develop over time. “Playing a musical instrument requires highly refined motor skills
that are acquired over many years of extensive training, and that have to be stored and
maintained as a result of further regular practice” (Altenmuller & McPherson, 2008).
Assuming students are provided excellent models of wind-band performances, tuning
skills are likely to improve. Research by Weinberger (2007, 2008) reports how animal
laboratory studies found that both appetitive and aversive stimuli paired with different
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tonal frequencies can alter auditory peripheral and cortex cells, “shifting” them to a new
frequency. The human equivalent is described by Long (1977), “It is generally accepted
that the player tunes the instrument. If a musician is not careful, however, the instrument
can detune the player. Continued exposure to a slightly out-of-tune note can make the
player feel that the note is in tune.”
According to Altenmueller and McPherson (2008), “Practicing an instrument
requires assembling, storing, and constantly improving complex sensorimotor programs
through prolonged and repeated execution of motor patterns under the controlled
monitoring of the auditory system.” Tuning accuracy seems to improve with experience.
Morrison (2000) found no significant difference in pitch accuracy for students with 1-7
years of experience when a predetermined tuning pitch was performed within a melodic
context. There was, however, a decrease in the absolute deviation in cents (¢) from year
one (16.09) to year seven (8.23).
Knowledge of instrument pitch tendencies. Tuning the adjustable mechanism
of a wind instrument at the beginning of rehearsal does not necessarily equal good
intonation. As Rawlins (1995) notes, “Although most students tune their instrument at
the beginning of each rehearsal, very few of them will adjust the intonation as they play.”
When students are aware of how their instrument deviates from equal temperament, their
ability to adjust pitch to a group mean is likely to improve, and these adjustments are
instrument specific. “Although most woodwind and brass players can appreciably alter
the pitch up and down by changing the embouchure pressure, clarinetists can only lower
the pitch; little can be done to raise it” (Maxey, 2003). Directors can teach students these
instrument specific tendencies. Fabrizio (1996) created charts depicting problematic
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notes for each instrument with the erroneous pitch direction, a suggestion for fixing the
pitch either through alternate fingerings, slide manipulation, or embouchure adjustment.
He also describes a process for warm-up and tuning the instruments of the wind-band.
The final part of this process consists of incorporating these cognitive skills in
performance context. A study by Duke (1985) found pitch accuracy was affected by
performance of melodic and harmonic intervals. Junior high, senior high, and college
students ( N = 48) were divided into control and experimental groups and asked to
perform melodic and harmonic intervals. Between-observation reliability of recorded
pitch deviations was .94. Although there were no significant differences in overall
intonation accuracy in relationship to performed ascending and descending directions
among the four test intervals, when subjects descended, intervals were performed slightly
sharper; when subjects ascended, intervals were performed slightly flatter ( p < .01).
Summary
One of the great difficulties in researching wind-band intonation is the amount of
literature pertaining to the topic. In addition, the literature is broad in scope as it deals
with topics including: acoustics, curriculum, cognitive perception, music theory, social
psychology, and teaching and learning. A hypothesized structural equation model was
developed based on the aforementioned literature and organized into four latent variables
that theoretically affect wind-band intonation: equipment, instruction and director and
student attributes. The literature suggests that the condition and quality of the
instruments used by the student performers as well as the instrumentation of the ensemble
are important aspects of equipment. Pedagogues consider content and quality of delivery
important factors defining instruction. Anecdotal evidence and research both describe
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how aural skills, experience and knowledge of instrument pitch tendencies define director
and student attributes. The literature suggests all of these components affect wind-band
intonation and should be considered in the hypothesized model.
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CHAPTER THREE
Method
The purpose of the study is to propose a theoretical model describing wind-band
intonation using equipment, instruction and director and student attributes as components.
Keith (2006) suggests that model components should be selected and structured based on
“theory, prior research and logic.” In order to satisfy this requirement and fulfill the
purpose of presenting a model of wind-band intonation, this study will investigate the
following research questions:
1.
What are the descriptive statistical characteristics of the observed variables?
2. What are the interrelationships among the observed variables?
3. Can a model of wind-band intonation be estimated? If so, what do post hoc
tests suggest about model fit?
4. Are there alternative models that fit the data?
This chapter will describe the participants, materials, assessments and procedures that
were used to collect and analyze the data needed to answer the research questions. An
explanation supporting the design and operational definitions of the variables will also be
provided.
Participants
The participants in this study were high school band directors ( N = 5) and their
students ( N = 200). Band directors were male, ages 27 to 45 ( M = 34.2, SD = 6.72, range
= 18) teaching in their current program for 2 to 5 years ( M = 3.8, SD = 1.10) with 4 to 12
years total teaching experience ( M = 7.20, SD = 3.35). The distribution of student
participants across instruments was as follows: Student gender was 63.5% male (n =
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127), 36.5% female (n = 73). Age ( M = 15.93, SD = 1.19) range was 4 (minimum 14,
maximum 18). Wind-bands were comprised of the following instruments: flute (n = 25),
oboe (n = 12), bassoon (n = 11), clarinet (n = 40), saxophone (n = 26), trumpet (n = 23),
French horn (n = 18), trombone (n = 23), euphonium (n = 9), and tuba (n = 13). Student
participants reported having participated in band for 1 to 10 years ( M = 4.77, SD = 1.91).
Measures
The terms describing model components within this research were drawn from
Byrne (2010), Keith (2006), and Schumacker and Lomax (2004). The preliminary model
consists of one dependent variable and four latent independent variables. The dependent
variable, wind-band intonation was defined by a spectrum analysis (SA) of chords scored
with a researcher designed chord calculator. The independent variables were defined by
a total of 10 observed indicator variables. Each observed indicator variable was defined
by questionnaires, observation forms and both published and researcher-designed tests.
All test names and corresponding abbreviations used in this study are listed and defined
in Table 2. Where applicable, test reliability is reported a priori when available,
otherwise estimations are reported ex post facto.
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Table 2
Defining Model Components for Latent and Observed Indicator Variables, Measure
Names and Abbreviations.
Model Components
Latent Variable Name
Observed Indicator Variable Measure Name Abbreviation
Wind-Band Intonation (DV)
Spectrum Analysis Spectrum Analysis SA
Equipment (IV)
Quality Measure of Equipment Quality ME_Qual
Instrumentation Band Instrumentation Measurement BIM
Instruction (IV)Warm-up Process Warm-up Measure WM
Tuning Process Tuning Measure TM
Music Rehearsal Rehearsal Measure RM
Director Attributes (IV)
Experience Director Questionnaire DQ_Exp
Aural Acuity Director Aural Discrimination Measure DADM
Student Attributes (IV)
Experience Student Questionnaire SQ_Exp
Aural Acuity Student Aural Discrimination Measure SADM
Instrument Tuning Skill Pitch Tendency Measure PTM
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The dependent latent variable: wind-band intonation. A significant challenge
for this study was creating an accurate assessment of wind-band intonation. Many
studies have measured how individual performers can improve tuning skills following
treatment (Dalby, 1992; Duke, 1985; Elliot, 1974; Ely, 1992; Graves, 1963; Karick,
1998; Kopiez, 2003; Madsen & Geringer, 1976; Miles, 1972; Pasqua, 2001; Swaffield,
1974; Swift, 2003; Yarborough, Morrison & Karrick, 1997). However, tuning in the
wind-band requires the necessity for compromise and few studies attempt to recognize
the importance of measuring intonation in this context (DeCarbo & Fiese, 1989; Millsap,
1999; Stoffer & Leukel, 2004). Wind-band intonation was measured through an acoustic
analysis of intonation. A researcher designed chorale was used as the performance
material. The underlying thought process behind creating a performance chorale to
measure wind-band intonation was to introduce a variety of tuning scenarios typically
encountered in wind-band literature. Since additional factors describing wind-band
intonation may have been inadvertently left out of the model, a prediction error (d1) on
wind-band intonation was depicted to account for unexplained variance.
Spectrum analysis. Wind-band intonation scores were derived from an average
score from six samples extracted from a recording of each band’s performance of the
Chorale in B b
Major (Appendix D). In order to accomplish this, audio files of the
Chorale in B b
Major were first extracted from the video recordings submitted by band
directors using GeoVid mp3 Extractor. Chord samples were extracted from the mp3 files
using Creative WaveStudio. The Chorale in B b
Major was designed to control for
possible pre-testing familiarity with a published chorale, to control for pitch deviations
due to extreme dynamics, to control for pitch inaccuracies due to extreme instrument
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ranges, to insert note errors to calculate the band director’s ability to detect and diagnose
errors during rehearsal, and to increase the variability of harmonic tuning difficulty in the
sample chords. The first sample extracted from the recording was designed to measure
tuning accuracy of octaves based upon a fundamental pitch reference of concert F2. The
remaining five samples extracted from the chorale for measuring harmonic intonation
include: B b
major in chord in first inversion, G minor chord in root position, C minor
chord in root position, dominant F7
chord in root position, and B b
major in chord in root
position.
Each chord sample was measured for tuning accuracy by creating a spectral slice
using the Praat phonetic analysis software (Boersma & Weenik, 2010). The spectral slice
provides a graphic representation of formant peaks. They are labeled by frequency (Hz)
along the horizontal X axis, and amplitude (dB) along the vertical Y axis. Analyzing
chord samples extracted from previous recordings revealed three distinct formants; single
peak, flat peak and split peaks. Single peak samples provide an exact frequency of the
chord partial being studied. Flat peak samples provide a mean frequency that is
determined by summing the two extreme frequencies prior to amplitude drop-off. The
most common example of formant found from live wind-band performances is the split
peak sample (Figure 6). This typically occurs when several performers double the same
pitch. Split peak formants share the characteristic of two or more distinct frequencies
that deviate from the location of where the chord partial frequency should occur based on
the harmonic series. In this case, all of the frequencies that are sharp, up to -10dB from
the strongest observed amplitude of that peak, are averaged to form a positive deviation
from the location of the chord partial frequency.
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Frequency (Hz)
S o u n d p r e s s u r e l e v e l ( d B / H z )
0
20
40
60
Range = 160 to 190 Hz
Figure 6. This formant depicts split peak variance around the expected frequency of
175.47 Hz. In Praat, positioning the cursor over each peak provides the exactfrequency (Hz) and amplitude (dB). This information is used to calculate
mean deviations from the expected frequency.
A chord calculator was created using Excel to enter the frequencies (Hz) of each
chord partial in order to: measure how chord partials either remain true to, or deviate
from the harmonic series, convert deviations from Hz to cents (¢), to sum all deviations
in ¢, and to subtract deviations from a positive whole number in order to obtain a wind-
band intonation score for each chord. Excel was programmed to calculate a harmonic
series from the frequency of a fundamental pitch using the following formula: f 0, 2 f 0, 3
f 0, 4 f 0, etc., where f 0 is the fundamental frequency and the whole numbers to the left of
each f 0 are the frequency multipliers (Helmholtz, 1954). Next, Excel was programmed to
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convert Hz to ¢ based on the following logarithmic formula:
¢ )/(log1200 122 f f ×= where 301029995.0log2 = (Helmholtz, 1954). This conversion
process provides musicians with a meaningful metric for interpreting the SA score.
Prior to incorporating the chord calculator in this study, it was tested using
identical chord samples performed by a sine tone generator, a MIDI sequencer, a high
school band and a middle school band. Results indicated that when the total adjusted
deviation (TAD) was subtracted from 300, Spectrum Analysis (SA) scores ranged from
102.48 for the middle school band to 282.66 for the sine tone generator. The high school
band’s SA score was 156.63 (Table 3). Essentially, the higher the SA score, the better
the band performs in tune. Further testing of the chord calculator revealed an increase in
SA scores following treatment. Three introductory chords from Rossini’s Ballet Music
from William Tell performed by the same high school band under identical conditions
before and after treatment revealed a SA mean difference score of 118.68. These results
support using the chord calculator as a means for deriving an intonation score from a
spectrum analysis due to its sensitivity in measuring small pitch differences between
different ensembles. Graphic representation of each chord sample analysis and the
corresponding SA scores estimated using the chord calculator for this study are
referenced in Appendix I.
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Table 3
Chord Calculator Depicting the Intonation Score for a High School Band
Bb Major Chord
Harmonic Series 1 2 3 4 5 6 7 10 16IAS Pitch Label B b1 B b2 F3 B b3 D4 F4 B b4 D5 B b5
Harmonic Series (Hz) 58.70 117.40 176.10 234.80 293.50 352.20 469.60 587.00 939.20
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 113.60 233.09 586.94 936.65
Performed (¢) -56.96 -12.65 -0.18 -4.71
Adjusted Deviation (¢) 56.96 12.65 0.18 4.71
SPM Sharp (Hz) 117.45 177.37 235.93 295.62 353.93 473.02 590.44 941.24
Deviation (¢) 0.74 12.44 8.31 12.46 8.48 12.56 10.12 3.76
Adj. Deviation (¢) 0.74 12.44 8.31 12.46 8.48 12.56 10.12 3.76
Total Adjusted Deviation (¢) 143.37
SA Score (300 − TAD) 156.63
Note: ¢ = Cents; Hz = Hertz (refers to the frequency of the pitch label); IAS = International Acoustic Society; SPM = Split Peaks
Mean, SA = Spectrum Analysis, TAD = Total Adjusted Deviation.
The latent variable: equipment. Equipment was defined by two indicator
variables: quality and instrumentation. Instrument, mouthpiece, and reed brands vary and
can be controlled by band directors and students. Band directors also can exert some
control on ensemble instrumentation and part assignments. Understanding how these
variables affect intonation can help band directors and students make intelligent choices
about choosing equipment. In this case, instrumentation refers to the quantity and
diversity of wind instruments in the band—not to be confused with the term
instrumentation that is sometimes used to describe tests.
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Quality. Instrument quality was measured by asking students to complete the
Measure of Equipment Quality (ME_Qual). The ME_Qual (Appendix F) contains
instrument specific questions and scores that range from 8 – 23 points. Because studies
have shown the effect of tone quality on the listener’s pitch perception (Geringer &
Worthy, 1999; Madsen & Geringer, 1976; Worthy, 2000), students were also asked to
describe their instrument accessories because custom mouthpieces, reeds and reed
ligatures can improve tone.
Band instrumentation. In theory, wind-band intonation improves when students
can easily hear the fundamental tone of a chord (Lee, 2001). The fundamental tone is the
foundation of the harmonic series as demonstrated by measuring intonation using the
chord calculator (Table 3). Good intonation is further defined by how well the upper
wind instrumentalists match their pitches to the overtones produced by the lower wind
instrumentalists. Achieving good wind-band intonation seems to be related to balanced
instrumentation. Therefore, ideal wind-band instrumentation was based upon the
instrumentation and distribution of part assignments that Fennell (1954) prescribed for
the 1952 Eastman Symphonic Wind Ensemble (Table 4).
Fennell’s instrumentation was divided into four voice groups. Doing so revealed
the following voice ratios: bass to tenor = 1:1.5, bass to alto = 1:1.5 and bass to soprano =
1:1. Combined, the ratio of summed woodwinds to summed brass was 1.5:1 and more
importantly, the ratio of summed upper voices to the bass voice was 5:1 (Table 4). These
ratios seem to support the relationship between wind-band intonation and balance. The
score for wind-band instrumentation was derived by subtracting the Eastman Wind
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Ensemble instrumentation ratios from each band’s instrumentation ratios, and subtracting
the summed difference from ten.
Table 4
Ideal Wind-Band Instrumentation and Voice Group Assignments for Octaves in F
Pitch Voice Group( N = 40)
Woodwinds(n = 24)
Brass(n = 16)
IV
Soprano
(n = 8)
1 piccolo(a)(b)
3 flutes
1 oboe
2 Bb clarinets(c)
1 Bb trumpet
III
Alto
(n = 12)
1 oboe
3 Bb clarinets
2 E b alto saxophones
2 French horns
4 Bb trumpets
II
Tenor
(n = 12)
3 Bb clarinets
1 tenor saxophone
1 bassoon
2 French horns
3 trombones
2 euphoniums
I
Bass
(n = 8)
1 bassoon
1 contrabassoon(d)(e)
1 Bb bass clarinet
1 contrabass clarinet(d)
1 E b baritone saxophone
1 string bass(d)
2 BB b tubas
Note: (a) = the pitch sounds 8va from written pitch; (b) = an additional flute may substitute for piccolo
in this distribution; (c) = E b clarinet would replace 1 B b clarinet if used; (d) = the pitch sounds 8vb fromwritten pitch; (e) = additional contra-clarinet would be an acceptable substitution for the
contrabassoon. In addition, English horn, which is typically unavailable for most school bands, would be placed in group III if used. This instrumentation is based upon 1952 Eastman Symphonic WindEnsemble (Fennell, 1954).
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The latent variable: instruction. This variable describes the teaching methods
and procedures that lead to better wind-band intonation. Warm-up, tuning and rehearsal
activities were evaluated for their level of effectiveness in terms of improving ensemble
tone and intonation. Effectiveness was measured through video observation using the
Video Observation Form (Appendix H). Two independent observations were recorded
by band directors with an average of 22 years of successful high school teaching
experience. Inter-rater reliability (WM r = .82, TM r = .87, RM r = .84) for these tests
were estimated ex post facto.
Warm-up, tuning and rehearsal. Despite a plethora of books, journal articles,
clinics, workshops and instructional videos dealing with improving wind-band intonation,
there is a lack of consistent pedagogy regarding when students should learn tuning
concepts, and how to structure meaningful lessons (Criswell, 2008). Video studies reveal
preservice teachers often base their acquisition of pedagogical content knowledge on
intuition rather than through undergraduate training experience (Hatson & Leon-
Guerrero, 2008). In other words, teachers tend to teach as they were taught. Although
addressing this problem exceeds the scope of this study, it does provide the basis for
creating a test designed to measure how learning activities that band directors choose
affect wind-band intonation. The Video Observation Form consists of three sections in
two parts. The first part investigates the specific kind and quality of the activity chosen
to improve ensemble intonation through warm-up, tuning and music rehearsal. The
second parts asks the observer to evaluate the overall effectiveness of the warm-up,
tuning and music rehearsal based upon best practices derived from the literature review.
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The latent variable: director attributes. It seems logical that aural skills and
experience have an influence on student performance outcomes. Therefore, director
attributes was defined by two observed indicators: aural acuity and teaching experience.
Band directors were asked to describe experience on the DQ_Exp (Appendix C) by the
total number of years of teaching high school band and the number of years teaching at
their current location. Aural acuity was measured by the DADM (Appendix G). A two-
part listening test, the DADM consisted of two published measures designed to test
perception of pitch deviation and major-minor chord discrimination.
Director experience. Detecting intonation errors is the first step towards
correcting them in rehearsal. DeCarbo (1986) performed a MANOVA and found that
instrumental music teachers with 11 or more years of teaching experience identified
intonation errors significantly better than teachers with less than 6 years of experience,
F (2,54) = 6.51, p = .003. This was confirmed by a Scheffe multiple comparison of
means for experience post hoc analysis ( p < .05). Consequently, only high school
experience will be considered. This is supported by a univariate ANOVA finding that
high school directors scored significantly higher when detecting and identifying errors
than junior high school teachers, F (1,54) = 7.24, p = .009 (DeCarbo, 1986). Since band
directors with high school teaching experience are required to discriminate intonation
errors at a more sophisticated level, elementary or middle school teaching experience was
not be included in the scoring criteria. Directors also reported the total number of years
teaching in their current location on the DQ_Exp.
Director aural acuity. Pitch acuity and chord recognition ability are important
skill sets for all musicians. Band directors need to be able to detect minute deviations in
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pitch in order to correct wind-band intonation errors. Furthermore, tuning intervals
depends upon the harmonic context (Stoffer & Leukel, 2004) suggesting that band
directors should posses an advanced ability to discriminate differences in chord quality.
Therefore, two pre-existing aural discrimination tests were included in the DADM. Part
seven of the K-D Music Test (Kwalwasser & Dykema, 1930) presents 40 items where a
three-second recorded tone is presented with or without change in pitch. Directors were
asked to respond that the pitch remains the same or whether a part of it is different. The
largest pitch deviation was .40 Hz and the smallest .01 Hz. Since the test was
administered in a single-administration, Chronbach’s alpha was calculated ex post facto
using director and students test scores to estimate internal consistency yielding a split-
half reliability coefficient (α = .89) for this portion of the K-D Music Test. Part one,
subtest a, test two of the Music Achievement Test (Colwell, 1969) contains 15 items
designed to measure the ability to discriminate between major and minor chords. An a
priori reliability score of r = .87 was reported for high school students on this portion of
the test.
The latent variable: student attributes. Since school populations are diverse,
defining and measuring student attributes can be difficult. In this model, student
attributes are defined by: experience, aural acuity, and instrument tuning skill
proficiency. Students described experience by answering questions pertaining to the
number of years of: band participation and private lessons on the SQ_Exp (Appendix F).
Each student’s aural acuity was measured by the SADM (Appendix G). Students also
answered questions related to instrument tuning proficiency on the PTM (Appendix G).
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Student experience. Sustaining a steady tone, maintaining adequate breath
support, and manipulating pitch through embouchure adjustments or alternate fingerings
are all prerequisites for performing in-tune. Since neuro-muscular development
associated with these skills tend to strengthen over time, it is logical to include
information pertaining to instrumental experience. In a univariate ANOVA, a significant
difference was found between private lesson participation and no private lesson
participation on tuning accuracy, F (1,113) = 7.97, p < .01 (Yarborough, et al., 1997).
Therefore, students were asked to list their experience in terms of the total number of
years performing on their instrument through participating in band and private lessons on
the SQ_Exp (Appendix F). A Spearman’s rank correlation coefficient (ρ = .89) was
estimated between reported age and grade level.
Student pitch acuity. Music educators would likely agree that the first step
toward teaching students how to perform in tune is to help them perceive out-of-tuneness.
Therefore, the rationale for administering the SADM to students was to quantify their
level of aural sophistication as it pertains to tuning related skills. The pitch
discrimination portion of the K-D Music Test was chosen because it is the only published
measure that requires the listener to make a judgment as to whether a pitch remains the
same or deviates from its initial tone (Colwell & Sigurjonsson, 1988). Virtually all other
measures testing pitch discrimination contain aural examples with two or three distinct
tones separated by brief periods of silence. Although a reliability rating is not reported in
the K-D Music Test Manual, it is a norm-referenced test that was based upon “scores of
thousands of grade and high school pupils” (Kwalwasser & Dykema, 1930). As
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previously mentioned a split-half reliability coefficient of α = .89 for this portion of the
K-D Music Test was estimated from student and band director scores ex post facto.
The Music Achievement Test 2, part one, subtest measures major-minor chord
discrimination. Unlike band directors who presumably have had aural training in college,
it is uncertain whether students have had formal aural training. Otherwise, this test was
administered to students for the same reason that it was administered to band directors:
recognizing the difference between major and minor is important because “intonation
depends upon the harmonic context in which the intervals (being tuned) occur” (Stoffer
& Leukel, 2004). A reliability score of r =.87 was reported by the publisher (Colwell,
1969) for high school students on this portion of the test.
Instrument tuning skill. Scholarly articles, instrumental pedagogy texts and
method books maintain that when students know how to correct their instrument’s pitch
tendencies, intonation improves considerably (Byo, 1990; Cooper, 2004; Garofalo, 1996;
Kohut, 1996; Nichols, 1987). Therefore, the Pitch Tendency Measure (PTM) was
measured by a researcher designed, open-ended response that asked students to write five
problematic notes relevant to their instrument on a staff, describe the pitch tendency of
each note in terms of being sharp or flat, and write a solution for each pitch tendency
such as alternate fingering or embouchure adjustment. Students were scored for item
accuracy using Fabrizio’s (1994) pitch correction charts. A reliability estimate of
(r = .71) was observed ex post facto after two evaluations separated by time. The
estimate was recalculated (r = .74) after a third evaluation of test scores. Further
estimation was discontinued after second estimation.
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Procedure
Invitations to participate in this study were sent to 132 high school band directors
in the Broward, Hillsborough, Orange, Miami-Dade, Monroe, and Palm Beach county
school districts (Appendix A). There were 26 directors who responded favorably. Of
these directors, 14 completed and returned the Director Inventory (Appendix C). After
Internal Review Board approval, the following testing materials were sent via U.S. mail:
• Director Checklist: Testing Instructions (Appendix E)
• Parental Consent Forms (Appendix B)
• Student Participant Assent Forms (Appendix B)
• Director Participant Assent Forms (Appendix B)
• Student Test Packets (Appendices F and G)
• Director Test Packets (Appendix G)
• Chorale in B b
Major: conductor full score (Appendix D)
• Compact Disc Recording of the ADM
• 1GB Flash Drive for returning video
• Taylor 5630 air temperature thermometer
• Return postage mailing envelope
All of the questionnaires, testing materials, and video media were labeled with random
numerical identifiers coded by school so as to protect the anonymity of the participants.
Prior to testing, directors collected all student assent and parental consent forms
and set-up the rehearsal room with the testing materials. First they placed the
thermometer on their podium so as to obtain an accurate reading of air temperature. It
should be noted that room air temperature, although recorded, is not included in the
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model. The rationale for this exclusion is that the effects of air temperature extremes on
wind instrument intonation are well documented and can cause unequal and diametrically
opposed pitch discrepancies (Kent, 1959; Kohut, 1996; Pottle, 1961). Therefore, air
temperature was recorded to control for distorted test results that would occur from
deviations of ±10° F from the standard of A=440 Hz at 72° F. No extreme temperatures
were reported (range = 8° F, minimum 68° F, maximum 76° F).
Next, directors placed their video camera in a location that captured as much of
the band as possible. Directors had the option of using the enclosed compact disc
recording of the ADM or uploading the digital audio file of the ADM on the flash drive
on their portable digital music player for playback. Finally directors placed the copy of
the Director Test Packet on their podium in order to take the test at the same time as their
students.
On the testing date, band directors passed out the part specific Student Test
Packets and asked students to check that they had the correct instrument part. Students
were given approximately 10-minutes to complete the SQ_Exp and ME_Qual. The band
director was allowed to help students determine the make and model of their instrument
and accessories if needed. Students were also told to complete the PTM to the best of
their knowledge and without help from the director or their classmates. Instructions on
this portion of the test indicated that students leave the section blank if they did not know
the answers and not to guess. Band directors were instructed not to assist students in
answering questions pertaining to instrument pitch tendencies.
After students completed the SQ_Exp, ME_Qual and PTM, the director instructed
the students to turn to the SADM. Instructions for completing the SADM and DADM
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were written on the tests and recorded on the compact disc. Space was provided on the
Director Test Packets for band directors to list any complications that may have occurred
while administering the test. One director indicated that the test was interrupted by a fire
drill, but that this occurred prior to administering the questionnaire portion of the test.
No other complications or interruptions were reported.
After completing the written portion of the test, directors were asked to video
record their normal warm-up and tuning procedure. The suggested time for this activity
was approximately 10-minutes. Participants generally adhered to this request. Next,
directors were instructed to take up to 10-minutes to rehearse the Chorale in B
b
Major
and conclude the session with one uninterrupted performance of the chorale. Following a
final performance of the chorale, directors collected the student test packets and placed
them in the return mailing envelope. A 1GB flash drive was provided for directors to
upload the video of their band’s performance.
Data Analysis
Prior to collecting and analyzing data, a hypothesized structural equation model
describing the effects of equipment, instruction and director student attributes on wind-
band intonation was developed (Figure 7). This model is specified as a latent variable
SEM and contains the following observed measurement equations:
BIM = function of Equipment + measurement error 1
ME-Qual = function of Equipment(1) + measurement error 2
WM = function of Instruction + measurement error 3
TM = function of Instruction(1) + measurement error 4
RM = function of Instruction + measurement error 5
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DQ_Exp = function of Director Attributes + measurement error 6
DADM = function of Director Attributes(1) + measurement error 7
SQ-Exp = function of Student Attributes + measurement error 8
SADM = function of Student Attributes(1) + measurement error 9
PTM = function of Student Attributes + measurement error 10
SA = function of Wind-Band Intonation(1) + measurement error 11
The hypothesized model does not indicate covariance between any of the measurement
errors. Although there is a possibility of covariance between the DADM and the SADM,
this relationship is not reflected in the model due to the age and training differences
between the test subjects. The hypothesized model also contains one prediction error on
Wind-Band Intonation.
Model identification is determined by comparing the number of distinct known
values in the sample variance-covariance matrix S with the theoretical unknown values
implied by the population–covariance matrix Σ. Identification is determined by solving
S − Σ = 0, with zero indicating a just-identified model. A positive value indicates an
over-identified model while a negative value indicates an under-identified model.
According to Byrne (2010), “the just-identified model is not scientifically interesting
because it has no degrees of freedom and therefore can never be rejected.” An
overidentified model is important because it can be rejected indicating that a revision of
the theory or model hypothesis is warranted. The hypothesized model contains 11
observed variables, thus 11(11+1)/2 accounts for 66 known values of S . There are a total
of 27 unknown values. Solving for S − Σ indicates 39 degrees of freedom, thus an over-
identified model.
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Descriptive statistics will be reported following data collection in order to
describe the sample, remedy missing data and outliers, and check assumptions for
multivariate normality in order to answer research question one. The second research
question will be addressed by generating a correlation matrix listing the coefficients that
describe the relationship between all observed variables. Model estimation will be
conducted using raw dated imported from SPSS –essentially, the correlation matrix
derived from this data used to answer research question two is automatically converted
into a variance-covariance matrix by AMOS. Model estimation will occur after all of the
requirements and conditions for the first two research questions have been met. A
determination as to whether to maintain, alter or abandon the hypothesized model will be
considered based upon these findings.
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Figure 7. A latent variable structural equation model describing the effects of equipment, instruction and director and student attributes on wind-band
intonation.
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CHAPTER FOUR
Analysis of Data
This study was designed to test a theoretical model describing the effects of
equipment, instruction and director and student attributes on wind-band intonation.
Published and researcher designed tests were administered to high school band directors
and their students in order to measure the model components. This chapter focused on
analyzing data collected from these tests in order to address the following research
questions:
1.
What are the descriptive statistical characteristics of the observed variables?
2. What are the interrelationships among the observed variables?
3. Can a model of wind-band intonation be estimated? If so, what do post hoc
tests suggest about model fit?
4. Are there alternative models that also fit the data?
Prior to testing the model, the observed variables in each model component were
evaluated for their propensity to describe the sample, remedy missing data, check for
outliers, note important group differences between observed variables and to check
assumptions for normality in order to answer research question one. Next, a correlation
matrix listing coefficients describing relationships between the observed variables was
generated in order to address research question two. Finally, raw data was imposed on
the hypothesized model using AMOS (Arbuckle, 2008) in an attempt to answer research
question three. Finally, alternative models were explored in an attempt to answer
research question four.
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Descriptive Statistics
The statistical analysis was facilitated by the use of SPSS (2008) and AMOS
(Arbuckle, 2008) computer programs. The sample consisted of five bands, their directors
( N = 5) and students ( N = 200). Band directors were all male. Age ( M = 34.2, SD =
6.72) range was 18 (minimum 27, maximum 45). Student gender was 63.5% male (n =
127), 36.5% female (n = 73). Age ( M = 15.93, SD = 1.19) range was 4 (minimum 14,
maximum 18). Wind-bands were comprised of the following instruments: flute (n = 25),
oboe (n = 12), bassoon (n = 11), clarinet (n = 40), saxophone (n = 26), trumpet (n = 23),
French horn (n = 18), trombone (n = 23), euphonium (n = 9), and tuba (n = 13). Air
temperature (range = 8° F, minimum 68° F, maximum 76° F) recorded at each testing site
were within acceptable norms. Since the written tests for students were conducted on the
same day as the video recording of the Chorale in B b
Major, student dropout was not
problematic.
Wind-band intonation. This variable is defined by a spectrum analysis of six
samples extracted from a recording of band performances ( N = 5) of the Chorale in B b
Major. Samples extracted from the recording include: 1) four octaves based upon a
fundamental pitch reference of concert F2 (SA_F8vas), 2) B b
major in chord in first
inversion (SA_I6), 3) G minor chord in root position (SA_vi), 4) C minor chord in root
position (SA_ii), 5) dominant F7
chord in root position (SA_V7) and 6) B b
major chord in
root position (SA_I). Deviations from the expected overtones of the harmonic series
were estimated for each sample using the researcher designed chord calculator to derive
the final score (SA) for each sample (Appendix I). The spectrum analysis scores for each
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chord sample were averaged to derive a final SA score for each band (Table 5). The final
SA scores ( M = 169.94, SD = 37.47) exhibit a non-normal distribution with skewness of
1.46 (SE = 0.91) and kurtosis of 3.05 (SE = 2.00) which is not surprising given the small
sample size.
Table 5
Spectrum Analysis Scores of Sample Extractions from Five Band Performances Listed by
Final Score in Ascending Order
Band SA_F8vas SA_I6 SA_vi SA_ii SA_V7 SA_I SA1008 226.82 138.13 97.04 28.68 148.53 113.53 125.46
1019 214.66 138.73 157.50 74.53 153.37 167.27 151.01
1009 205.46 133.94 158.38 83.18 156.75 200.07 156.30
1002 252.55 159.40 192.32 64.81 142.66 151.51 160.54
1001 234.15 250.63 200.87 236.74 186.95 248.95 226.38
Equipment. This model component was measured by two observed variables:
instrument quality (ME_Qual) and band instrumentation (BIM). Students ( N = 200) were
asked to describe the quality of their instrument and accessories on the ME_Qual in their
student test packets. Results from the instrument specific student questionnaires indicate
the majority of instruments were in better than average condition ( M = 18.93, SD = 2.48)
with a normal distribution (skewness = -0.64, SE = 0.17, kurtosis = 0.87, SE = 0.34).
Potential scores for this test can range from 8-23 with the lowest score indicating a
virtually unplayable instrument with the poor quality mouthpieces and accessories to 23
indicating a professional model instrument in perfect condition. The observed range was
13 (minimum 10, maximum 23). Analysis of variance showed a main effect of group
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differences (bands) on instrument quality (ME_Qual), F (4, 195) = 6.19, p = .001, η p2 =
.09. The effect size was small. Levene’s test for homogeneity indicated the error of
variance was equal across all groups, F (4,195) = 4.17, p = .003. Posthoc analysis (LSD)
suggest instrument quality in band 1019 was better ( p = .05) than bands 1002 and 1008,
1001 was better than 1008, and 1009 was better than 1008 (Figure 8).
Figure 8. This graph depicts mean differences of instrument quality between bands.
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The score for band instrumentation (BIM) was derived by summing each band’s
ratios of upper wind instruments to the bass instrument voice from the ratios based on the
instrumentation and distribution of part assignments that Fennell (1954) prescribed for
the 1952 Eastman Symphonic Wind Ensemble. Scores for this test are continuous with a
score of 10 points representing voice ratios identical to Fennell’s (Table 4).
Theoretically, there is no lower limit, but such a case is difficult to imagine. The average
BIM score of participating bands was 8.15 (SD = 1.06). A comparison of observed and
expected frequencies indicated no extreme deviations from Fennell’s part assignments
(Table 6).
Table 6
Instrument Part Assignments by Voice and BIM Score Comparisons
IV Sop III Alto II Tenor I Bass BIM χ 2 df p
EWE 8 12 12 8 10.0
1001 10 9 11 5 8.00 2.10 3 .55
1002 11 16 13 6 7.35 1.86 3 .61
1008 9 8 12 8 9.63 1.33 3 .72
1009 7 10 11 4 7.00 1.17 3 .76
1019 10 11 12 8 8.75 0.55 3 .91
Note: EWE = Eastman Wind Ensemble, Bands = Band Instrumentation Measure.
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Instruction. Video recordings of each band’s ( N = 5) warm-up (WM), tuning
(TM) and rehearsal (RM) activities were analyzed by two band directors (Table 7).
Potential scores for the WM can range from 9-78 with the lowest score indicating an
insufficient, ineffective or complete lack of a warm-up process and a high score
indicating highly effective activities with clear and consistent evidence of improving
intonation in both design and implementation. The observed range on the WM ( M =
38.20, SD = 10.31) was 21 (minimum 26, maximum 47). The TM was designed to
measure the effectiveness of the tuning process. Scores can range from 9-82 with the
lowest score representing an unorganized, inefficient or lack of a tuning process. Bands
that score low on this measure tend to rely on non-aural based procedures while high
scores provide a stable reference pitch for students to match individually, in small groups
and as an ensemble. The highest score represents a highly effective routine with clear
goals designed to teach performers how to make adjustments on their instruments without
assistance from the band director. The observed range on the TM ( M = 47.20, SD =
23.17) was 51 (minimum 27, maximum 78).
The final portion of the video observation measured rehearsal content quality and
effectiveness. RM scores can range from 9-82 with the lowest score indicating
insufficient preparation, unproductive activities or no rehearsal prior to performing the
chorale. A high score represents a variety of highly effective activities designed to build
intonation awareness and clear evidence of improving intonation in the chorale. The
observed range on the RM ( M = 47.40, SD = 19.71) was 53 (minimum 17, maximum 70).
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Table 7
Video Observation Scores from Five Bands for Observed Variables Describing
Instruction
Bands
1001 1002 1008 1009 1019
WM 47 44 26 28 46
TM 66 78 31 34 27
RM 70 55 17 53 42
Note: Bands are listed by school code. RM = Rehearsal measure, TM = Tuning
Measure, WM = Warm-up Measure.
Director attributes. Band directors ( N = 5) reported teaching experience ( M =
11, SD = 3.74) on the DQ_Exp in terms of the summed number of years teaching high
school and the number of years in their current position. The observed number of years
teaching high school ( M = 7.20, SD = 3.35) range was 8 years (minimum 4, maximum
12). The observed number of years teaching in their current school ( M = 3.8, SD = 1.10)
range was 3 years (minimum 2, maximum 5).
The observed variable describing aural acuity on the DADM ( M = 41.20, SD =
4.55) was derived from two published tests. The first part was a pitch discrimination test
( M = 27.6, SD 3.51) from the norm-referenced K-D music test (Kwalwasser & Dykema,
1930a). Range for this administration was 7 (minimum 24, maximum 31). Percentile
rankings for senior high school (grades 10-12) indicate the mean band director score
ranked in the 72 percentile with the lowest score (24) in the 40 percentile and the highest
score (31) in the 94 percentile. Percentile ranking scores are not published for adults.
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The second part of the DADM was a test of major-minor chord discrimination test
( M = 13.60, SD = 1.70) from the Music Achievement Test 2 (Colwell, 1969). Range for
this administration was 4 (minimum 11, maximum 15). Although the Music
Achievement Tests are norm-referenced for high school students, percentile rankings can
not be accurately reported because the major-minor discrimination is a subtest. However,
to provide context of where these scores might rank based on the data provided in the test
book, the following formula was used to calculate an estimate: )(1528 oser = where er
= estimated rank, 28 = maximum raw test score on the major-minor discrimination test,
15 = maximum raw test score on the major-minor chord discrimination subtest, and os =
observed score on the major-minor chord discrimination subtest. Based on this formula,
percentile rankings indicate the mean band director score ranked in the 97 percentile with
the lowest score (11) in the 88 percentile and the highest score (15) in the 99 percentile.
Percentile ranking scores are not published for adults.
Student attributes. This component measured musical experience, aural acuity,
and knowledge of pitch tendencies relevant to their instrument. Students ( N = 200)
reported musical experience ( M = 6.09, SD = 3.21) on the SQ_Exp in terms of the
number of years participating in band and the number of years taking private lessons.
The observed number of years in band ( M = 4.77, SD = 1.91) range was 9 years
(minimum 1, maximum 10) was a normal distribution with skewness of 0.32 (SE = 0.17)
and kurtosis of -0.06 (SE = 0.34). The observed number of years taking private lessons
( M = 1.28, SD = 1.75) range was 8 years (minimum 0, maximum 8) and was a non-
normal distribution with skewness of 1.51 (SE = 0.17) and kurtosis of 1.96 (SE = 0.34).
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Analysis of variance showed a main effect of group differences (bands) on
musical experience (SQ_Exp), F (4, 195) = 23.93, p < .001, η p2 = .33. The effect size was
large. Levene’s test for homogeneity indicated the error of variance was equal across all
groups, F (4,195) = 2.78, p = .03. Posthoc analysis (LSD) indicate significant differences
in the number of years of musical experience between 1001 ( p ≤ .001) and all other
groups, and 1019 ( p < .001) and all other groups (Figure 9).
Figure 9. This graph depicts mean differences of musical experience between bands.
As band director aural acuity was measured on the DADM ( M = 41.20, SD =
4.55), student aural acuity was similarly measured using the SADM ( M = 40.37, SD =
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3.83). The first part of the SADM was a pitch discrimination test ( M = 27.73, SD 2.76)
from the norm-referenced K-D music test (Kwalwasser & Dykema, 1930a). Range for
this administration was 15 (minimum 19, maximum 34). Percentile rankings for senior
high school (grades 10-12) indicate the mean student score ranked in the 72 percentile
with the lowest score (19) in the 11 percentile and the highest score (34) in the 98
percentile.
Analysis of raw scores from Colwell’s (1969) norm-referenced major-minor
chord discrimination test ( M = 12.60, SD = 2.61) indicated a range of 11 (minimum 4,
maximum 15). To provide context of where these scores might rank, the same formula
used to calculate director rankings on the DADM was used to calculate student rankings
on the SADM. Based on this formula, percentile rankings indicate the mean student
score ranked in the 95 percentile with the lowest score (4) in the 03 percentile and the
highest score (15) in the 99 percentile. Analysis of variance showed no group differences
on aural acuity.
Results from the PTM ( M = 3.97, SD = 3.61) indicated a full range (15, minimum
0, maximum 15) of scores. This can be interpreted to mean that for every three points;
which equates to a little less than one SD, students can correctly identify and correct one
inherent pitch problem for their instrument. Despite the statistics describing the
distribution (skewness of 0.81, SE = 0.17, and kurtosis of 0.08, SE = 0.34), 25% of the
students tested (n = 50) did not correctly identify any pitch problems on their instrument
(Figure 10). Analysis of variance showed no significant group differences on knowledge
of instrument pitch tendencies.
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Figure 10. Distribution of student test scores on the PTM.
Interrelationships between the Observed Variables
One of the difficulties with this study was examining individual and group level
data sets simultaneously −in this case students within bands. Cohen et al. (2003) referred
to this as clustered data sets due to the multiple levels of measurement. The initial intent
of this study was to compare the observed variable group mean scores and impose them
on the hypothesized model of wind-band intonation. Taking the mean scores of all the
individual level data and comparing it to the group scores for the spectrum analysis,
director attributes, band instrumentation and instruction is an aggregated analysis (Cohen
et al., 2003). As the study progressed, it became evident that the small sample size would
insufficiently express the profundity of the interrelationships between the variables due to
the generalization from results at one level of aggregation to another. Therefore, scores
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for the spectrum analysis, director attributes, band instrumentation and instruction were
also reported on the student level within corresponding band-groupings. Cohen et al.
(2003) refers to this as a disaggregated analysis. Whereas the aggregated analysis led to
an under-representation of statistical significance –also likely due to the small sample
size– the disaggregated analysis led to alpha-level inflation. As a result of this
dichotomy, the correlation coefficients for the aggregated and disaggregated analysis are
simultaneously provided for comparison in Table 8.
The relationship between the observed variables of instruction and wind-band
intonation were seemingly congruent. The correlation between RM and SA (r = .87) was
only different by the alpha-level as predicted by Cohen et al. (2003). At the very least,
the relationship is significant at the p = .05 level. Likewise, the disaggregated correlation
(r = .61, p < .001) and aggregated correlation between WM and SA (r = .63, p = .25), and
the disaggregated correlation (r = .56, p < .001) and aggregated correlation between TM
and SA (r = .59, p = .29) also followed this trend. The observed variables defining
instruction also seem to be related with each other in a similar manner:
• the disaggregated correlation between WM and TM (r = .51, < .001), and the
aggregated correlation (r = .54, p = .34).
• the disaggregated correlation between WM and RM (r = .65, < .001), and the
aggregated correlation (r = .63, p = .25).
• the disaggregated correlation between TM and RM (r = .66, < .001), and the
aggregated correlation (r = .65, p = .23).
In each case, it seems safe to assume that these variables are correlated because it fits
both prevailing theory and logic.
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The difficulty with interpreting causality solely based on correlations was
exemplified by the relationship between band instrumentation and band director
experience. For example, comparing the disaggregated correlation between BIM and
DQ_Exp (r = .59, < .01), and the aggregated correlation (r = .88, p < .05) suggests that
band directors with more experience also have increasingly balanced instrumentation.
However, a comparison between the disaggregated correlation between the BIM and SA
(r = −.34, < .001), and the aggregated correlation (r = −.39, p = .51) might lead to the
spurious conclusion that band intonation gets worse with better balanced instrumentation.
In addition, continuing to interpret the data using this same logic would also suggest a
negative relationship between band director experience and all facets of instruction.
Although there might be instances where teachers become less effective with age, these
results are likely an anomaly in this study and highlight the problems associated with
trying to investigate relationships between observed variables with a small sample size.
Reviewing student attributes suggested there were two important relationships to
consider. First, the disaggregated correlation between the SQ_Exp and SA (r = .36, <
.001), and the aggregated correlation (r = .61, p = .27) are both positive, but at different
magnitudes and alpha-levels. Similarly, the disaggregated correlation between aural
acuity (SADM) and SA (r = .15, < .05), and the aggregated correlation (r = .88, p < .05)
are positive with similar alpha-levels –the magnitude of the correlation is uncertain.
Nonetheless, both variables dealing with the relationship of these student attributes and
wind-band intonation were noteworthy due to their positive relationship.
Although the tactic employed for describing the relationships between these
variables may seem unusual, the comparisons are important. It is likely that, in the case
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of coefficient congruencies for instruction, alpha-level estimates likely fall somewhere
in-between those reported. The same can be said for the differences between the
observed variables describing student attributes. In this case, the alpha-levels seem to
match, but actual correlation may be represented somewhere between the coefficients
reported.
Model Estimation
Since the initial intent of this study was to compare observed variable group mean
scores, the aggregated data was imposed on the hypothesized model (figure 7) using
AMOS (Arbuckle, 2008). The method for estimating fit was Maximum Likelihood (ML)
with a bootstrap factor of 200 cases imposed on the model. The analysis summary
reported that minimization was unsuccessful, the solution inadmissible and would likely
require 18 additional constraints. In addition, the extreme negative value (V = -514.73)
on error variance 11 associated with the dependent variable (SA) suggested that the
problem is likely due, at least in part to the small sample size.
The next step was to impose the disaggregated data on the model. Once again,
the method for estimating fit was Maximum Likelihood (ML). Bootstrapping was not
used in the estimation. The analysis summary reported that minimization was
unsuccessful, the solution inadmissible and would likely require 10 additional constraints.
Even though the estimation made allowances for non-positive definite sample covariance
matrices, the sample moment matrix was not positive definite. Three negative error
variances were reported. A negative value (V = -7.09) on error variance 2 associated with
the observed independent variable (ME_Qual), a negative value (V = -5.22) on error
variance 6 associated with the observed independent variable (DQ_Exp), and an extreme
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negative value (V = -905.15) on error variance 11 associated with the dependent variable
(SA).
Based on the correlation output (Table 8) and AMOS analysis summary, the non-
positive definite error was likely caused by negative multicollinearity between DQ_Exp
and the other observed variables. Rather than imposing additional constraints, further
attempts to confirm the hypothesized model were halted in order to explore alternative
constructs.
Model Respecification
Jöreskog (1993) proposed a general strategic framework for testing structural
equation models describing three scenarios: strictly confirmatory (SC), alternative models
(AM) and model generating (MG). In the SC approach a theoretical model is proposed
and data is collected to test the model. The researcher either rejects or fails to reject the
model. Byrne (2010) noted that costs associated with data collection probably explain
the exclusion of the SC scenario from practice. The AM and MG approaches, although
exploratory, differ slightly. In the AM scenario, several competing theoretical models are
tested using the same data resulting in the researcher choosing one model that best fits the
data. The MG approach begins with a theoretical model that, after having been rejected
due to poor fit from the sample data, is respecified based on an investigation conducted to
find and eliminate the source of misfit. According to Byrne (2010), “even a cursory
review of the empirical literature will clearly show the MG situation to be the most
common of the three scenarios.”
This study conforms to the MG scenario. Since the hypothesized model could not
be confirmed, an exploratory approach ensued. Prior to trimming the hypothesized
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model, the following statistics derived from descriptive data, correlation estimates and
model estimation error reports were considered:
• Using the aggregated data prevented model estimation using the latent
variable design due to the small group sample size ( N = 5).
• Estimating the hypothesized model using disaggregated data led to an
exaggeration of error variance on the dependent variable (V error11 = -905.15).
• Negative correlations in the disaggregated data between director experience
(DQ_Exp) and instruction (WM r = -.52, p < .001; TM r = -.51, p < .001;
RM r = -.36, p < .001) seemed to contradict theory and research.
• Correlations in the disaggregated data between director aural acuity
(DADM) and instruction (WM r = .22, p < .01; TM r = .71, p < .01; RM r =
-.01, p > .05) were contradictory.
• There were moderate to large significant differences of student experience
(SQ_Exp) between bands ( p < .001, η p2 = .33).
• There were no significant student aural acuity (SADM) differences between
bands, F (4, 195) = 21.50, p = .21.
• There are small differences of instrument quality (EQ_Qual) between bands
( p = .001, η p2 = .09).
• There is a significant positive relationship between band rehearsal activities
and wind-band intonation (r = .87, p < .05, n = 5).
The first exploratory tactic involved down-sizing from a five-factor latent variable
model to a four-factor design by deleting director attributes. This decision was based on
data that seemingly contradicted prevailing theory, logic and research. These
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contradictions may have been the result of a small sample size, a lack of test validity or
both. For example, the data from this study indicate negative correlations between
DQ_Exp and instruction and no correlation between DQ_Exp and SA (r = .06, p > .05)
whereas DeCarbo (1986) found that instrumental teachers ( N = 60) with at least eleven
years teaching experience (n = 15) identified intonation errors significantly better ( p <
.05) than teachers (n = 21) with five years or less (DeCarbo, 1986). It is possible that
defining experience by years did not reliably reflect experience in this model because
other factors such as mentorship, education, teacher development, and conducting
opportunities may have accounted for unexplained variance. Furthermore, DeCarbo was
only measuring the ability to detect errors and not prescribe solutions to errors where
outcomes are clearly an important consideration in this model.
The relationships between director aural acuity and other variables were also
troublesome. Detecting errors and providing feedback to the students is the director’s
primary responsibility in rehearsal and is ultimately a function of perception. The
relationship between DADM and TM seemed to support this idea (r = .71, p = < .01)
while the lack of correlation between DADM and RM (r = -.01, p = > .05) seemed to
contradict it. These findings were especially suspect considering the relatively high
reliability scores for these measures (TM r = 0.87, RM r = 0.84) as well as the construct
validity –the tests were in a similar format in terms of layout and design of questions
(Appendix H). Therefore, criterion-related validity of the DADM was suspect. Although
pitch discrimination and major-minor chord discrimination skills are relevant, they
probably do not represent the type of skill sophistication needed to assess ensemble
intonation in order to provide meaningful feedback to student performers. It is also
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possible that an accurate representation of the true population was not represented due to
the small sample size.
When the data was imposed upon the four-factor model describing the effects of
equipment, instruction and student attributes on wind-band intonation, the analysis
summary reported that minimization was unsuccessful, the solution inadmissible and
would likely require 3 additional constraints. The method for estimating fit was
Maximum Likelihood (ML). Even though the estimation made allowances for non-
positive definite sample covariance matrices, the sample moment matrix was not positive
definite. Two negative error variances were reported. A negative value (V = -210.62) on
error variance 2 and a negative value (V = -2877.17) on error variance 11 associated with
the dependent variable (SA).
Revised four-factor model. Estimation with a revised four-factor model was
achieved using ML after additional constraints (Figure 11). First, to diminish the extreme
variance associated with the dependent variable (V error11), SA was removed from the
latent variable describing wind-band intonation and isolated as the observed dependent
variable with a prediction error (d1). Next, the observed variable describing
instrumentation (BIM) was removed from the latent trait defining equipment. Although
the idea of trying to measure instrument balance to a standard had merit, the validity of
the procedure was questionable. It may be more useful to use the χ 2
test to compare
observed and expected frequencies of instrument part assignments to exclude ensembles
with extremely poor instrumentation scores much in the same manner air temperature
was measured to control for adverse effects on pitch. Further research using the BIM as
an accurate assessment tool is needed. Finally, ME_Qual was removed from the latent
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variable describing equipment and isolated as an independent observed variable with a
direct effect on wind-band intonation.
Figure 11. Revised four-factor model of wind-band intonation.
Model fit for the revised four-factor model was less than adequate. When
measuring model fit, the minimum discrepancy (CMIN) between the unrestricted sample
covariance matrix S and the restricted covariance matrix ∑(θ) should be non-significant
( p > .05). Although the various baseline scores were relatively high, they did not satisfy
the target scores between .90 and 1.00 suggested by statisticians (Byrne 2010, Keith
2010, Schumacker & Lomax 2004). The Root Mean Square Error of Approximation
(RMSEA) also suggested that there may be problems due to model misspecification. An
RMSEA score lower than .10 is desired.
CMIN (χ 2) = 111.506
df = 19 p = .000
GFI = .895
IFI = .853CFI = .851
RMSEA = .156AIC = 145.506
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Figure 12. Three-factor model of wind-band intonation.
Three-factor model. Another troubling aspect of the revised four-factor model
was the use of ME_Qual as an independent exogenous variable that did not take error
into consideration. Even though differences in equipment quality between bands were
small (η p2 = .09), there were differences. It is unlikely that ME_Qual has no effect on
intonation as reflected in the four-factor model. Therefore, the decision was made to
attach ME_Qual to the latent trait describing student attributes. Respecification to a
three-factor model (Figure 12) seemed logical for two reasons: 1) ME_Qual is something
that can be directly controlled by students even if that control is only limited to care and
maintenance, and 2) the error for ME_Qual is represented in the design.
CMIN (χ 2) = 111.269df = 19
p = .000GFI = .894IFI = .853
CFI = .851
RMSEA = .156AIC = 145.269
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Figure 13. Three-factor covariate model of wind-band intonation
Three-factor covariate model. Although the three-factor model seemed more
conceptually sound than the revised four-factor model, fit differences between the two
designs were negligible. Therefore, a covariance between instruction and student
attributes was incorporated into the design –teaching and learning are reciprocal.
Estimating a three-factor correlation model revealed improvements to model-fit (Figure
13). Although the Goodness-of-Fit Index (GFI) was adequate, the other baseline
comparisons were still lacking. The RMSEA still suggested problems with parsimony.
Furthermore, the covariance between instruction and student attributes seemed to
overestimate the relationship between instruction and student attributes. But for the
medium positive correlations between TM and SQ_Exp (r = .37, p = < .001), and RM
CMIN (χ 2) = 97.110
df = 18 p = .000
GFI = .907IFI = .874
CFI = .872RMSEA = .149
AIC = 133.110
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and SQ_Exp (r = .23, p < .01) noted in Table 9, the correlations between the remaining
observed variables associated with instruction and student attributes were not robust.
Three-factor adjusted model. In an attempt to find a more parsimonious design,
a standardized residual covariance report for the three-factor correlation model was
created using AMOS. The report (table 9) was examined to check for values greater than
2.58 –the suggested cutoff suggested by Jöreskog & Sörbom (as cited in Byrne, 2010). A
residual value of 2.682 was observed between SQ_Exp and TM. Based on this evidence,
the mechanics of scoring and weighting the observed variables for instruction were
reconsidered. Keith (2006) suggested that combining multiple tests into one observed
variable is an acceptable practice for model trimming. After consultation with the
adjudicators who evaluated the video observations, the WM, TM and RM scores were
averaged resulting in a new observed variable −the warm-up, tuning, rehearsal measure
(WTRM). In addition to this alteration, the observed variable SQ_Exp was relocated to
the latent trait describing instruction. Since SQ_ Exp is an expression of the number of
years involved in band and the number of years taking private lessons the move seemed
logical.
Reviewing the data-set led to a re-evaluation of the PTM. Recall the PTM was
scored three times in hope of achieving higher reliability. Each time Fabrizio’s (1994)
instrument pitch tendency charts were used to score the PTM. In the third evaluation,
points were awarded for correct responses and negative points were separately summed
for errors. Although students were directed to leave the PTM blank if they did not know
out-of-tune notes for their instrument –there was no consequence or reward for leaving
this section blank –a majority of students (n = 145) in the sample received point
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deductions. In addition to awarding points for correct answers, negative values
accumulated for one or more of the following reasons: 1) labeling generally acceptable
notes as deficient, 2) labeling sharp notes flat and flat notes sharp, and 3) prescribing the
need to lower the pitch for flat notes and raise the pitch for sharp notes. As depicted in
Figure 14, summing the correct responses with the errors resulted in an adjusted PTM
score ( M = -0.01, SD = 5.13) with a range of 30 (minimum -15, maximum 15) and a
normal distribution (skewness of 0.05, SE = 0.17, and kurtosis of 1.02, SE = 0.34).
Table 9.
Standardized Residual Covariances for a Three-factor Correlation Model of Wind-Band
Intonation
ME_Qual SA RM WM TM PTM SQ_Exp SADM
ME_Qual 0
SA 0.663 0
RM 1.226 0.008 0
WM 2.126 0.203 -0.095 0
TM -1.373 -0.413 0.061 0.83 0
PTM 0.955 -0.354 0.779 -1.516 1.407 0
SQ_Exp -0.878 -0.018 -0.377 -2.48 2.682 0.376 0
SADM 1.477 0.004 0.117 0.196 -0.839 1.789 -0.561 0
Note: the emboldened covariance between SQ_Exp and TM indicates a value > than 2.58. ME_Qual =
Musical Equipment Quality, PTM = Pitch Tendency Measure, RM = Rehearsal Measure, SA = SpectrumAnalysis, SADM = Student Aural Discrimination Measure, SQ_Exp = Student Experience, TM = Tuningmeasure, WM = Warm-up Measure.
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Figure 14. Distribution of student test scores on the PTM with adjustment
Estimating the three-factor adjusted model (Figure 15) indicated good fit (χ 2 =
3.486, df = 7, p > .837). The model accounts for an estimated 99.3 percent of the
variance in the observed variable wind-band intonation. In addition, the baseline indices
also suggested good fit. The RMSEA describes how well the model, with unknown but
optimally chosen parameter values would fit the theoretically ideal population covariance
if it existed. An RMSEA below .05 suggests a close fit to the degrees of freedom.
Finally, Akaike’s Information Criterion (AIC) provides a useful cross-validation of
competing model comparison. Keith (2006) suggests smaller AIC values represent a
better fit of the hypothesized model when compared to competing, non-nested designs.
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Figure 15. Three-factor adjusted model of wind-band intonation
Discussion.
Garafalo (1996) described six factors that cause poor intonation in band and
orchestra: 1) condition and quality of the instrument and accessories, 2) fundamental
performance procedures, 3) insufficient warm-up, 4) deviating from standard tuning
frequency of A = 440 Hz, 5) psychological or perceptual issues, and 6) pitch tendencies
of instruments and performers. That all six factors were represented by observed
variables in the three-factor adjusted model is noteworthy because it reinforces the idea
that the model was founded on theory and research. This model, although exploratory,
has the potential to provide scholarly insight by lending credibility to performance
practices that are being used effectively by band directors and their students.
CMIN (χ 2) = 3.486
df = 7 p = .837
GFI = .994IFI = 1.015
CFI = 1.000RMSEA = .000
AIC = 31.486
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Instruction, as defined by the WTRM and SQ_Exp, is a significant ( p < .001)
predictor of wind-band intonation. For each SD increase in the latent instruction variable,
wind-band intonation increases by .95 a SD. Warmup, tuning and rehearsal procedures
and activities employed by directors are important components of instruction. Miles
(1972) advocated teaching students to eliminate beats from mismatched pitches when
tuning perfect intervals. In this study, bands with good intonation also scored high on the
WTRM and exhibited tasks such as tuning intervals and chords using beat elimination.
In addition, students in these bands were responsible for making these adjustments
supporting Byo’s (1990) claim that students should “make the tuning decisions,”
When providing a tuning reference pitch, it did not seem to matter if it was
produced acoustically or electronically so long as it was stable. Of import was the
register of the tuning reference. When band directors provided register specific tuning
references, the intonation scores also tended to be higher. This seems to support findings
from a recent study that found a significant difference ( p < .001) on tuning accuracy
when instrumentalists were provided with register specific tuning notes (Byo et al.,
2011). Ineffective practices observed included tuning each instrument in the ensemble
individually with an electronic tuner, tuning to only one reference pitch, and sustaining a
group tuning note for approximately five-minutes. Boone (2004) noted the
ineffectiveness of using an electronic device to tune instruments claiming that “it
divorces the ear from the tuning process.” Several pedagogues advocate using more than
one reference pitch for tuning (Barnes, 2010; Fabrizio, 1994; Garofalo, 1996; Kohut,
1996; Pottle, 1962).
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A seemingly neglected aspect hindering desirable intonation was insufficient,
inappropriate or ineffective warm-up activities. Milsap (1999) noted significant
improvement ( p < .05) to ensemble intonation through the daily implementation of
sequential sustained tone studies. Bands with higher intonation scores performed
sustained tones descending chromatically or intervallically. More importantly, the
director provided specific feedback to the student performers regarding tone production,
breath support and pitch while performing these activities. Least effective activities
included rapid technical or scale studies with little regard to tone quality.
Results from SQ_Exp revealed another significant ( p < .001) facet of instruction,
for each SD increase in the latent instruction variable, SQ_Exp increases by .35 of a SD.
This supports the oft cited study (Yarbrough, et al., 1997) that found participation in
private instruction as having a significant effect on tuning accuracy, F (1,113) = 7.97, p <
.01. It is likely that students receive instrument specific information in private lessons
they wouldn’t otherwise receive during group instruction. In addition to skill attainment,
Altenmuller & McPherson (2008) noted that instrument performance “…requires highly
refined motor skills that are acquired over many years of extensive training.”
Student attributes seem to have less of an effect on wind-band intonation than
instruction. For each SD increase in the latent student attributes variable, wind-band
intonation increases by .16 a SD. Aural discrimination skills, while important, account
for less variance in the model than band directors might assume. This supports findings
by Ely (1992) who found a very low correlation (r = .07) between subjects’ abilities to
play in tune and their abilities to detect intonation problems. Another aspect of student
attributes that may be over-estimated by directors is instrument and equipment quality.
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What seemed more important was the condition of the instruments and accessories as
opposed to the brand and model. While professional model instruments may assist
performers with improved tone and technique, their influence on intonation seems
limited. Although research in this area is primarily limited to qualitative studies, it does
support Hindsley (1971) who noted that student-line instruments are capable of being
played in-tune when properly adjusted.
Finally, it is important to recognize that although this model fits the data well and
provides consistent findings, there is a possibility that there may be equivalent models
that also fit the data. In addition, there may also be non-equivalent models that fit the
data better than this theoretical design. Perhaps the more important proposition is that
wind-band intonation can be measured scientifically in order to improve teaching and
learning. Further research is encouraged to test and rule out likely alternative models
whenever possible.
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CHAPTER FIVE
Conclusion
The purpose of this study was to test a model describing the effects of equipment,
instruction, and student and director attributes on wind-band intonation. The study was
guided by the following research questions:
1. What are the descriptive statistical characteristics of the observed variables?
2. What are the interrelationships among the observed variables?
3. Can a model of wind-band intonation be estimated? If so, what do post hoc
tests suggest about model fit?
4. Are there alternative models that also fit the data?
Published and researcher designed tests were administered to high school band directors
( N = 5) and their students ( N = 200) in order to measure the model components. A
detailed analysis of the descriptive statistical characteristics of the observed variables
revealed relatively normal distributions despite a small sample of participating schools.
The interrelationships among the observed variables were estimated with aggregated and
disaggregated correlation comparisons. It was suggested that, in certain cases, actual
alpha-levels resided between the aggregated and mean disaggregated comparisons but
were significant none-the-less. Structural equation modeling (SEM) using AMOS
(Arbuckle, 2008) was the method chosen to analyze and interpret the data.
Although the original model describing wind-band intonation could not be
estimated using the data collected, a MG approach consisting of model trimming,
variable reconfiguration and respecification resulted in estimating four models of wind-
band intonation. A post hoc analysis suggested that a three-factor adjusted model best fit
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the data when compared with competing designs. This revised model describes the
effects of instruction and student attributes on wind-band intonation (Figure 16). A
correlation matrix listing means scores and the SD for each observed variables in the
model is provided in accordance with SEM reporting practice (Table 10). Although there
is a possibility that there may be equivalent models that also fit the data, the current
model depicts six factors described by Garafalo (1996) that cause poor intonation in band
and orchestra. This suggests that the model is supported by prevailing theory regarding
causes and corrections for poor wind-band intonation.
Figure 16. A model describing the effects of instruction and student attributes on wind-
band intonation.
CMIN (χ 2) = 3.486
df = 7 p = .837
GFI = .994IFI = 1.015
CFI = 1.000RMSEA = .000
AIC = 31.486
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Table 10.
Correlations, Mean Scores and Standard Deviations for a Model Describing the Effects of
Instruction and Student Attributes on Wind-Band Intonation ( N = 200)
WTRM SQ_Exp ME_Qual SADM PTM SA
WTRM −
SQ_Exp .28** −
ME_Qual .07 .02 −
SADM .07 .11 .14* −
PTM -.01 .08 .13 .14 −
SA .78** .36** .13 .15* .10 −
Mean 45.19 6.10 18.93 40.37 -0.02 164.11
SD 13.83 3.20 2.25 3.83 5.13 33.0
Notes: * p < .05, ** p < .001. ME_Qual = Musical Equipment Quality, PTM = Pitch Tendency Measure,SA = Spectrum Analysis (Wind-Band Intonation), SADM = Student Aural Discrimination Measure,SQ_Exp = Student Experience, WTRM = Warm-up Tuning & Rehearsal Measure.
Findings suggest that instruction is an important influence for producing desirable
wind-band intonation. According to the model, as wind-band intonation increases one
SD, instruction increases .95 a SD. A substantial component of instruction is defined by
the kind and quality of activities that band directors present their students in order to
improve intonation. As instruction increases one SD, warm-up, tuning and rehearsal
quality improves .80 a SD. Instruction is also defined as the number of years students
participate in band and private instruction. These experiences, although not as influential
as classroom instruction are important nonetheless. As instruction increases one SD,
student experience increases .35 a SD.
Although student attributes do not exert the same influence on wind-band
intonation at as instruction, this relationship should not be dismissed as inconsequential.
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Aural discrimination skills, music equipment quality and knowledge of instrumental pitch
tendencies are significant ( p < .005) predictors defining student attributes. When
combined, as wind-band intonation increases one SD, student attributes increase by .16 a
SD. As the results from the spectrum analysis (Appendix I) suggest, even minute pitch
deviations resulting from these factors can account for large differences in wind-band
intonation scores.
Implications.
As this model suggests, band directors exert a tremendous influence on the
intonation of their ensemble. High wind-band intonation scores were evidenced when
band directors took time to tune octaves and chords. Video observation revealed the
director from band 1001 invested rehearsal time tuning octaves in F concert before
proceeding to the chorale. While tuning octaves, the director helped build aural
awareness by having students listen for and sing the resultant tone that sounds a perfect
twelfth above the fundamental. This director also instructed the upper winds to match
pitch with the resultant tone and to tune this interval using the beat elimination method.
In addition, this director also invested considerable time tuning octaves in C concert. Part
of this process involved tuning the bass voice down to the expected pitch in equal
temperament (65.41 Hz) as the tubas tend to play this pitch quite sharp. Spectrum
analysis revealed this band scored 154 points (2.17 SD) higher than the next highest band
on the C minor chord. Furthermore, the overall intonation score for band 1001 was 66
points (2.00 SD) higher than the next highest band. In addition to the activities observed
in the video, the band director used the free response section to describe the following
tuning activities regularly employed during rehearsals:
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• Tuning perfect intervals by voice groups.
• Building chords in the order of root, fifth, third, and then performing the chord
ascending and descending by semitone.
• Performing exercises from the Treasury of Scales book in all keys and then
stopping on chords to identify what instruments are performing what partials of
the chord (root, third, fifth, seventh, etc.).
Building an awareness of intonation through the beat elimination process also
seemed to help students in band 1002. The students in this band were younger in terms of
grade level when compared with students in all the other participating bands, F (4, 195) =
10.01, p < .001, η p2 = .17). Despite this difference, the band’s final intonation score
(160.54) was only nine points, or .25 a SD below the mean ( M = 169.94) intonation score.
These findings suggest that band directors can affect intonation outcomes despite student
grade level. Video observation revealed the warm-up process for band 1002 consisted of
performers sustaining descending long tones and stopping on out-of-tune notes to receive
feedback and reference pitches from the band director. In addition, the band director
asked students to sing reference pitches before performing them on instruments.
During the tuning procedure, students in band 1002 performed an ascending
tetrachord (sol–la–ti–do) to a register specific drone reference pitch. While performing,
the students listened for beats and processed this information to make determinations
about how to adjust the tuning mechanism on their instrument. The director occasionally
provided visual cues to help students build an awareness of pitch direction. This
procedure conforms to tuning pedagogues who advocate using multiple notes or portions
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of a scale to provide a context with which to compare the performed pitch with the
reference pitch (Garofalo, 1996; Kohut, 1996; Pottle, 1962; Wuttke, 2010).
Inasmuch as student attributes are concerned, they do influence wind-band
intonation and should not be ignored. It does not appear that the instrument brand and
model impacts intonation –although it certainly may affect tone and technique. Although
there was a difference in instrument quality between bands ( F (4, 195) = 6.19, p = .001,
η p2 = .09), the small effect size suggests that there was not a large difference in
instrument quality between bands. Reviewing the raw data suggests that the observed
differences may have been due to the condition of the instruments rather than the brand
or model. More students in band 1019 seemed to report that their instruments were in
excellent or perfect condition when compared to the other bands. This makes sense
because the school-owned instruments that the students use in this program are no more
than two-years old –the school opened two-years prior to this study.
Although this model of wind-band intonation fits the data well and provides
consistent findings, there is a possibility that there may be equivalent models that also fit
the data; it is a theoretical design after all. There may also be non-equivalent models that
fit the data better than this model. More research is needed, and more data needs to be
collected for cross-validation. Ultimately, the model supports the idea that wind-band
intonation, and the effects that impact this elusive outcome can be measured scientifically
in order to improve teaching and learning.
Future Research
After reviewing the literature and considering the findings, there are three
important areas that need further investigation. First, director attributes needs to be
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redefined. It seems that measuring experience in terms of the quantity of years teaching
is insufficient. What needs to be addressed is the kind and quality of the experiences that
have influenced the curriculum the director has chosen to teach. The idea that the
younger directors in this study −in both age and teaching experience− seemed to produce
more substantive results does not seem logical. However, it could be a matter of
mentoring, where younger teachers recently out of college are more receptive to new
teaching strategies. At any rate, the question remains as to what knowledge, skills and
past experiences account for this aspect of director attributes. Since instruction has such
a significant effect on wind-band intonation, leaving director attributes out of future
model designs seems counterintuitive.
Another question that needs to be investigated is the extent that chord tuning
influences wind-band intonation. Duffin (2007) relates a story regarding the difficulty
that Cleveland Symphony Orchestra conductor Christoph von Dohnányi experienced
while preparing the beginning of Beethoven’s ninth symphony. When rehearsing the
opening chord shift from D minor B b major, Dohnányi expressed frustration trying to
tune the B b
major chord. According to Duffin (2007), Dohnányi did not seem to
understand that the D in the root of D minor shifting to the major third in B b
Major
needed adjustment down 14 cents from equal temperament to conform to a just-tuned
chord. If this master musician had trouble recognizing this problem, it is likely that band
directors are going to have the same problem on a larger scale because they do not deal
with professionally trained musicians.
Although this study suggests that regular chord tuning produces desirable results,
the small sample size hinders a final verdict. Creating a repeated measures design with a
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treatment and control group might provide some answers to this question. Since
spectrum analysis has been shown to be an accurate measuring tool for wind-band
intonation, this kind of study could have an important influence on the kind of curriculum
Latten (2005) describes as leading toward improved intonation.
A troubling aspect of this study was uncovered when attempting to measure what
students believe to be correct about making adjustments to inherently out-of-tune notes
on their instruments. The fact that 72.5% of the sample population indicated incorrect
pitch tendencies and adjustments for their instruments is disturbing. With so many errors
on the PTM, directors have to wonder if wind-band intonation would actually improve if
students made no corrections at all. Although it is possible that the errors on this test may
be due to faulty design, the raw data suggest that these kinds of errors were committed
consistently between students in all ensembles. In addition, analysis of variance
indicated no difference between bands, years of experience, and grade level of the
adjusted pitch tendency score. Since pedagogues (Fabrizio, 1996; Garafalo, 1994; Kohut,
1991) emphasize how important pitch tendency knowledge and skills are for correcting
intonation problems, further study is needed to focus on this variable and determine the
extent of its influence.
Wind-band intonation is a multi-faceted concept. This model has provided a top-
down approach to investigating and uncovering common intonation problems that
interfere with more important activities such as creating musical expression. If this
model can describe the conditions for helping band directors create and implement a set
of efficient and effective warm-up, tuning and rehearsal procedures, then it will have
served a useful purpose. Stravinski reportedly said “harpists spend 90 percent of their
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lives tuning their harps and 10 percent of their lives playing out of tune.” Hopefully this
does not have to be the case for band directors and their students.
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APPENDIX A
Research Announcement
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APPENDIX B
Informed Consent Forms
Parental Informed Consent Form................................................................................. 102
Student Informed Assent Form.................................................................................... 104
Teacher Informed Consent Form................................................................................. 105
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APPENDIX C
Band Director Inventory
Director Experience (DQ_Exp) ................................................................................... 108
Band Instrumentation Measure (BIM)......................................................................... 109
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APPENDIX D
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APPENDIX E
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APPENDIX F
Student Test Packets1
Flute
Student Questionnaire Experience (SQ_Exp)........................................................ 114Music Equipment Quality (ME_Qual)................................................................... 115
OboeStudent Questionnaire Experience (SQ_Exp)........................................................ 117
Music Equipment Quality (ME_Qual)................................................................... 118
Bassoon
Student Questionnaire Experience (SQ_Exp)........................................................ 120
Music Equipment Quality (ME_Qual)................................................................... 121
ClarinetStudent Questionnaire Experience (SQ_Exp)........................................................ 123
Music Equipment Quality (ME_Qual)................................................................... 124
Saxophone
Student Questionnaire Experience (SQ_Exp)........................................................ 126Music Equipment Quality (ME_Qual)................................................................... 127
TrumpetStudent Questionnaire Experience (SQ_Exp)........................................................ 129
Music Equipment Quality (ME_Qual)................................................................... 130
French horn
Student Questionnaire Experience (SQ_Exp)........................................................ 132Music Equipment Quality (ME_Qual)................................................................... 133
Trombone
Student Questionnaire Experience (SQ_Exp)........................................................ 135Music Equipment Quality (ME_Qual)................................................................... 136
EuphoniumStudent Questionnaire Experience (SQ_Exp)........................................................ 138
Music Equipment Quality (ME_Qual)................................................................... 139
Tuba
Student Questionnaire Experience (SQ_Exp)........................................................ 141
Music Equipment Quality (ME_Qual)................................................................... 142
1 Note: In the case of multiple part assignments, only the first part is represented. Refer to the
conductor score to the Chorale in B b Major (Appendix D) to view these parts.
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major PICCOLO & FLUTE
SCHOOL CODE:
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Chorale
in B b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the keys on your instrument:
a. All keys move freely
b. A few keys seem to stick
c. Many keys stick, some are frozen
3. Describe the condition of the pads on your
instrument:
a. Like new
b. Slight wear
c. Moderate wear/1-2 need replacement
d. Severe wear/3+ need replacement
4. The head joint and foot fit firmly to the body,
there are no loose parts.
a. True
b. False
5. The cork in the tip of the head joint is firm and
does not move easily when pressed.
a. True
b. False
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. When placing a cleaning rod in my headjoint,
the line on the cleaning rod appears in the
center of the embouchure hole (as shown inthe picture).
a. True
b. False
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
SCHOOL CODE:
Chorale in Bb Major OBOE 1
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test PacketMusical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Chorale
in B b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the keys on your
instrument:
a. All keys move freely
b. A few keys seem to stick
c. Many keys stick, some are frozen
3. Describe the condition of the pads on your
instrument:
a. Like new
b. Slight wear
c. Moderate wear/1-2 need replacement
d. Severe wear/3+ need replacement
4. What reeds do you regularly perform on? a. Custom made reeds (I, a friend or my
private teacher makes them for me)
b.Manufactured reeds (purchased from
the music store, online or from my
band director)
5. The age of the reed I am currently performing
with can best described as:
a. New to 2 weeks old
b. More than 2 weeks old
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Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. I, my private teacher and/or my band director makes adjustments to my reeds.
a. True
b. False
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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120
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major BASSOON 1
SCHOOL CODE:
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121
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test PacketMusical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Chorale
in B b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the keys on your
instrument:
a. All keys move freely
b. A few keys seem to stick
c. Many keys stick, some are frozen
3. Describe the condition of the pads on your
instrument:
a. Like new
b. Slight wear
c. Moderate wear/1-2 need replacement
d. Severe wear/3+ need replacement
4. What reeds do you regularly perform on? a. Custom made reeds (I, a friend or my
private teacher makes them for me)
b. Manufactured reeds (purchased from
the music store, online or from my band director)
5. The age of the reed I am currently performing
with can best described as:
a. New to 2 weeks old
b. More than 2 weeks old
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. I, my private teacher and/or my band director makes adjustments to my reeds.
a. True
b. False
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major B
bCLARINET 1
SCHOOL CODE:
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124
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test PacketMusical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Chorale
in B b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the keys on your
instrument:
a. All keys move freely
b. A few keys seem to stick
c. Many keys stick, some are frozen
3. Describe the condition of the pads on your instrument:a. Like new
b. Slight wear
c. Moderate wear/1-2 need replacement
d. Severe wear/3+ need replacement
4. List the brand of the mouthpiece you use with
your instrument (if you do not know, write “Ido not know”).
5. List the brand of the ligature you use with your
instrument (if you do not know, write “I do notknow” or “It came with the instrument”).
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Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the brand (i.e. Rico, etc.) of the reeds thatyou regularly use with your instrument:
7. I would describe the overall condition of my
instrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major E
bALTO SAXOPHONE 1
SCHOOL CODE:
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Choralein B
b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the keys on your
instrument:
a. All keys move freely
b. A few keys seem to stick
c. Many keys stick, some are frozen
3. Describe the condition of the pads on your
instrument:
a. Like new
b. Slight wear
c. Moderate wear/1-2 need replacement
d. Severe wear/3+ need replacement
4. List the brand of the mouthpiece you use withyour instrument (if you do not know, write “I
do not know”).
5. Describe the condition of the cork on the neck of your instrument:
a. Excellent, like new
b. Worn or cracked
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the brand (i.e. Rico, etc.) of the reeds thatyou regularly use with your instrument:
7. I would describe the overall condition of my
instrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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129
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major B
bCORNET/TRUMPET 1
SCHOOL CODE:
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130
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Choralein B
b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the valves on your
instrument:
a. All valves move freely
b. A few valves seem to stick
c. 1 or more valves are frozen
3. Describe the condition of the slides on your
instrument:
a. They all move freely
b. They move slow
c. 3rd Valve slide is stuck
4. Describe the condition of the tubing and bell on
your instrument:
a. Like new
b. A few (no more than 3) tiny dings
c. Many (more than 3) dings and/or dents
5. Describe the condition of the water keys onyour instrument:
a. Corks and springs seal opening
b. Opening sealed with paper or held by
tape/rubber band
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the make of the mouthpiece you use withyour instrument (if you do not know, write “I
do not know”).
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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132
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major FRENCH HORN 1
SCHOOL CODE:
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133
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Choralein B
b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the valves on your
instrument:
a. All valves move freely
b. A few valves seem to stick
c. 1 or more valves are frozen
3. Describe the condition of the slides on your
instrument:
a. They all move freely
b. One or mores slides move slowly
c. One or mores slides is stuck
4. Describe the condition of the tubing and bell on
your instrument:
a. Like new
b. A few (no more than 3) tiny dings
c. Many (more than 3) dings and/or dents
5. Describe the condition of the water keys onyour instrument:
a. Corks and springs seal opening
b. Opening sealed with paper or held by
tape/rubber band
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the make of the mouthpiece you use withyour instrument (if you do not know, write “I
do not know”).
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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135
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major TROMBONE 1
SCHOOL CODE:
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136
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Choralein B
b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the slide (NOT the
tuning slide) on your instrument:
a. It moves freely
b. It sticks slightly
c. It is stuck or frozen
3. My trombone has an F attachment or thumb
trigger:
a. True
b. False
4. Describe the condition of the tubing and bell onyour instrument:
a. Like new
b. A few (no more than 3) tiny dings
c. Many (more than 3) dings and/or
dents
5. Describe the condition of the TUNING slide: a. It moves freely
b. It sticks slightly
c. It is stuck or frozen
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137
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the make of the mouthpiece you use withyour instrument (if you do not know, write “I
do not know”).
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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138
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in:Freshman (9) Sophomore (10)
Junior (11) Senior (12)
32. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major BARITONE/EUPHONIUM BC
SCHOOL CODE:
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139
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Choralein B
b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the valves on your
instrument:
a. All valves move freely
b. A few valves seem to stick
c. 1 or more valves are frozen
3. My instrument has a 4th
valve or compensating
valve:
a. True
b. False
4. Describe the condition of the tubing and bell onyour instrument:
a. Like new
b. A few (no more than 3) tiny dings
c. Many (more than 3) dings and/or
dents
5. Describe the condition of the slides on your
instrument:
a. They all move freely
b. One or more slides move slowly
c. One or more slides are stuck
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the make of the mouthpiece you use withyour instrument (if you do not know, write “I
do not know”).
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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141
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Student Experience (SQ_Exp)
1. Circle your gender: Male Female
2. Circle the grade you are currently in: Freshman (9) Sophomore (10)
Junior (11) Senior (12)
3. List the zip code of your home address:
4. List your current age:
5. List the total number of years you have
participated in band (include elementary,middle and high school experience)
6. List the total number of years you have taken private lessons on your instrument (write 0 if
you have never taken private lessons):
Chorale in Bb Major TUBA
SCHOOL CODE:
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142
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
Musical Equipment Quality (ME_Qual)
1. Write the make and model of the instrument that you used to perform the Choralein B
b. (ask your band director if you are not sure how to answer this).
Make (manufacturer): _______________________________________________
Model: _______________________________________________
2. Describe the condition of the valves on your
instrument:
a. All valves move freely
b. A few valves seem to stick
c. 1 or more valves are frozen
3. My instrument has a 4th
valve or compensating
valve:
a. True
b. False
4. Describe the condition of the tubing and bell onyour instrument:
a. Like new
b. A few (no more than 3) tiny dings
c. Many (more than 3) dings and/or
dents
5. Describe the condition of the slides on your
instrument:
a. They all move freely
b. One or more slides move slowly
c. One or more slides are stuck
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction and
Director and Student Attributes on Wind-Band Intonation.
Student Test Packet
6. List the make of the mouthpiece you use withyour instrument (if you do not know, write “I
do not know”).
7. I would describe the overall condition of myinstrument as:
a. Perfect
b. Very Good
c. Fair
d. Poor
e. Unplayable
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APPENDIX G
Supplementary Testing Materials1
Aural Discrimination Measure (SADM & DADM) .................................................... 145
Pitch Tendency Measure (PTM).................................................................................. 147
1 Note: The Aural Discrimination Measure is the same test for directors and students. Only the student form
(SADM) is depicted in this appendix
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APPENDIX H
Video Observation Form
Warm-up Measure (WM) ............................................................................................ 149
Tuning Measure (TM).................................................................................................. 151
Rehearsal Measure (RM) ............................................................................................. 153
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University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction
and Director and Student Attributes on Wind-Band Intonation.
Video Observation Form
Warm-up Measure (WM) page 1
DIRECTIONS: Use this form to evaluate the content and quality of instruction during the band’s warm-up procedure as it relates to improving ensemble intonation.
Activity Effectiveness Score
Long Tone Study1 Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
There was no long tone study.
Performing 8vas
/5ths
Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
There was no tuning 8vas/5ths study.
Tuning Chords Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
There was no chord tuning study.
Round Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
There was no round.
Chorale Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
There was no chorale.
Other (Specify) Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
Other (Specify) Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
Other (Specify) Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
SUBTOTAL
KEY: SA = strongly agree, A = agree, D = disagree, SD = strongly disagree
1This may include Remington studies, scales performed as long tones (as opposed to being performed
quickly), lip slurs performed slowly without extreme ranges, etc.
SCHOOL CODE:
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University of Miami , Frost School of Music
A Model Describing the Effects of Equipment, Instructionand Director and Student Attributes on Wind-Band Intonation.
Video Observation Form
Warm-up Measure (WM) page 2
Score
1. The ensemble consistently demonstrates a serious
demeanor during the warm-up session.SA A D SD
2. The warm-up activities are consistently presented in a
manner to teach, reinforce and improve ensemble
intonation.
SA A D SD
3. The director consistently elicits appropriate musical
responses from the performers prior to moving to the
next exercise or activity.
SA A D SD
4. The director responds to unacceptable tone and/or
intonation with appropriate feedback.SA A D SD
5. The director’s instructions to the ensemble are clear
and concise.SA A D SD
6. The director’s instructions to the ensemble are
presented in a sequential and logical manner.SA A D SD
7. The director’s explanations to the ensemble to
improve tone and/or intonation are pedagogically
sound.
SA A D SD
8. Overall, the selection of warm-up activities areappropriate towards helping the ensemble realize the
performance goal.2
SA A D SD
9. Overall, the director’s implementation of warm-up
activities demonstrate excellent time management and
pacing skills.
SA A D SD
SUBTOTAL
SUBTOTAL from page 1
10. Rate the overall effectiveness of the warm-up activities from 1 – 10 with 10 being
as effective as possible and 1 being ineffective. If the ensemble does not warm-up,
write 0 (zero).
TOTAL
KEY: SA = strongly agree, A = agree, D = disagree, SD = strongly disagree
2Performance Goal – The ensemble will perform the Chorale in Bb Major with flawless intonation.
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151
University of Miami , Frost School of Music
A Model Describing the Effects of Equipment, Instructionand Director and Student Attributes on Wind-Band Intonation.
Video Observation Form
Tuning Measure (TM) page 1
DIRECTIONS: Use this form to evaluate the content and quality of instruction during the band’s tuning process as it relates to improving ensemble intonation.
Activity Effectiveness Score
Reference Pitch The reference pitch was stable.
CIRCLE ONE: SA A D SD
A reference pitch was not provided.
Individual Pitch Matching Individuals performed up to [i.e. sol-do] reference pitch.
CIRCLE ONE: SA A D SD
There was no individual pitch matching.
Small Group Pitch
Matching
Performers matched the reference pitch in small groups.
CIRCLE ONE: SA A D SD
Small group or sectional pitch matching was not evident.
Ensemble Pitch Matching The ensemble matched the reference pitch together.
CIRCLE ONE: SA A D SD
There was no ensemble pitch matching.
Reference Pitch Variety Instrument specific reference pitches were provided.
CIRCLE ONE: SA A D SD
Only one or no reference pitch was provided.
Adjustments Performers made adjustments to their instruments.
CIRCLE ONE: SA A D SD
Performers did not make instrument adjustments.
Other (Specify) Activity accomplished goal to improve intonation.
CIRCLE ONE: SA A D SD
Other (Specify) Exercise accomplished goal to improve intonation.
CIRCLE ONE: SA A D SD
Other (Specify) Exercise accomplished goal to improve intonation.
CIRCLE ONE: SA A D SD
SUBTOTAL
KEY: SA = strongly agree, A = agree, D = disagree, SD = strongly disagree
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152
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction
and Director and Student Attributes on Wind-Band Intonation.
Video Observation Form
Tuning Measure (TM) page 2
Score
1. The ensemble consistently demonstrates a serious
demeanor during the tuning routine.SA A D SD
2. All tuning activities are consistently presented in a
manner to teach, reinforce and improve ensemble
intonation.
SA A D SD
3. The director consistently elicits appropriate musicalresponses from the performers prior to moving to the
next student, group or section.
SA A D SD
4. The director responds to unacceptable intonation with
appropriate feedback.SA A D SD
5. The director’s instructions to the ensemble are clear
and concise.SA A D SD
6. The director’s instructions to the ensemble are
presented in a sequential and logical manner.SA A D SD
7. The director’s explanations to the ensemble toimprove intonation are pedagogically sound.
SA A D SD
8. Overall, the tuning routine is well established with
all performers aware of their individual roles and
responsibilities.
SA A D SD
9. Overall, the director’s implementation of tuning
activities demonstrate excellent time management and
pacing skills.
SA A D SD
SUBTOTAL
SUBTOTAL from page 1
10. Rate the overall effectiveness of the tuning routine from 1 – 10 with 10 being
as effective as possible and 1 being ineffective. If the ensemble does not tune,
write 0 (zero).
TOTAL
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153
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction
and Director and Student Attributes on Wind-Band Intonation.
Video Observation Form
Rehearsal Measure (RM) page 1
DIRECTIONS: Use this form to evaluate the content and quality of instruction during the
band’s rehearsal as it relates to improving intonation in the Chorale in Bb Major .
Activity Effectiveness Score
Reference Pitch Students were provided in-tune pitches to adjust to.
CIRCLE ONE: SA A D SD
Reference pitches were not provided.
Individual Pitch
Adjustments
Individuals made appropriate pitch adjustments.
CIRCLE ONE: SA A D SD
Individuals were not asked to, or did not adjust pitches.
Small Group PitchMatching
Intonation was fixed by matching pitches in groups.
CIRCLE ONE: SA A D SD
Small group or sectional pitch matching was not evident.
Tuning Octaves Exercise accomplished goal to improve tone/intonation.
CIRCLE ONE: SA A D SD
There was no octave tuning during the rehearsal.
Tuning Chords Exercise accomplished goal to improve tone/intonation.CIRCLE ONE: SA A D SD
There was no chord tuning during the rehearsal.
Error Correction (E/Eb) The director solved the part error on the ii chord.
CIRCLE ONE: SA A D SD
The director did not detect and/or solve this problem.
Other (Specify) Activity accomplished goal to improve intonation.
CIRCLE ONE: SA A D SD
Other (Specify) Exercise accomplished goal to improve intonation.
CIRCLE ONE: SA A D SD
Other (Specify) Exercise accomplished goal to improve intonation.
CIRCLE ONE: SA A D SD
SUBTOTAL
KEY: SA = strongly agree, A = agree, D = disagree, SD = strongly disagree
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154
University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction
and Director and Student Attributes on Wind-Band Intonation.
Video Observation Form
Rehearsal Measure (RM) page 2
Score
1. The ensemble consistently demonstrates a serious
demeanor during the rehearsal.SA A D SD
2. All rehearsal activities are consistently presented in a
manner to teach, reinforce and improve ensemble
intonation.
SA A D SD
3. The director consistently elicits appropriate musicalresponses from the performers prior to moving to the
next student, group or section.
SA A D SD
4. The director responds to unacceptable intonation with
appropriate feedback.SA A D SD
5. The director’s instructions to the ensemble are clear
and concise.SA A D SD
6. The director’s instructions to the ensemble are
presented in a sequential and logical manner.SA A D SD
7. The director’s explanations to the ensemble toimprove intonation are pedagogically sound.
SA A D SD
8. Overall, the rehearsal is well organized with
all performers aware of their individual roles and
responsibilities.
SA A D SD
9. Overall, the director’s implementation of tuning
activities demonstrate excellent time management and
pacing skills.
SA A D SD
SUBTOTAL
SUBTOTAL from page 1
10. Rate the overall effectiveness of the rehearsal from 1 – 10 with 10 being
as effective as possible and 1 being ineffective. If the ensemble does not rehearse,
write 0 (zero).
TOTAL
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APPENDIX I
Spectrum Analysis Results
Band 1001 .............................................................................................................. 156
Band 1002 .............................................................................................................. 162
Band 1008 .............................................................................................................. 168
Band 1009 .............................................................................................................. 174
Band 1019 .............................................................................................................. 180
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Band 1001: Octaves in F, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1001 SA_F8vas
F in Octaves
Harmonic Series 1 2 4 8 16 32
I.A.S. Pitch Label (F1) F2 F3 F4 F5 (F6)
Harmonic Series (Hz) 43.80 87.60 175.20 350.40 700.80 1401.60
Spectrum AnalysisSingle Peak (Hz) 174.20
Deviation (¢) -9.91
Adjusted Deviation (¢) 9.91
SPM Flat (Hz) 86.83 348.92 699.41
Performed (¢) -15.28 -7.33 -3.44
Adjusted Deviation (¢) 15.28 7.33 3.44
SPM Sharp (Hz) 88.38 352.00 703.50
Deviation (¢) 15.35 7.89 6.66
Adj. Deviation (¢) 15.35 7.89 6.66
Total Adjusted Deviation (¢) 65.85
SA Score (300-TAD) 234.15
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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Band 1001: Bb Major Chord in First Inversion, 40–1200 Hz
Frequency (Hz)100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1001 SA_I6
Bb Major Chord in First Inversion
Harmonic Series 1 5/4 3 4 6 8 12 16
I.A.S. Pitch Label (Bb1) D2 F3 Bb3 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.62 73.28 175.86 234.48 351.72 468.96 703.44 937.92
Spectrum AnalysisSingle Peak (Hz) 73.61 175.71 234.46 351.30
Deviation (¢) 7.90 -1.48 -0.15 -2.07
Adjusted Deviation (¢) 7.90 1.48 0.15 2.07
SPM Flat (Hz) 466.39 699.63 934.22
Performed (¢) -9.51 -9.40 -6.84
Adjusted Deviation (¢) 9.51 9.40 6.84
SPM Sharp (Hz) 471.37 704.72
Deviation (¢) 8.87 3.15
Adj. Deviation (¢) 8.87 3.15
Total Adjusted Deviation (¢) 49.37
SA Score (300-TAD) 250.63
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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158
Band 1001: G Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1001 SA_vi
G Minor Chord in Root Position
Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2
I.A.S. Pitch Label G2 D3 G3 Bb3 D4 G4 Bb4 G5 Bb5
Harmonic Series (Hz) 98.10 147.15 196.20 232.99 294.30 392.40 465.98 784.80 931.95
Spectrum Analysis
Single Peak (Hz) 147.73 197.70 931.07Deviation (¢) 6.81 13.19 -1.64
Adjusted Deviation (¢) 6.81 13.19 1.64
SPM Flat (Hz) 292.30 391.25 464.77 781.04
Performed (¢) -11.81 -5.08 -4.48 -8.31
Adjusted Deviation (¢) 11.81 5.08 4.48 8.31
SPM Sharp (Hz) 234.10 296.22 394.34 469.77 787.40
Deviation (¢) 8.25 11.26 8.54 14.04 5.73
Adj. Deviation (¢) 8.25 11.26 8.54 14.04 5.73
Total Adjusted Deviation (¢) 99.13
SA Score (300-TAD) 200.87
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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159
Band1001: C Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1001 SA_ii
C Minor Chord in Root Position
Harmonic Series 1 2 3 4 19/4 6 8 12 16
I.A.S. Pitch Label C2 C3 G3 C4 Eb4 G4 C5 G5 C6
Harmonic Series (Hz) 65.88 131.76 197.64 263.52 312.93 395.28 527.04 790.56 1054.08
Spectrum Analysis
Single Peak (Hz) 131.39 197.28Deviation (¢) -4.87 -3.16
Adjusted Deviation (¢) 4.87 3.16
SPM Flat (Hz) 262.80 312.00 392.60 522.93 783.00 1053.40
Performed (¢) -4.74 -5.15 -11.78 -13.55 -16.64 -1.12
Adjusted Deviation (¢) 4.74 5.15 11.78 13.55 16.64 1.12
SPM Sharp (Hz) 527.73
Deviation (¢) 2.27
Adj. Deviation (¢) 2.27
Total Adjusted Deviation (¢) 63.26
SA Score (300-TAD) 236.74
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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160
Band1001: F7
Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1001 SA_V7
F7 Chord in Root Position
Harmonic Series 1 2 5/2 3 7/2 5 6 8 10
I.A.S. Pitch Label F2 F3 A3 C4 Eb4 A4 C5 F5 A5
Harmonic Series (Hz) 87.70 175.40 219.25 263.10 306.95 438.50 526.20 701.60 877.00
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 175.35 216.86 261.46 436.83 523.47 699.73 874.26
Performed (¢) -0.49 -18.98 -10.83 -6.61 -9.01 -4.62 -5.42
Adjusted Deviation (¢) 0.49 18.98 10.83 6.61 9.01 4.62 5.42
SPM Sharp (Hz) 176.36 219.44 264.06 310.55 440.79 526.60 703.01 879.97
Deviation (¢) 9.45 1.50 6.31 20.19 9.02 1.32 3.48 5.85
Adj. Deviation (¢) 9.45 1.50 6.31 20.19 9.02 1.32 3.48 5.85
Total Adjusted Deviation (¢) 113.05SA Score (300-TAD) 186.95
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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Band1001: Bb Major Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1001 SA_I
Bb Major Chord in Root Position
Harmonic Series 1 2 3 4 5 6 7 12 16
I.A.S. Pitch Label Bb1 Bb2 F3 Bb3 D4 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.51 117.02 175.53 234.04 292.55 351.06 468.08 702.12 936.16
Spectrum Analysis
Single Peak (Hz) 117.24 932.15
Deviation (¢) 3.25 -7.43
Adjusted Deviation (¢) 3.25 7.43
SPM Flat (Hz) 175.95 233.68 350.25 466.88 699.62
Performed (¢) 4.14 -2.67 -4.00 -4.44 -6.18
Adjusted Deviation (¢) 4.14 2.67 4.00 4.44 6.18
SPM Sharp (Hz) 234.86 293.77 351.90 702.75
Deviation (¢) 6.06 7.20 4.14 1.55
Adj. Deviation (¢) 6.06 7.20 4.14 1.55
Total Adjusted Deviation (¢) 51.05SA Score (300-TAD) 248.95
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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Band 1002: Octaves in F, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1002 SA_F8vas
F in Octaves
Harmonic Series 1 2 4 8 16 32
I.A.S. Pitch Label (F1) F2 F3 F4 F5 (F6)
Harmonic Series (Hz) 43.85 87.70 175.40 350.80 701.60 1403.20
Spectrum Analysis
Single Peak (Hz) 87.70
Deviation (¢) 0.00
Adjusted Deviation (¢) 0.00
SPM Flat (Hz) 173.69 348.60 698.10
Performed (¢) -16.96 -10.89 -8.66
Adjusted Deviation (¢) 16.96 10.89 8.66
SPM Sharp (Hz) 175.75 352.32
Deviation (¢) 3.45 7.49
Adj. Deviation (¢) 3.45 7.49
Total Adjusted Deviation (¢) 47.45SA Score (300-TAD) 252.55
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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Band 1002: Bb Major Chord in First Inversion, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1002 SA_I6
Bb Major Chord in First Inversion
Harmonic Series 1 5/4 3 4 6 8 12 16
I.A.S. Pitch Label (Bb1) D2 F3 Bb3 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.60 73.25 175.80 234.40 351.60 468.80 703.20 937.60
Spectrum Analysis
Single Peak (Hz) 174.48
Deviation (¢) -13.05
Adjusted Deviation (¢) 13.05
SPM Flat (Hz) 231.76 351.28 464.10 697.57 935.62
Performed (¢) -19.61 -1.58 -17.44 -13.92 -3.66
Adjusted Deviation (¢) 19.61 1.58 17.44 13.92 3.66
SPM Sharp (Hz) 74.11 235.92 353.69 473.05 705.60 942.03
Deviation (¢) 20.21 11.19 10.26 15.62 5.90 8.16
Adj. Deviation (¢) 20.21 11.19 10.26 15.62 5.90 8.16
Total Adjusted Deviation (¢) 140.60SA Score (300-TAD) 159.40
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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Band 1002: G Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1002 SA_vi
G Minor Chord in Root Position
Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2
I.A.S. Pitch Label G2 D3 G3 Bb3 D4 G4 Bb4 G5 Bb5
Harmonic Series (Hz) 97.60 146.40 195.20 231.80 292.80 390.40 463.60 780.80 927.20
Spectrum Analysis
Single Peak (Hz) 146.14 392.66
Deviation (¢) -3.08 9.99
Adjusted Deviation (¢) 3.08 9.99
SPM Flat (Hz) 290.58 459.85
Performed (¢) -13.18 -14.06
Adjusted Deviation (¢) 13.18 14.06
SPM Sharp (Hz) 196.68 233.02 293.57 467.24 784.60 937.28
Deviation (¢) 13.08 9.09 4.55 13.54 8.41 18.72
Adj. Deviation (¢) 13.08 9.09 4.55 13.54 8.41 18.72
Total Adjusted Deviation (¢) 107.68SA Score (300-TAD) 192.32
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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Band 1002: C Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1002 SA_ii
C Minor Chord in Root Position
Harmonic Series 1 2 3 4 19/4 6 8 12 16
I.A.S. Pitch Label C2 C3 G3 C4 Eb4 G4 C5 G5 C6
Harmonic Series (Hz) 66.05 132.10 198.15 264.20 313.74 396.30 528.40 792.60 1056.80
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 130.58 194.17 259.96 310.54 392.10 520.80 782.16 1046.30
Performed (¢) -20.04 -35.13 -28.01 -17.73 -18.45 -25.08 -22.96 -17.29
Adjusted Deviation (¢) 20.04 35.13 28.01 17.73 18.45 25.08 22.96 17.29
SPM Sharp (Hz) 134.25 200.03 264.59 396.67 1058.05
Deviation (¢) 27.95 16.35 2.55 1.62 2.05
Adj. Deviation (¢) 27.95 16.35 2.55 1.62 2.05
Total Adjusted Deviation (¢) 235.19SA Score (300-TAD) 64.81
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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Band 1002: F7
Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1002 SA_V7
F7 Chord in Root Position
Harmonic Series 1 2 5/2 3 7/2 5 6 8 10
I.A.S. Pitch Label F2 F3 A3 C4 Eb4 A4 C5 F5 A5
Harmonic Series (Hz) 87.55 175.10 218.88 262.65 306.43 437.75 525.30 700.40 875.50
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 173.70 218.03 260.36 436.12 521.90 697.77 872.09
Performed (¢) -13.90 -6.70 -15.16 -6.46 -11.24 -6.51 -6.76
Adjusted Deviation (¢) 13.90 6.70 15.16 6.46 11.24 6.51 6.76
SPM Sharp (Hz) 175.74 220.98 263.90 311.00 440.03 526.55 705.50 879.65
Deviation (¢) 6.32 16.57 8.22 25.66 8.99 4.11 12.56 8.19
Adj. Deviation (¢) 6.32 16.57 8.22 25.66 8.99 4.11 12.56 8.19
Total Adjusted Deviation (¢) 157.34
SA Score (300-TAD) 142.66
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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Band 1002: Bb Major Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1002 SA_I
Bb Major Chord in Root Position
Harmonic Series 1 2 3 4 5 6 7 12 16
I.A.S. Pitch Label Bb1 Bb2 F3 Bb3 D4 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 57.88 115.76 173.64 231.52 289.40 347.28 463.04 694.56 926.08
Spectrum Analysis
Single Peak (Hz) 116.12
Deviation (¢) 5.38
Adjusted Deviation (¢) 5.38
SPM Flat (Hz) 173.14 231.58 346.24 459.71 694.30
Performed (¢) -4.99 0.45 -5.19 -12.50 -0.65
Adjusted Deviation (¢) 4.99 0.45 5.19 12.50 0.65
SPM Sharp (Hz) 175.70 234.15 293.90 349.97 467.30 698.41 933.53
Deviation (¢) 20.42 19.56 26.71 13.36 15.85 9.57 13.87
Adj. Deviation (¢) 20.42 19.56 26.71 13.36 15.85 9.57 13.87
Total Adjusted Deviation (¢) 148.49SA Score (300-TAD) 151.51
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis, TAD= Total Adjusted Deviation.
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Band 1008: Octaves in F, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1008 SA_F8vas
F in Octaves
Harmonic Series 1 2 4 8 16 32
I.A.S. Pitch Label (F1) F2 F3 F4 F5 (F6)
Harmonic Series (Hz) 43.90 87.80 175.60 351.20 702.40 1404.80
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 87.49 174.65 349.40 695.29
Performed (¢) -6.12 -9.39 -8.90 -17.61
Adjusted Deviation (¢) 6.12 9.39 8.90 17.61
SPM Sharp (Hz) 87.81 176.46 354.25 705.46
Deviation (¢) 0.20 8.46 14.97 7.53
Adj. Deviation (¢) 0.20 8.46 14.97 7.53
Total Adjusted Deviation (¢) 73.18SA Score (300-TAD) 226.82
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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169
Band 1008: Bb Major Chord in First Inversion, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1008 SA_I6
Bb Major Chord in First Inversion
Harmonic Series 1 5/4 3 4 6 8 12 16
I.A.S. Pitch Label (Bb1) D2 F3 Bb3 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.80 73.50 176.40 235.20 352.80 470.40 705.60 940.80
Spectrum Analysis
Single Peak (Hz) 73.93
Deviation (¢) 10.10
Adjusted Deviation (¢) 10.10
SPM Flat (Hz) 173.90 234.04 348.66 467.30 696.60 927.92
Performed (¢) -24.71 -8.56 -20.44 -11.45 -22.22 -23.87
Adjusted Deviation (¢) 24.71 8.56 20.44 11.45 22.22 23.87
SPM Sharp (Hz) 236.96 355.15 474.51 941.38
Deviation (¢) 12.91 11.49 15.06 1.07
Adj. Deviation (¢) 12.91 11.49 15.06 1.07
Total Adjusted Deviation (¢) 161.87
SA Score (300-TAD) 138.13
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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170
Band 1008: G Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1008 SA_vi
G Minor Chord in Root Position
Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2
I.A.S. Pitch Label G2 D3 G3 Bb3 D4 G4 Bb4 G5 Bb5
Harmonic Series (Hz) 97.92 146.88 195.84 232.56 293.76 391.68 465.12 783.36 930.24
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 146.37 194.40 296.60 387.58 462.52 777.73 922.71
Performed (¢) -6.02 -12.78 16.66 -18.22 -9.70 -12.49 -14.07
Adjusted Deviation (¢) 6.02 12.78 16.66 18.22 9.70 12.49 14.07
SPM Sharp (Hz) 148.74 197.74 234.49 291.04 393.56 469.51 787.13 936.30
Deviation (¢) 21.79 16.72 14.31 -16.10 8.29 16.26 8.31 11.24
Adj. Deviation (¢) 21.79 16.72 14.31 16.10 8.29 16.26 8.31 11.24
Total Adjusted Deviation (¢) 202.96SA Score (300-TAD) 97.04
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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171
Band 1008: C Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1008 SA_ii
C Minor Chord in Root Position
Harmonic Series 1 2 3 4 19/4 6 8 12 16
I.A.S. Pitch Label C2 C3 G3 C4 Eb4 G4 C5 G5 C6
Harmonic Series (Hz) 66.48 132.96 199.44 265.92 315.78 398.88 531.84 797.76 1063.68
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 130.06 197.47 262.38 311.24 391.20 523.61 782.20 1051.10
Performed (¢) -38.18 -17.19 -23.20 -25.07 -33.66 -27.00 -34.10 -20.60
Adjusted Deviation (¢) 38.18 17.19 23.20 25.07 33.66 27.00 34.10 20.60
SPM Sharp (Hz) 133.62 200.13 267.22 403.30 535.00
Deviation (¢) 8.57 5.98 8.44 19.08 10.26
Adj. Deviation (¢) 8.57 5.98 8.44 19.08 10.26
Total Adjusted Deviation (¢) 271.3SA Score (300-TAD) 28.68
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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172
Band 1008, F7
Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1008 SA_V7
F7 Chord in Root Position
Harmonic Series 1 2 5/2 3 7/2 5 6 8 10
I.A.S. Pitch Label F2 F3 A3 C4 Eb4 A4 C5 F5 A5
Harmonic Series (Hz) 87.58 175.16 218.95 262.74 306.53 437.90 525.48 700.64 875.80
Spectrum Analysis
Single Peak (Hz) 176.59
Deviation (¢) 14.08
Adjusted Deviation (¢) 14.08
SPM Flat (Hz) 259.66 435.44 521.34 699.70 871.43
Performed (¢) -20.41 -9.75 -13.69 -2.32 -8.66
Adjusted Deviation (¢) 20.41 9.75 13.69 2.32 8.66
SPM Sharp (Hz) 220.05 263.00 311.70 441.51 528.02 704.05 882.01
Deviation (¢) 8.68 1.71 28.96 14.21 8.35 8.41 12.23
Adj. Deviation (¢) 8.68 1.71 28.96 14.21 8.35 8.41 12.23
Total Adjusted Deviation (¢) 151.47SA Score (300-TAD) 148.53
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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173
Band 1008: Bb Major Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1008 SA_I
Bb Major Chord in Root Position
Harmonic Series 1 2 3 4 5 6 7 12 16
I.A.S. Pitch Label Bb1 Bb2 F3 Bb3 D4 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 59.00 118.00 177.00 236.00 295.00 354.00 472.00 708.00 944.00
Spectrum Analysis
Single Peak (Hz) 116.88
Deviation (¢) -16.51
Adjusted Deviation (¢) 16.51
SPM Flat (Hz) 175.02 233.50 293.31 349.61 466.43 698.98 935.38
Performed (¢) -19.48 -18.44 -9.95 -21.60 -20.55 -22.20 -15.88
Adjusted Deviation (¢) 19.48 18.44 9.95 21.60 20.55 22.20 15.88
SPM Sharp (Hz) 177.75 237.63 296.01 476.31 708.40
Deviation (¢) 7.32 11.92 5.92 15.74 0.98
Adj. Deviation (¢) 7.32 11.92 5.92 15.74 0.98
Total Adjusted Deviation (¢) 186.47SA Score (300-TAD) 113.53
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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174
Band 1009: Octaves in F, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1009 SA_F8vas
F in Octaves
Harmonic Series 1 2 4 8 16 32
I.A.S. Pitch Label (F1) F2 F3 F4 F5 (F6)
Harmonic Series (Hz) 43.66 87.32 174.64 349.28 698.56 1397.12
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 86.49 173.44 347.44 695.59
Performed (¢) -16.53 -11.94 -9.14 -7.38
Adjusted Deviation (¢) 16.53 11.94 9.14 7.38
SPM Sharp (Hz) 88.15 175.63 352.21 702.17
Deviation (¢) 16.38 9.79 14.46 8.92
Adj. Deviation (¢) 16.38 9.79 14.46 8.92
Total Adjusted Deviation (¢) 94.54SA Score (300-TAD) 205.46
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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175
Band 1009: Bb Major Chord in First Inversion, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1009 SA_I6
Bb Major Chord in First Inversion
Harmonic Series 1 5/4 3 4 6 8 12 16
I.A.S. Pitch Label (Bb1) D2 F3 Bb3 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.87 73.59 176.61 235.48 353.22 470.96 706.44 941.92
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 72.36 174.60 234.54 350.63 463.55 699.21 931.10
Performed (¢) -29.12 -19.82 -6.92 -12.74 -27.46 -17.81 -20.00
Adjusted Deviation (¢) 29.12 19.82 6.92 12.74 27.46 17.81 20.00
SPM Sharp (Hz) 74.00 235.50 355.09 472.59 709.40
Deviation (¢) 9.68 0.15 9.14 5.98 7.24
Adj. Deviation (¢) 9.68 0.15 9.14 5.98 7.24
Total Adjusted Deviation (¢) 166.06SA Score (300-TAD) 133.94
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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176
Band 1009: G Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1009 SA_vi
G Minor Chord in Root Position
Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2
I.A.S. Pitch Label G2 D3 G3 Bb3 D4 G4 Bb4 G5 Bb5
Harmonic Series (Hz) 98.08 147.12 196.16 232.94 294.24 392.32 465.88 784.64 931.76
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 194.48 291.40 390.42 463.08 784.45 924.16
Performed (¢) -14.89 -16.79 -8.40 -10.44 -0.42 -14.18
Adjusted Deviation (¢) 14.89 16.79 8.40 10.44 0.42 14.18
SPM Sharp (Hz) 148.55 197.71 234.44 294.38 393.60 470.00 787.44 935.61
Deviation (¢) 16.75 13.63 11.11 0.82 5.64 15.24 6.17 7.14
Adj. Deviation (¢) 16.75 13.63 11.11 0.82 5.64 15.24 6.17 7.14
Total Adjusted Deviation (¢) 141.62SA Score (300-TAD) 158.38
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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177
Band 1009: C Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1009 SA_ii
C Minor Chord in Root Position
Harmonic Series 1 2 3 4 19/4 6 8 12 16
I.A.S. Pitch Label C2 C3 G3 C4 Eb4 G4 C5 G5 C6
Harmonic Series (Hz) 66.50 133.00 199.50 266.00 315.88 399.00 532.00 798.00 1064.00
Spectrum Analysis
Single Peak (Hz) 197.19
Deviation (¢) -20.16
Adjusted Deviation (¢) 20.16
SPM Flat (Hz) 130.05 262.57 309.90 393.75 522.92 788.51 1046.81
Performed (¢) -38.83 -22.47 -33.06 -22.93 -29.80 -20.71 -28.20
Adjusted Deviation (¢) 38.83 22.47 33.06 22.93 29.80 20.71 28.20
SPM Sharp (Hz) 133.05
Deviation (¢) 0.65
Adj. Deviation (¢) 0.65
Total Adjusted Deviation (¢) 216.82
SA Score (300-TAD) 83.18
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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178
Band 1009: F7
Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1009 SA_V7
F7 Chord in Root Position
Harmonic Series 1 2 5/2 3 7/2 5 6 8 10
I.A.S. Pitch Label F2 F3 A3 C4 Eb4 A4 C5 F5 A5
Harmonic Series (Hz) 87.68 175.36 219.20 263.04 306.88 438.40 526.08 701.44 876.80
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 86.90 173.77 218.84 260.30 437.67 521.73 700.04 875.44
Performed (¢) -15.47 -15.77 -2.85 -18.13 -2.89 -14.37 -3.46 -2.69
Adjusted Deviation (¢) 15.47 15.77 2.85 18.13 2.89 14.37 3.46 2.69
SPM Sharp (Hz) 88.47 176.96 220.57 265.08 310.78 439.35 528.31 701.85 881.51
Deviation (¢) 15.53 15.72 10.79 13.37 21.86 3.75 7.32 1.01 9.27
Adj. Deviation (¢) 15.53 15.72 10.79 13.37 21.86 3.75 7.32 1.01 9.27
Total Adjusted Deviation (¢) 143.25Final Intonation Score (300-TAD) 156.75
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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179
Band 1009: Bb Major Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1009 SA_I
Bb Major Chord in Root Position
Harmonic Series 1 2 3 4 5 6 7 12 16
I.A.S. Pitch Label Bb1 Bb2 F3 Bb3 D4 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.61 117.22 175.83 234.44 293.05 351.66 468.88 703.32 937.76
Spectrum Analysis
Single Peak (Hz) 116.90
Deviation (¢) -4.73
Adjusted Deviation (¢) 4.73
SPM Flat (Hz) 175.19 233.58 291.40 350.97 466.08 699.00 929.35
Performed (¢) -6.31 -6.36 -9.78 -3.40 -10.37 -10.67 -15.60
Adjusted Deviation (¢) 6.31 6.36 9.78 3.40 10.37 10.67 15.60
SPM Sharp (Hz) 175.91 234.90 294.60 352.81 471.00 705.37 938.25
Deviation (¢) 0.79 3.39 9.13 5.65 7.81 5.04 0.90
Adj. Deviation (¢) 0.79 3.39 9.13 5.65 7.81 5.04 0.90
Total Adjusted Deviation (¢) 99.93SA Score (300-TAD) 200.07
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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180
Band1019: Octaves in F, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1019 SA_F8vas
F in Octaves
Harmonic Series 1 2 4 8 16 32
I.A.S. Pitch Label (F1) F2 F3 F4 F5 (F6)
Harmonic Series (Hz) 43.58 87.16 174.32 348.64 697.28 1394.56
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 86.77 173.42 348.50 696.41
Performed (¢) -7.76 -8.96 -0.70 -2.16
Adjusted Deviation (¢) 7.76 8.96 0.70 2.16
SPM Sharp (Hz) 87.55 177.06 352.85 701.42
Deviation (¢) 7.73 27.00 20.78 10.25
Adj. Deviation (¢) 7.73 27.00 20.78 10.25
Total Adjusted Deviation (¢) 85.34SA Score (300-TAD) 214.66
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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181
Band 1019: Bb Major Chord in First Inversion, 40–1200 Hz
Frequency (Hz)100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1019 SA_I6
Bb Major Chord in First Inversion
Harmonic Series 1 5/4 3 4 6 8 12 16
I.A.S. Pitch Label (Bb1) D2 F3 Bb3 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.21 72.76 174.63 232.84 349.26 465.68 698.52 931.36
Spectrum Analysis
Single Peak (Hz) 74.32Deviation (¢) 36.67
Adjusted Deviation (¢) 36.67
SPM Flat (Hz) 231.50 346.45 462.64 695.54 926.91
Performed (¢) -9.99 -13.99 -11.34 -7.40 -8.29
Adjusted Deviation (¢) 9.99 13.99 11.34 7.40 8.29
SPM Sharp (Hz) 176.73 234.14 352.46 468.65 700.95 937.00
Deviation (¢) 20.69 9.64 15.79 11.01 6.01 10.45
Adj. Deviation (¢) 20.69 9.64 15.79 11.01 6.01 10.45
Total Adjusted Deviation (¢) 161.27
SA Score (300-TAD) 138.73
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis, TAD
= Total Adjusted Deviation.
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182
Band 1019: G Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1019 SA_vi
G Minor Chord in Root Position
Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2
I.A.S. Pitch Label G2 D3 G3 Bb3 D4 G4 Bb4 G5 Bb5
Harmonic Series (Hz) 98.65 147.98 197.30 234.29 295.95 394.60 468.59 789.20 937.18
Spectrum Analysis
Single Peak (Hz)Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 147.35 195.60 231.84 293.01 391.04 465.00 780.80 929.30
Performed (¢) -7.33 -14.98 -18.23 -17.28 -15.69 -13.31 -18.53 -14.61
Adjusted Deviation (¢) 7.33 14.98 18.23 17.28 15.69 13.31 18.53 14.61
SPM Sharp (Hz) 198.30 471.35 939.14
Deviation (¢) 8.75 10.18 3.63
Adj. Deviation (¢) 8.75 10.18 3.63
Total Adjusted Deviation (¢) 142.50
SA Score (300-TAD) 157.50
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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183
Band 1019: C Minor Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1019 SA_ii
C Minor Chord in Root Position
Harmonic Series 1 2 3 4 19/4 6 8 12 16
I.A.S. Pitch Label C2 C3 G3 C4 Eb4 G4 C5 G5 C6
Harmonic Series (Hz) 66.46 132.92 199.38 265.84 315.69 398.76 531.68 797.52 1063.36
Spectrum Analysis
Single Peak (Hz)Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 130.69 197.13 261.05 310.54 392.02 523.25 786.08 1043.53
Performed (¢) -29.29 -19.65 -31.48 -28.45 -29.51 -27.67 -25.01 -32.59
Adjusted Deviation (¢) 29.29 19.65 31.48 28.45 29.51 27.67 25.01 32.59
SPM Sharp (Hz) 132.98 199.50
Deviation (¢) 0.78 1.04
Adj. Deviation (¢) 0.78 1.04
Total Adjusted Deviation (¢) 225.47
SA Score (300-TAD) 74.53
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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184
Band 1019: F7
Chord in Root Position, 40–1200 Hz
Frequency (Hz)100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1019 SA_V7
F7 Chord in Root Position
Harmonic Series 1 2 5/2 3 7/2 5 6 8 10
I.A.S. Pitch Label F2 F3 A3 C4 Eb4 A4 C5 F5 A5
Harmonic Series (Hz) 86.89 173.78 217.23 260.67 304.12 434.45 521.34 695.12 868.90
Spectrum Analysis
Single Peak (Hz) 217.25 262.20Deviation (¢) 0.20 10.13
Adjusted Deviation (¢) 0.20 10.13
SPM Flat (Hz) 172.76 433.45 693.77
Performed (¢) -10.19 -3.99 -3.37
Adjusted Deviation (¢) 10.19 3.99 3.37
SPM Sharp (Hz) 174.28 311.30 436.82 523.00 696.60 873.30
Deviation (¢) 4.97 40.43 9.42 5.50 3.68 8.74
Adj. Deviation (¢) 4.97 40.43 9.42 5.50 3.68 8.74
Total Adjusted Deviation (¢) 100.63
SA Score (300-TAD) 199.37
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,
TAD = Total Adjusted Deviation.
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Band 1019: Bb Major Chord in Root Position, 40–1200 Hz
Frequency (Hz)
100 100020050 500
S o u n d p r e s s u r e l e v e l ( d B / H z )
20
40
60
1019 SA_I
Bb Major Chord in Root Position
Harmonic Series 1 2 3 4 5 6 7 12 16
I.A.S. Pitch Label Bb1 Bb2 F3 Bb3 D4 F4 Bb4 F5 Bb5
Harmonic Series (Hz) 58.80 117.60 176.40 235.20 294.00 352.80 470.40 705.60 940.80
Spectrum Analysis
Single Peak (Hz)
Deviation (¢)
Adjusted Deviation (¢)
SPM Flat (Hz) 116.28 175.30 233.00 291.60 350.03 466.29 700.08 931.07
Performed (¢) -19.54 -10.83 -16.27 -14.19 -13.65 -15.19 -13.60 -18.00
Adjusted Deviation (¢) 19.54 10.83 16.27 14.19 13.65 15.19 13.60 18.00
SPM Sharp (Hz) 117.63 176.62 295.51
Deviation (¢) 0.44 2.16 8.87
Adj. Deviation (¢) 0.44 2.16 8.87
Total Adjusted Deviation (¢) 132.73SA Score (300-TAD) 167.27
Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,TAD = Total Adjusted Deviation.
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