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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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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



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



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



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.



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.



iv

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



v

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



vi

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



vii

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



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



ix

Figure 16. A model describing the effects of instruction and student attributeson wind-band intonation ............................................................................ 92



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



1

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



2

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



3

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.



4

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).



5

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



6

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



7

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



8

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



9

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



10

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,



11

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



12

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



13

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).



14

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



15

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).



16

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



17

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



18

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



19

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



20

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.”



21

“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.



22

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



23

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



24

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.”



25

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



26

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.”



27

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



28

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).



29

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.



30

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



31

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



32

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



33

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.



34

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



35

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



36

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



37

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



38

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



39

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



40

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.



41

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?


3. Can a model of wind-band intonation be estimated? If so, what do post hoc


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 =



42

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.



43

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



44

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



45

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.



46

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



47

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.



48

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.



49

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



50

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).



51

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.



52

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



53

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).



54

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



55

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.



56

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



57

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



58

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



59

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.



60

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.



61

Figure 7. A latent variable structural equation model describing the effects of equipment, instruction and director and student attributes on wind-band

intonation.



62

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?





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.



63

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



64

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



65

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.



66

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.



67

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).



68

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.



69

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).



70

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 =



71

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.



72

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



73

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


• the disaggregated correlation between TM and RM (r = .66, < .001), and the


In each case, it seems safe to assume that these variables are correlated because it fits

both prevailing theory and logic.



74



75

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



76

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



77

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



78

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



79

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



80

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



81

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



82

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



83

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



84

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



85

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.



86

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.



87

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



88

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).



89

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.



90

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.



91

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?





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



92

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



93

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.



94

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:



95

• 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



96

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



97

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



98

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



99

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.



100

APPENDIX A

Research Announcement



101

APPENDIX B

Informed Consent Forms

Parental Informed Consent Form................................................................................. 102

Student Informed Assent Form.................................................................................... 104

Teacher Informed Consent Form................................................................................. 105



102



103



104



105



106



107

APPENDIX C

Band Director Inventory

Director Experience (DQ_Exp) ................................................................................... 108

Band Instrumentation Measure (BIM)......................................................................... 109



108



109



110

APPENDIX D



111

APPENDIX E



112



113

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


ClarinetStudent Questionnaire Experience (SQ_Exp)........................................................ 123


Saxophone


TrumpetStudent Questionnaire Experience (SQ_Exp)........................................................ 129


French horn


Trombone


EuphoniumStudent Questionnaire Experience (SQ_Exp)........................................................ 138


Tuba

Student Questionnaire Experience (SQ_Exp)........................................................ 141


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.



114

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:



115



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



116



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



117



Student Test Packet











SCHOOL CODE:

Chorale in Bb Major OBOE 1



118



Student Test PacketMusical Equipment Quality (ME_Qual)




Model: _______________________________________________

2. Describe the condition of the keys on your

instrument:





instrument:

a. Like new

b. Slight wear



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



119



Student Test Packet

6. I, my private teacher and/or my band director makes adjustments to my reeds.

a. True

b. False


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



120



Student Test Packet











Chorale in Bb Major BASSOON 1

SCHOOL CODE:



121







Model: _______________________________________________


instrument:





instrument:

a. Like new

b. Slight wear



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



122



Student Test Packet

6. I, my private teacher and/or my band director makes adjustments to my reeds.

a. True

b. False


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



123



Student Test Packet











Chorale in Bb Major B

bCLARINET 1

SCHOOL CODE:



124







Model: _______________________________________________


instrument:




3. Describe the condition of the pads on your instrument:a. Like new

b. Slight wear



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”).



125



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



126



Student Test Packet











Chorale in Bb Major E

bALTO SAXOPHONE 1

SCHOOL CODE:



127



Student Test Packet


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).


Model: _______________________________________________


instrument:





instrument:

a. Like new

b. Slight wear



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



128



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



129



Student Test Packet











Chorale in Bb Major B

bCORNET/TRUMPET 1

SCHOOL CODE:



130



Student Test Packet





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



131



Student Test Packet

6. List the make of the mouthpiece you use withyour instrument (if you do not know, write “I

do not know”).


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



132



Student Test Packet











Chorale in Bb Major FRENCH HORN 1

SCHOOL CODE:



133



Student Test Packet





Model: _______________________________________________


instrument:





instrument:


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


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



134



Student Test Packet


do not know”).


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



135



Student Test Packet











Chorale in Bb Major TROMBONE 1

SCHOOL CODE:



136



Student Test Packet





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


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



137



Student Test Packet


do not know”).


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



138



Student Test Packet



2. Circle the grade you are currently in:Freshman (9) Sophomore (10)








Chorale in Bb Major BARITONE/EUPHONIUM BC

SCHOOL CODE:



139



Student Test Packet





Model: _______________________________________________


instrument:




3. My instrument has a 4th

valve or compensating

valve:

a. True

b. False


a. Like new



dents


instrument:


b. One or more slides move slowly

c. One or more slides are stuck



140



Student Test Packet


do not know”).


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



141



Student Test Packet











Chorale in Bb Major TUBA

SCHOOL CODE:



142



Student Test Packet





Model: _______________________________________________


instrument:




3. My instrument has a 4th

valve or compensating

valve:

a. True

b. False


a. Like new



dents


instrument:


b. One or more slides move slowly

c. One or more slides are stuck



143



Student Test Packet


do not know”).


a. Perfect

b. Very Good

c. Fair

d. Poor

e. Unplayable



144

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



145



146



147



148

APPENDIX H

Video Observation Form

Warm-up Measure (WM) ............................................................................................ 149

Tuning Measure (TM).................................................................................................. 151

Rehearsal Measure (RM) ............................................................................................. 153



149

University of Miami , Frost School of Music A Model Describing the Effects of Equipment, Instruction

and Director and Student Attributes on Wind-Band Intonation.


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.


There was no tuning 8vas/5ths study.

Tuning Chords Exercise accomplished goal to improve tone/intonation.


There was no chord tuning study.

Round Exercise accomplished goal to improve tone/intonation.


There was no round.

Chorale Exercise accomplished goal to improve tone/intonation.


There was no chorale.

Other (Specify) Exercise accomplished goal to improve tone/intonation.






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:



150

University of Miami , Frost School of Music

A Model Describing the Effects of Equipment, Instructionand Director and Student Attributes on Wind-Band Intonation.


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


2Performance Goal – The ensemble will perform the Chorale in Bb Major with flawless intonation.



151

University of Miami , Frost School of Music

A Model Describing the Effects of Equipment, Instructionand Director and Student Attributes on Wind-Band Intonation.


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.


Reference Pitch The reference pitch was stable.


A reference pitch was not provided.

Individual Pitch Matching Individuals performed up to [i.e. sol-do] reference pitch.


There was no individual pitch matching.

Small Group Pitch

Matching

Performers matched the reference pitch in small groups.


Small group or sectional pitch matching was not evident.

Ensemble Pitch Matching The ensemble matched the reference pitch together.


There was no ensemble pitch matching.

Reference Pitch Variety Instrument specific reference pitches were provided.


Only one or no reference pitch was provided.

Adjustments Performers made adjustments to their instruments.


Performers did not make instrument adjustments.

Other (Specify) Activity accomplished goal to improve intonation.


Other (Specify) Exercise accomplished goal to improve intonation.




SUBTOTAL




152




Tuning Measure (TM) page 2

Score


demeanor during the tuning routine.SA A D SD

2. All tuning activities are consistently presented in a


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





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


pacing skills.

SA A D SD

SUBTOTAL


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



153




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 .


Reference Pitch Students were provided in-tune pitches to adjust to.


Reference pitches were not provided.

Individual Pitch

Adjustments

Individuals made appropriate pitch adjustments.


Individuals were not asked to, or did not adjust pitches.

Small Group PitchMatching

Intonation was fixed by matching pitches in groups.


Small group or sectional pitch matching was not evident.

Tuning Octaves Exercise accomplished goal to improve tone/intonation.


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.


The director did not detect and/or solve this problem.

Other (Specify) Activity accomplished goal to improve intonation.






SUBTOTAL




154




Rehearsal Measure (RM) page 2

Score


demeanor during the rehearsal.SA A D SD

2. All rehearsal activities are consistently presented in a


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





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


pacing skills.

SA A D SD

SUBTOTAL


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



155

APPENDIX I

Spectrum Analysis Results

Band 1001 .............................................................................................................. 156

Band 1002 .............................................................................................................. 162

Band 1008 .............................................................................................................. 168

Band 1009 .............................................................................................................. 174

Band 1019 .............................................................................................................. 180



156

Band 1001: Octaves in F, 40–1200 Hz

Frequency (Hz)

100 100020050 500


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


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.



157

Band 1001: Bb Major Chord in First Inversion, 40–1200 Hz

Frequency (Hz)100 100020050 500


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


SPM Flat (Hz) 466.39 699.63 934.22

Performed (¢) -9.51 -9.40 -6.84


SPM Sharp (Hz) 471.37 704.72

Deviation (¢) 8.87 3.15

Adj. Deviation (¢) 8.87 3.15



Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis,

TAD = Total Adjusted Deviation.



158

Band 1001: G Minor Chord in Root Position, 40–1200 Hz

Frequency (Hz)100 100020050 500


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


Spectrum Analysis

Single Peak (Hz) 147.73 197.70 931.07Deviation (¢) 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


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







159

Band1001: C Minor Chord in Root Position, 40–1200 Hz

Frequency (Hz)100 100020050 500


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


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







160

Band1001: F7

Chord in Root Position, 40–1200 Hz

Frequency (Hz)

100 100020050 500


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


Spectrum Analysis

Single Peak (Hz)

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





161

Band1001: Bb Major Chord in Root Position, 40–1200 Hz

Frequency (Hz)

100 100020050 500


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


Spectrum Analysis

Single Peak (Hz) 117.24 932.15

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





162


Frequency (Hz)

100 100020050 500


20

40

60

1002 SA_F8vas

F in Octaves




Spectrum Analysis

Single Peak (Hz) 87.70

Deviation (¢) 0.00


SPM Flat (Hz) 173.69 348.60 698.10

Performed (¢) -16.96 -10.89 -8.66


SPM Sharp (Hz) 175.75 352.32

Deviation (¢) 3.45 7.49






163


Frequency (Hz)

100 100020050 500


20

40

60

1002 SA_I6





Spectrum Analysis




SPM Flat (Hz) 231.76 351.28 464.10 697.57 935.62

Performed (¢) -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






164


Frequency (Hz)

100 100020050 500


20

40

60

1002 SA_vi


Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2



Spectrum Analysis

Single Peak (Hz) 146.14 392.66

Deviation (¢) -3.08 9.99


SPM Flat (Hz) 290.58 459.85

Performed (¢) -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






165

Band 1002: C Minor Chord in Root Position, 40–1200 Hz

Frequency (Hz)

100 100020050 500


20

40

60

1002 SA_ii


Harmonic Series 1 2 3 4 19/4 6 8 12 16



Spectrum Analysis

Single Peak (Hz)

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





166

Band 1002: F7


Frequency (Hz)

100 100020050 500


20

40

60

1002 SA_V7


Harmonic Series 1 2 5/2 3 7/2 5 6 8 10



Spectrum Analysis

Single Peak (Hz)

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


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







167

Band 1002: Bb Major Chord in Root Position, 40–1200 Hz

Frequency (Hz)

100 100020050 500


20

40

60

1002 SA_I





Spectrum Analysis


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


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


Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis, TAD= Total Adjusted Deviation.



168


Frequency (Hz)

100 100020050 500


20

40

60

1008 SA_F8vas

F in Octaves




Spectrum Analysis

Single Peak (Hz)

Deviation (¢)


SPM Flat (Hz) 87.49 174.65 349.40 695.29

Performed (¢) -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





169


Frequency (Hz)

100 100020050 500


20

40

60

1008 SA_I6





Spectrum Analysis


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


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






170


Frequency (Hz)

100 100020050 500


20

40

60

1008 SA_vi


Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2



Spectrum Analysis

Single Peak (Hz)

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


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






171


Frequency (Hz)

100 100020050 500


20

40

60

1008 SA_ii


Harmonic Series 1 2 3 4 19/4 6 8 12 16



Spectrum Analysis

Single Peak (Hz)

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


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





172

Band 1008, F7


Frequency (Hz)

100 100020050 500


20

40

60

1008 SA_V7


Harmonic Series 1 2 5/2 3 7/2 5 6 8 10



Spectrum Analysis


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


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






173


Frequency (Hz)

100 100020050 500


20

40

60

1008 SA_I





Spectrum Analysis




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


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





174


Frequency (Hz)

100 100020050 500


20

40

60

1009 SA_F8vas

F in Octaves




Spectrum Analysis

Single Peak (Hz)

Deviation (¢)


SPM Flat (Hz) 86.49 173.44 347.44 695.59

Performed (¢) -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





175


Frequency (Hz)

100 100020050 500


20

40

60

1009 SA_I6





Spectrum Analysis

Single Peak (Hz)

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


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





176


Frequency (Hz)

100 100020050 500


20

40

60

1009 SA_vi


Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2



Spectrum Analysis

Single Peak (Hz)

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


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





177


Frequency (Hz)

100 100020050 500


20

40

60

1009 SA_ii


Harmonic Series 1 2 3 4 19/4 6 8 12 16



Spectrum Analysis




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


SPM Sharp (Hz) 133.05

Deviation (¢) 0.65

Adj. Deviation (¢) 0.65






178

Band 1009: F7


Frequency (Hz)

100 100020050 500


20

40

60

1009 SA_V7


Harmonic Series 1 2 5/2 3 7/2 5 6 8 10



Spectrum Analysis

Single Peak (Hz)

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


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





179


Frequency (Hz)

100 100020050 500


20

40

60

1009 SA_I





Spectrum Analysis




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


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





180

Band1019: Octaves in F, 40–1200 Hz

Frequency (Hz)

100 100020050 500


20

40

60

1019 SA_F8vas

F in Octaves




Spectrum Analysis

Single Peak (Hz)

Deviation (¢)


SPM Flat (Hz) 86.77 173.42 348.50 696.41

Performed (¢) -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





181


Frequency (Hz)100 100020050 500


20

40

60

1019 SA_I6





Spectrum Analysis

Single Peak (Hz) 74.32Deviation (¢) 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


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



Note: (¢) = Cents; Hz = Hertz (refers to the frequency of the pitch label); SPM = Split Peaks Mean; SA = Spectrum Analysis, TAD

= Total Adjusted Deviation.



182


Frequency (Hz)100 100020050 500


20

40

60

1019 SA_vi


Harmonic Series 1 3/2 2 19/8 3 4 19/4 8 19/2



Spectrum Analysis

Single Peak (Hz)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


SPM Sharp (Hz) 198.30 471.35 939.14

Deviation (¢) 8.75 10.18 3.63

Adj. Deviation (¢) 8.75 10.18 3.63







183


Frequency (Hz)

100 100020050 500


20

40

60

1019 SA_ii


Harmonic Series 1 2 3 4 19/4 6 8 12 16



Spectrum Analysis

Single Peak (Hz)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


SPM Sharp (Hz) 132.98 199.50

Deviation (¢) 0.78 1.04








184

Band 1019: F7


Frequency (Hz)100 100020050 500


20

40

60

1019 SA_V7


Harmonic Series 1 2 5/2 3 7/2 5 6 8 10



Spectrum Analysis

Single Peak (Hz) 217.25 262.20Deviation (¢) 0.20 10.13


SPM Flat (Hz) 172.76 433.45 693.77

Performed (¢) -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







185


Frequency (Hz)

100 100020050 500


20

40

60

1019 SA_I





Spectrum Analysis

Single Peak (Hz)

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


SPM Sharp (Hz) 117.63 176.62 295.51

Deviation (¢) 0.44 2.16 8.87

Adj. Deviation (¢) 0.44 2.16 8.87





186

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