Rifkin Stoecker Music Learning Taxonomy

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A Revised TAxonomy foR music LeARning

A Revised Taxonomy for Music Learning

DeborahrifkinanDPhiliPStoecker

IntroductIon

Among college music teachers, it is commonly lamented thatear-training skills develop more slowly than other kinds ofmusical knowledge, such as written theory skills. Informally, theear develops more slowly than the mind. Intrigued by thisphenomenon, which suggests that the learning process for auralskills could be different compared to other types of knowledge, wehave evaluated our students and our own pedagogy for years withthe intent of developing a learning taxonomy for aural development.That is, we sought adaptations that catered specically to musiclearning by accommodating the time-sensitive nature of performedarts, rather than the more spatial emphasis that we believe persistswith most prior learning theories. This article has two goals: the

rst goal is to present our revised taxonomy of learning for musicclasses; the second goal is to demonstrate how our taxonomy can

be used to design classroom activities for both tonal and atonalaural skills courses.

A learning taxonomy classies learning objectives and identiesdifferent levels of learning, which are typically arranged from low-order objectives on the bottom to higher ones at the top. Why developa new learning taxonomy? It can help a teacher design effective

lesson plans and coursework, and it can also inform decisions aboutbetter ways to evaluate and assess student learning. One thingthat differentiates a good aural-skills teacher from an excellentone is the ability to diagnose a problem in class and improvise animpromptu exercise to address it. A learning taxonomy can helpa teacher with this formidable task because it provides categoriesfor types of problems and a framework for advancing learning. Alearning taxonomy can also help students by making them self-

aware of their own learning process. For example, when a studentcomes to our ofce hours for a problem they are having in an auralskills course, it is not uncommon for them to begin the conversationwith a self-assessment of the challenge, including which stage ofthe taxonomy they believe it resides in. This kind of introspection

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makes it easier for them to self-diagnose and to come up with theirown strategies for success.

Although there have been some notable exceptions in the lastfew years, aural skills pedagogy has been a woefully neglectedarea of study in modern American colleges, universities, andconservatories. Consider the question: how many music theorytextbooks can you name? Now, how many aural skills textbooks?Do you consider the books you named for aural skills as actualtextbooks? Some of the most widely used aural skills textse.g.,Ottman and Rogers m r sht-sare essentiallyanthologies.1Although there is a pedagogical impetus behind theorganization and chronology of excerpts within these texts, the

guidance is hiddenimplicit, rather than explicit. With the rise ofcomprehensive musicianship curricula, recent college textbookstake a more integrative approach, providing more structuredguidance on aural skills development within theory courses.2Ourtaxonomy is intended as a continuing step toward a pedagogicalmethod for an essential, yet elusive, part of every musiciansundergraduate experienceear training.3

1 Robert W. Ottman and Nancy Rogers,m r sht s, 8thed. (Upper Saddle River, NJ: Prentice Hall, 2010); Gary Karpinski andRichard Kram, Athl r sht s(New York: W.W. Norton,2007); Thomas Benjamin, Michael M. Horvit, and Robert Nelson,mr sht s, 4thed. (Belmont, CA: Thomson/Schirmer, 2005); BruceBenward and Maureen A. Carr, sht cplt, 7thed. (Boston,MA: McGraw-Hill, 2006); Sol Berkowitz, Gabriel Fontrier, and Leo Kraft,A nw Apprah t sht s, 5thed. (New York: W.W. Norton, 2011);David Damschroder, Lt a s: L ear-Tra a sht-s(New York: Schirmer Books, 1995).

2 Steven G. Laitz, Th cplt ma: A itrat Apprah tTal Thr, Aal, a Lt, 3rd ed. (New York: Oxford UniversityPress, 2011); Jane Piper Clendinning and Elizabeth West Marvin, Thma g t Thr a Aal(New York: W.W. Norton, 2nd ed.,2010); Michael R. Rogers discusses the advantages and disadvantages tointegrated approaches to theory and aural skills. See the second chapter(Philosophical Orientations, pp. 1530) of Michael R. Rogers, TahApprah m Thr: A orw Paal Phlph,

2nd ed. (Carbondale: Southern Illinois University Press, 2004). In thischapter he discusses the strengths and weaknesses of the comprehensivemusicianship approach to teaching.

3 Although we use the word ear training, other terms that could beused interchangeably include aural skills, sight singing, and musicianship.


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In 2000, Gary Karpinski published a seminal guide entitledAral skll Aqt: Th dlpt Lt, Ra, aPrr skll cll-Ll ma.4 This book launchedaural skills pedagogy to new heights by basing its recommendationson experimental studies in music cognition and perception. Hiscentral tenet, grounding aural skills pedagogy with our knowledgeof perception and cognition, has been the driving force behindour taxonomy. A few years later, Karpinski published a maal

r ear Tra a sht s, which is an aural skills textbookdesigned according to the research, techniques and philosophiesin his rst book.5This resource demonstrates how to incorporatethe abstract principles of Aral skll Aqt into pedagogical

practice. The text is comprehensive, but also linear in its design,which makes it somewhat challenging to use if your school doesnot adopt the curriculum wholesale.6 Our taxonomy provides ageneralized learning theory based upon Karpinskis recommendedtechniques. In other words, it provides a framework for designingand implementing best practices in aural skills pedagogy that can beadopted to suit any curricular needs. With the aid of our taxonomy,teachers can develop their own teaching strategies geared for their

specic students. In the following paragraphs, we will introduceour taxonomy, comparing it to prior learning taxonomies anddescribing the evidence-based cognition studies that inspired ourrevisions for music learning.

4 Gary Karpinski, Aral skll Aqt: Th dlpt Lt,Ra, a Prr skll cll-Ll ma(New York:Oxford University Press, 2000).

5 Gary Karpinski,maal r ear Tra a sht s(NewYork: W.W. Norton, 2007).

6 For instance, Karpinskis text assumes a four-semester tonalsequence, yet many schools use a three-semester tonal sequence with thefourth semester devoted to atonal music.


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taxonomIes

In 1956, Benjamin Bloom edited a handbook titled Ta eatal objt: Th claat eatal gal, which

became a seminal document for assessing pedagogical efcacy.7In the original conception of the taxonomy, Bloom identied threedomains: cognitive (i.e., mental skills), affective (i.e., emotionalareas), and psychomotor (i.e., physical skills). Beginning with thecognitive domain, Bloom provided a list of educational objectivesor goals followed by a later publication of the educational goalsfor the affective domain.8Taxonomies for the psychomotor domainwere completed by other scholars.9

Bloom, 1956 Anderson and Krathwohl, 2001 present authors, 2010

Create EvaluateEvaluation

ImproviseEvaluateSynthesis

ApplyAnalysis Analyze

Comprehension

ConceptualizeApplyApplication

Understand

Recognize

(Short and long-term memory)

Imitate

Knowledge Remember

Example 1. Comparison of Learning Taxonomies

Our interest is in Blooms taxonomy for the cognitive domain. Asshown in Example 1, Bloom identied a sequence of six cognitive

7 Benjamin S. Bloom, Ta eatal objt: Thclaat eatal gal, 1st ed. (New York: Longmans, Green,1956).

8 Benjamin Bloom, Anderson Krathwohl, and Bertram Masia, eds.,Ta eatal objt: Th At da, vol. 2 (NewYork: David McKay, 1964).

9 Ravindrakumar Dave, Psychomotor Levels, in dlp aWrt Bharal objt, ed. Robert Armstrong (Tucson, AZ:Educational Innovators Press, 1970); Anita Harrow, A Ta thPhtr da: A g r dlp Bharalobjt(NewYork, NY: David McKay, 1972); Elizabeth Simpson, Th claat eatal objt: Th Phtr da, vol. 3 (Washington, DC:Gryphon House, 1972).

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levels that lead from basic to advanced stages of learning. For Bloom,the beginning stages of learning include kwl(recalling specic

bits of information), prh(understanding the meaning ofcommunicated material), and applat(the use of learned materialin different, concrete situations); his later stages are aal(abilityto break down material into its component parts to understand itspatterns), th(the ability to put parts together to form a newwhole), and alat(the ability to judge the value of a productfor a given purpose). Although Blooms Ta eatalobjthas been translated into 22 languages and is one of themost widely applied and most often cited references in education,the taxonomy was intended for general, traditional classrooms, not

necessarily for the specic needs of music students.In the past decade, there have been numerous revisions of

Blooms taxonomy based on research in cognitive developmentand educational psychology. Arguably, the most famous of theseis a publication edited by Anderson and Krathwohl (2001), whichwas the culmination of six years of collaboration between cognitivepsychologists, curriculum theorists, instructional researchers, andassessment specialists.10The middle column of Example 1 illustrates

the changes recommended by Anderson and Krathwhol.11One oftheir most signicant revisions is the emphasis on active learning,represented by a switch from nouns, originally listed by Bloom,to verbs in their taxonomy. In addition, Anderson and Krathwohlreverse the order of the last two stages so that ratbecomes thehighest learning level above alat.12

In our music taxonomy, shown on the right of Example 1, wehave re-ordered and re-named some of Anderson and Krathwohls

learning stages to better represent our understanding of how10 Lorin W. Anderson and David R. Krathwohl, eds., A Ta

r Lar, Tah, a A: A R Bl Ta eatal objt(New York: Longman, 2001).

11 The Anderson and Krathwohl revision had two signicantcomponents. The rst was to redesign Blooms original taxonomy; thesecond was to distinguish between different kinds of knowledge, which theydescribed as factual, conceptual, procedural, and metacognitve. Example 1

only references the rst part of Anderson and Krathwohls revisions.12 For an excellent review of Anderson and Krathwohls revisions of

Blooms taxonomy and its implications for national standards in musiceducation, see Wendell Hanna, The New Blooms Taxonomy: Implicationsfor Music Education, Art eat Pl Rw108, no. 4 (2007), 716.


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information is processed when it is presented aurally. For us, thebeginning stages of music learning include rz (rememberprevious music events), tat (recall and repeat previous musicevents), and ptalz (analyze and concretize in ones mind);our later stages are appl(the use of learned material in different,musical environments and contexts), pr(create music withintemporal constraints), and alat (the ability to judge the valueof a product for a given purpose). In each case, our new namefor the learning level changes the general verb in Anderson andKrathwohls taxonomy to a more specic term that accounts foran ephemeral, aural source stimulus. For instance, we have re-named their rbrstage to rz. When a listener recognizes

or recalls that a musical pattern has repeated, this cognitive actis a specialized type of remembering that centralizes the auralevent.13Our new label emphasizes the idea that there are differenttypes of remembering.14We base this revision on experiments thatconrm, for example, that the contour of a melody is rememberedindependently and more accurately than specic pitches.15 Thus,a contour is recognized, before the pitches of a melody areremembered.

13 Several experiments support the idea that music training affectssome kinds of memory and not others. Specically, studies suggest thatmusicians have better verbal memory, not visual memory. See, MichaelFranklin et al., The Effects of Musical Training on Verbal Memory,Phl m36, no. 3 (2008), 35365; Yim-Chi Ho, Mei-ChunCheung, and Agnes S. Chan, Music Training Improves Verbal butNot Visual Memory: Cross-Sectional and Longitudinal Explorations inChildren, nrphl17, no. 3 (2003), 43950.

14 For another implementation of Blooms taxonomy, see JamesCaldwell, Using Blooms Taxonomy to Develop an Approach toAnalysis,Jral m Thr Pa3, no. 2 (1989), 22332. Heincludes a list of related verbs for each stage. For example, the verbslisted under Blooms Knowledge stage include list, recall, remember,dene, identify, label, [and] recognize.

15 W. Jay Dowling, Melodic Contour in Hearing and RememberingMelodies, inmal Prpt, eds. Rita Aiello and John Sloboda (NewYork: Oxford University Press, 1994), 17390; W. Jay Dowling, Scaleand Contour: Two Components of a Theory of Memory for Melodies,Phlal Rw85, no. 4 (1978), 34154.


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In addition to modications at the rst level, we have also madechanges to higher levels. For example, we have changed Andersonand Krathwohls rtastage to tat. In the earlier study, thertaphase includes the ability to classify, identify, or describeevents. In music, the main method for classifying, identifying, anddescribing events is to perform them back, to imitate them. Last, were-named Anderson and Krathwohls ratstage to pr, whichis creating music within a time constraint. Our term emphasizes theperformance-based context of creating.

One of our signicant ordering revisions is shifting the applstage toward a more advanced stage of learning, as a synthesizinglevel, which is similar to Blooms original version. This alteration

attends to the ephemeral nature of a musical stimulus. Apploccurs when a student uses the information in a new way or in anew context. Music students often need some sort of conceptualmap, usually a visual or kinesthetic representation before they canapply and synthesize a new musical concept.

To conceptualize a musical event is to analyze it and create a wayto concretize it in ones mind.16Often, this type of conceptualizationis built around musical expectations. In tonal music, pitch

expectations are commonly modeled by scale-degree function(e.g., moveable do solfge).17Many cognitive studies indicate thatexpectations play a signicant role in musical conceptualization.18An especially well-designed experiment was published in 1988 byYoko Oura and Giyoo Hatano, which not only compares children toyoung adults, and musically experienced versus inexperienced, butalso musical memory versus verbal memory. The study conrmedthat knowing what to expect musically was much more important

for melody recall than general cognitive development or age.1916 We have not eliminated aal/aalzfrom our taxonomy but

placed it under the umbrella of ptalz.

17 It is much harder to process, recognize, and recall atonal melodiessince musical ptatare much less circumscribed.

18 For a summary of cognitive studies supporting the role ofexpectation in musical conceptualization, see Lyle Davidson and Patricia

Welsh, From Collections to Structure: The Developmental Path of TonalThinking, in grat Pr m: Th Phl Prra,iprat, a cpt, ed. John Sloboda (New York: ClarendonPress/Oxford University Press, 1988), 261.

19 Yoko Oura and Giyoo Hatano, Memory for Melodies Among


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According to Oura and Hatano, grade-school children who hadmusical experienceyears of music studytended to rememberand process melodies better than college-aged students who hadconsiderably better cognitive skills and memory capabilities.Because of studies like this one, we place conceptualization in themiddle of our taxonomy; conceptualization affects both low and highstages of learning. Upon reection, we believe conceptualizationplays a role in transferring knowledge from short- to long-termmemory. Looking forward, our classroom experience tells us thatthe mindful mapping of the conceptualize stage needs to happen

before a student can apply their knowledge to new situations.20Another reason for the centrality of ptalzatis that it is

the stage that has the most potential for improving real-time sight-singing. When a student sings an unknown pitch pattern, rhythmpattern, or melody for the rst time and produces an error, thaterror can often be corrected by some ptalguidance from theteacher. Indeed, many of the tools used by sight-singing teachers,(e.g., pitch and rhythm solfge, harmonic analysis, registralconnection of anchor pitches, resolution patterns, sequentialpatterns, etc.,) are effective because they encourage some form of

conceptual mapping. Often, sight-reading errors can be correctedby simply encouraging an alternate conceptualization of musicalevents.

Finally, we consider the pinnacle of the learning triangle tobe alat, similar to Blooms original conception in 1956. Weadvocate this arrangement because students need to examine and

judge their own creative output in order to reinvigorate the learningprocess for the next learning task. Placing alatat the top of the

taxonomy encourages a circular process in which a student usesthe insights from their evaluation stage as the starting point fortheir next learning objective. In other words, having improvised amusical event a student can advance their learning by identifyingits strengths and weaknesses and then these results to informtheir next attempt.

Subjects Differing in Age and Experience in Music, Phl m16, no. 2 (1988), 91109.

20 For an experimental study that supports a correlation betweensolfge instruction and successful application in sightreading, seeMichele Len Henry, The Use of Targeted Pitch Skills for Sight-SingingInstruction in the Choral Rehearsal,Jral Rarh meat52, no. 3 (2004), 20617.


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Not coincidentally, the reader will notice a strong correspondencebetween the learning stages of our taxonomy and Karpinskis stagesof dictation. Table 1 summarizes the correlations.

Karpinskis Our Corresponding Dictation Stages Taxonomy Levels

Hear n/a

Remember Recognize

Understand Conceptualize

Notate Apply

Table 1. Correlations between Karpinskis stages of dictation and ourstages of learning.21

By designing a learning taxonomy similar to Karpinskis outlineof the dictation process, we aim to generalize his pedagogicalprinciples so that they can be applied to other pedagogical pursuitsin the aural skills classroom.

We end this introduction to our taxonomy with a brief note onimplementation. With the immense amount of data conrmingthe importance of active learning, we retain Anderson andKrathwohls use of verbs throughout the taxonomy. When usingthis taxonomy to develop pedagogical strategies, there should be astrong emphasis on active and cooperative learning. We will nowturn our discussion to the role of memory in music learning, a topicthat motivated our changes to the bottom stages of our learning

taxonomy.

theroleofmemoryInmusIclearnIng

Karpinksi writes that musical memory seems to be differentthan other types of brain functions.22Similarly, Howard Gardnerclassies musical intelligence separately from other kinds ofintelligences,23and Diana Deutsch has shown that pitch memory

21 Karpinski, Aral skll Aqt, 62103.

22 Karpinski, Aral skll Aqt, 37.

23 Howard Gardner,mltpl itll: Th Thr Prat(NewYork: Basic Books, 1993).


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is coded in a nonverbal way.24 From a neuroscience perspective,Marin and Perrys ndings suggest that musical working memorymay be a specialized subsystem of general working memory.25Our revisions of the learning taxonomy were motivated bythe distinctive role memory plays in music learning. WhereasAnderson and Krathwohl describe their rst rbr stage asextracting information from long-term memory, we include short-term memory in our rst stage because it is an essential step leadingtoward long-term memory for musical information perceived intime. As we will demonstrate, memory is thprimary element of thelearning process for music because without it there is no retentionof the stimulus. To emphasize the importance of memory for music

learning, we have provided three rhythmic excerpts in Example2. Consider each of the rhythmic patterns and assess how easy ordifcult it would be to memorize the pattern from a harstimulus,i.e., without reading notation.

& 4

First pattern

&

Second pattern

&

Third pattern

Example 2. Rhythmic patterns

According to George Millers seminal article in 1956, an averageperson can retain ve to nine discrete items in short-term memory.26

24 Diana Deutsch, Tones and numbers: Specicity of interference inimmediate memory, s168 (1970), 160405.

25 Oscar S. M. Marin and David W. Perry, Neurological Aspects ofMusic Perception and Performance, in Th Phl m, 2nd ed.(San Diego, CA: Academic Press, 1999), 653724.

26 George A. Miller, The Magical Number Seven, Plus or Minus Two:


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In the rst pattern there are 16 attacks, which is beyond what mostcan retain in short-term memory. However, one probably wouldnot have trouble remembering what to clap. There might be troubleknowing when to end the pattern, but using Gestalt principles onewould probably recognize that there is a very consistent pattern. Infact, every clap lasts the same duration.

The second pattern has more diversity of rhythmic gures andhas a higher number of attacks, but it would probably be easierto remember when to end. The differentiation between long andshort notes helps a listener segment the pattern into larger chunks.Karpinski names this cognitive task, appropriately enough,hk.27Depending how large a chunk one chooses the second

pattern could be conceptualized as three repetitions of a six-notepattern or six repetitions of a three-note pattern. In fact, introducingstudents to hkstrategies like this is one way to help studentsimprove their musical memory. The third pattern uses the samerhythmic gures as the second one and has fewer attacks, yet itwould probably be harder to memorize. Because the pattern of longand short notes is not consistent, it is harder to chunk the rhythminto a memorable sequence.

This experiment highlights the close association that existsbetween our rz, tat, and ptalz stages. Theconceptual process of hk, which provided a hierarchy ofrhythmic proportions and metrical grouping, helped organizemusical entities so that they would be easier to recognize andimitate. Similarly, in the pitch realm l ahr can workin conjunction with hk to organize sounds into memorableunits.ml ahris a conceptualizing activity that processes

melodic pitches into hierarchical relationships according to theirrelative stability, which is assessed by their consonance-dissonance

Some Limits on Our Capacity for Processing Information, PhlalRw63 (1956), 8197.

27 Karpinski, Aral skll Aqt, 7378. Karpinski is not the rstto use the term hk. Generally, George Miller is attributed withcoining the term in his 1956 article, The Magical Number Seven. In the1970s, Herbert Simon and W. Jay Dowland rened the concept throughcognitive experiments. Some of their most-often cited references includethe following: Herbert Simon, How Big is a Chunk? s183,no. 4124 (1974), 48288; and, W. Jay Dowling, Rhythmic Groupsand Subjective Chunks in Memory for Melodies, Prpt aPhph14 (1973), 3740.


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status, temporal order, and relative duration.28 In other words,how one conceptualizes a pattern can inuence how one imitatesand remembers it. And, vice versa: how one retains informationin short-term memory can effect how one conceptualizes thepattern.29 In music learning, we nd that our students do notnecessarily progress in a linear fashion through the learning stages.Instead, adjacent (and even non-adjacent) stages can affect oneanother. This association between conceptualization and memoryis strengthened by several studies that show that musical contextis an important factor for memory.30In sum, a conceptual map can

be important for promoting long-term memory retention, as wellas serving as the foundation for the next learning levelappl

musical knowledge to new situations and contexts.31

28 J. J. Bharucha, Anchoring Effects in Music: The Resolution ofDissonance, ct Phl16, no. 4 (1984), 485518; Bernice

Laden, Melodic Anchoring and Tone Duration,m Prpt12, no.2 (1994), 199212.

29 For experimental support of this claim, see Nancy Rogers,Solmization Expertise Correlates with Superior Pitch Memory, epata: Rta r p-raa tra a18, no. 30(2007), 13152.

30 For a summary of studies showing the effect of context on memory,see Eric G. Freedman, The Role of Diatonicism in the Abstraction and

Representation of Contour and Interval Information,m Prpt16, no. 3 (1999), 36587; John Sloboda, Th mal m: Th ctPhl m(Oxford: Clarendon Press, 1985); Kathryn M. Dewar,Lola L. Cuddy, and Douglas J. K. Mewhort, Recognition Memoryfor Single Tones with and Without Context,Jral eprtalPhl3, no. 1 (1977), 6067; Lola L. Cuddy, Annabel J. Cohen, andJanet Miller, Melody Recognition: The Experimental Application ofMusical Rules, caaa Jral Phl33, no. 3 (1979), 14857;Carol L. Krumhansl, The Psychological Representation of Musical Pitch

in a Tonal Context, ct Phl11, no. 3 (1979), 34674.31 One notable study that links conceptualizing processes to

knowledge application is Philip A. Fine, Anna Berry, and Burton S.Rosner, The Effect of Pattern Recognition and Tonal Predictability onSight-Singing Ability, Phl m34, no. 4 (2006), 43147.


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melodIcapplIcatIonsofthetaxonomy

The following discussion will demonstrate how our taxonomyprovides a pedagogical framework for an activity in an aural skills

class. This activity was designed for a rst-semester undergraduatecourse, and the goal of the lesson plan was to provide studentswith the skills to understand neighbor notes. To achieve this goalthe students were given the seven brief pitch patterns, shown inExample 3. Since the learning objective for this exercise focuses onpitch, we have minimized rhythmic considerations by using thesame rhythm for every pitch. This activity works best if the lastpitch pattern, (e.g., #7 of Example 3) is revealed only at the end

of the activity. Each successive melody is slightly different, andthrough a process of incremental changes the rst pitch patterngradually morphs into a short excerpt from the music literature.32As shown in the example, the exercise concludes with a familiarfolk tune that consists of various types of neighbor motionupper,double, and small and large-scale neighbors. To ensure that thestudents grasp the neighbor concept, the lesson was coordinatedto traverse through our taxonomy of learning. Below is a detailed

discussion of each pitch pattern of Example 3 and how it relates toour new taxonomy.

Pitch Pattern #1

The rst, three-note pitch pattern includes an upper neighbor.We have the students sing this pitch pattern and use thisopportunity to dene the concept of an upper neighbor note.

Pitch Pattern #2

The lowest stage of our taxonomy, rz, is invoked whenstudents recognize that the upper neighbor note that they sangfrom the rst pitch pattern is included here.

itat, our second stage, occurs when students sing the upperneighbor note, thus imitating the rst pitch pattern.

32 Our pitch pattern exercises are similar to David DamschrodersQuick Switches in his textbook Lt a s. Unlike our approach,Damschroder does not end his exercises with music from the literature.Additional differences between our pitch patterns and DamschrodersQuick Switches will become more apparent as our discussion unfolds.


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&

#1 ww

w

&

#2 ww

w

w

w

&

#3 w ww

w

&

#4

&

#5

&

#6

&

#7

Example 3. Pitch patterns

Pitch Pattern #2 (t)

cptalz, our third stage, occurs when students grasp theconcept of a neighbor note and then generalize this idea toinclude lower neighbors. cptalzoccurs when a student

analyzes and organizes the musical material in his/her mind.Some students will learn neighbor notes visually by analyzingthe notation, taking into consideration the contour, harmony,and meter. Other students may ptalzby listening,


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singing the neighbor motion, or even using a kinestheticapproach, such as hand gestures, to physically show theneighbor motion.

Pitch Pattern #3 The lowest stage of our taxonomy is invoked when students

recall that both the upper and lower neighbor notes they sangfrom the rst two pitch patterns are also included here.

Our second stage occurs when students tatand sing theupper and lower neighbor notes.

cptalz, our third stage, occurs when studentscomprehend the concept of a neighbor note and then

generalize this idea to establish the double neighbor note thatappears in this exercise.

Pitch Pattern #4

Like the previous pitch patterns rzand tatareinvoked here. By introducing the idea of a compound melody,the students must analyze and organize the material on theirown, using the best strategy that works for them, such assinging the music, using a visual cue, or a kinesthetic hand

gesture to show the different registers. Once the students feel comfortable with the idea of a

compound melody, we then ask them to transpose this melodyto different keys or modes. By asking the students to producethe same melodic shape in a different contexte.g., minorinstead of majorthey are invoking our applstage.

Pitch Pattern #5

Again, the lower and middle stages of our taxonomy are

invoked here when the students recall previous material. Once the students sing this pitch pattern, we then ask them

to prby adding the lower pitch anywhere in this pitchpattern.

Next, we ask them to prneighbor notes of their choiceupper, lower, or doubleto the pitch in the lower register.

Pitch Pattern #6

This pitch pattern may resemble an improvisation performed

by a student. We have added upper neighbors to the lower voice, but the

student could have used lower or double neighbors.


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Pitch Pattern #7

The nal pitch pattern is the familiar tune Happy Birthday.Here, students see the context of the resultant pitch pattern

in a score from music literature, incorporating other musicalparameters such as meter and rhythm. In our exercises, thenal pitch pattern will always be a passage of music fromtheliterature or a folk tune, which we reveal only after studentshave navigated the prior patterns. Ending with an excerptfrom the literature is important: it is essential for students tomake a connection from the abstract pitch-pattern exercisesto real music, and it is crucial for students to realize thatan innite number of melodies can be derived from a fewmelodic gestures.

We now ask our students to alatby comparing their ownimprovised melodies to the Happy Birthday tune.

In our taxonomy of learning, alatis the highest of ourlearning stages. Once a student performs their improvisedmelody, they do not walk away. They will alatbycomparing their improvised melody with the folk tune.Some of the questions they may ask themselves during the

evaluation stage include: Did I actually sing neighbor notes?or Did I add too many neighbor notes? or even That wasreally cool, how I added a double neighbor that began with thelower neighbor note before I sang the upper neighbor note.And so on.

After singing and discussing the pitch patterns and the structureof the folk tune, we provide students with a new pitch pattern,

Twinkle, Twinkle, Little Star. This familiar folk tune includes anupper neighbor note pattern (5-6-5) and contains a new musicaldevice, passing tones. We then ask the students to create their ownpitch patterns that they will share with their peers for the next classsession. By creating their own pitch patterns, students will alattheir processes, and, as a result, our learning taxonomy beginsagain.


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harmonIcapplIcatIonsofthetaxonomy

We now turn to the harmonic realm, demonstrating how ourtaxonomy can provide a pedagogical framework for harmonic

activities in an aural skills class. This exercise is designed for asecond-semester aural skills course, and the goal of the lesson planis to provide students with the skills to understand pre-dominantseventh chords.

We begin with the rz stage: A teacher establishes a keyand then plays a root-position pre-dominant seventh chord, suchas ii7. Next, the instructor plays a series of four-chord progressions(TPDDT, which we refer to as paradigms), which may or may

not include the ii7chord. For each paradigm that includes a ii7, thestudent writes a tick mark on their page. The teacher then describesthe quality of the pre-dominant seventh chord, which in this case isa minor-seventh harmony, and the solfege/scale degrees afliatedwith the bass note of each inversion of the supertonic seventhchord. On the second round of recognition of the paradigms,students are asked to recognize whether the ii7 chord is presentin either root-position or inversion. Throughout this phase of the

exercise, students not only learn to recognize the ii7 chord, butthey also recognize the typical context of the pre-dominant chordas a connecting harmony between tonic and dominant. A similarprocedure can be used to introduce the IV7chord. In the last partof the recognition exercises, a teacher plays paradigms with ii7,IV7, their inversions, or none of the above. Students are asked todetermine whether a pre-dominant seventh chord was used and torecognize whether it was a supertonic or a subdominant harmony.

Moving on to the tatstage of our harmonic activities, theteacher plays an isolated pre-dominant seventh chord on the piano,and students sing it back on a neutral syllable. When arpeggiatingchords in this call-and-response activity, students should imitate the

bass note as played by the teacher and then ll in the rest of the chordin singing the next closest note of the harmony. For instance, if theteacher plays the chord in Example 4(a), students would sing CDFA as shown. This method of arpeggiation preserves the proper

inversion of the chord, but minimizes the difculty of hearing theexact register of the inner voices that a teacher performs. Next, theteacher performs a four-chord paradigm, pausing after each chordfor the students to respond with their arpeggiations. Example 4(b)shows what one round of this activity would look like.


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a) Imitatestage of the taxonomy

C: ii4

2 teacher plays: students sing

b)

C: I ii65 V I

c) Conceptualizestage of the taxonomy: Call and Response

C: I ii65 V I

d)

C: I ii

6

5 V I

e)

C: I vii6 I6 IV7

&

?

w

w

la la la la

&

?

w

w

w

w

w

w

w

w

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&

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w

w

w

w

w

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&

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w

ww

w

w

w

w

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ww

&

?

w

w

ww

&

?

w

w

ww

la la la

w

ww

la la la la

w

ww

la la la

w

w

ww

la la la

&

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w

w

w

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w

w

w

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w

w

&

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w

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w

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w

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&

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w

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w

maj or

w

w

w

minor seventh

w

w

w

maj or

w

w

w

maj or - - -

&

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w

w

w

w

w

w

w

w

w

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&

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w

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w

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&

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w

w

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w

&

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w

w

w

1 3 5

do mi sol

w

w

w

4 6 1 2

fa la do re

w

w

w

5 7 2

sol ti re

w

w

w

1 3 5

do mi sol

&

?

??

&

?

w

w

w

w

w

w

w

w

w

w

w

w

w

w

Example 4. Harmonic applications


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degree function to notes within each chord, students build a map ofhow the chords function within the tonal system. For example, theymay discover that aand la(or 4 and 6) are shared between mostpre-dominant-seventh chords. If students have difculty assigningsolfge syllables from an aural stimulus in this call-and-responsefashion, an easier, intermediary ptalz exercise would beto provide Roman numerals and gures of various paradigmsthat include pre-dominant seventh chords. While reading Romannumerals and gures, students can arpeggiate the chords on solfge.

Another useful exercise for the ptalz stage is for theteacher to play a bass line and ask students to identify the mostlikely Roman numerals and gures that could harmonize that bass

line. For pre-dominant harmonies, a teacher might play al(1451) bass line and students could identify ii6, ii6

5, IV, or IV7as

the likely pre-dominant choices for the second chord. One positiveoutcome of this exercise is that students realize for themselvesthe limited harmonic possibilities, constrained by a well-formedsyntax. Alternatively, a teacher could play the beginning part of aprogression, but stop midway through a harmonic succession. Afterthe abrupt stop, the teacher would call on an individual student to

arpeggiate the next chord, making sure it preserves a well-formedsyntactic ow. For example, a teacher might perform the incompleteprogression shown in Example 4(e), and then call on a student toarpeggiate the next chord after the IV7. In this case, a student mightchoose to prolong the pre-dominant function by arpeggiating aIV6

5chord, or they could move on to the dominant function of the

phrase. In either case, the student had to ptalz the properfunction of the IV7chord in relation to its context. Class discussion

might revolve around metric considerations, for example how aprolongation of the pre-dominant function across the next bar linefrom weak to strong beat would be contrary to common-practiceprinciples.

The applstage involves utilizing concepts in new environments,appl them to new situations. Typical exercises for this stageinvolve re-contextualizing prior material, such as converting aparadigm that had been sung in major to the minor mode. After

playing the major-mode progression in the rst four measuresof Example 4(f), students would respond with the minor-modeversion shown in the next four measures. Thus, a student wouldnavigate the different chord qualities found in the minor mode.Not only does this activity invoke the apply stage, but it also relies


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heavily on tat because students would tat all the scaledegrees inected by modal mixture. This kind of interconnection

between taxonomy levels is not uncommon.A more complex activity within the appl stage would entail

asking students to identify pre-dominant seventh chords within alonger harmonic progression, one that included nested TPDDTprogressions, e.g., iiv7Viii7V i. In this progression, the iv7ispart of the rst TPDDT, which prolongs the initial tonic. The ii7,on the other hand, is the structural pre-dominant of the phrase.33Understanding both of these chords as pre-dominant sevenths thathave different contexts, and thus different meanings, within thephrase would fall within the applstage of our taxonomy.

Dictation is another common tool for the appl stage of ourtaxonomy because it involves translating an aural stimulus (oneform of information) to a written conguration (a different formof the same information). Thus, the typical harmonic dictationexercises used in aural skills classes, in which students write outervoices, Roman numerals and gures of a performed progressionare instances of applknowledge.

ipris a high-order learning stage in which students build

facility by spontaneously creating musical utterances that featuretheir new knowledge, in this case the new harmonic category ofpre-dominant seventh chords. For this stage to be productive,students need clear constraints on their improvised compositionsso that they focus on the topic at hand and so that the teacher canknow for certain that they are pre-planning their work and not

just haphazardly coming upon a possible solution. For instance, ateacher could ask a student to improvise a four-chord arpeggiated

progression that includes a pre-dominant seventh chord and thatends with a half cadence. These specic directions will lead to betterresults compared to more general directions, such as, include apredominant-seventh chord in an improvised phrase.

One improvisation exercise that is very effective, which studentsenjoy because they can see the real-world relevance of the endeavor,is to ask for improvised bass lines to a given melody. The melodyitself provides the necessary constraints to the creative process,

with its dened cadence points, established harmonic rhythm, and33 Laitz would refer to the opening TPDDT progression at the

beginning of this phrase as an embedded phrase model, whichprolongs the tonic before the structural pre-dominant (ii7) and dominant(V) arrives. See Laitz, Th cplt ma, 25154.


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a sketch of harmonic options. For example, if students were askedto improvise a bass line to the melody in Example 4(g), they wouldrst need to know that there are two cadences (an IAC in m. 4 and aPAC in m. 8), that the harmonic rhythm is likely to be one-chord permeasure, and that the melody traverses a predictable TPDDTprogression. When rst attempting improvisatory exercises likethis one, it is useful to allow students time to analyze the melodyand write out their own framework, such as identifying locationsof tonic, predominant, and dominant structural harmonies. Once aharmonic framework is agreed upon by the class, the teacher cansing the melody as all students try out their improvised bass linessimultaneously. While everyone is busy improvising, students feel

less self-conscious about their individual attempts, and all of theimprovisations are likely to sound consonant with one anotherdue to the shared framework. After several run-throughs, it can beuseful to have the class sing the melody and call upon individualsto improvise a bass line, which allows students to share theiraccomplishments.

The last step of our taxonomy is the alat stage, in whichstudents examine and judge their own creative output. A goodevaluative exercise is to notate on the board some of the improvised

bass lines just performed by the students and to discuss theirqualities. Example 4(h) compares two possible bass lines. Whereasthe rst bass line conforms to harmonic expectations and syntax, itis repetitive and the downbeats in mm. 23 and mm. 67 introduceparallel octaves between the bass and melody. In the secondimprovisation, the student implies an inverted dominant in m. 3,creating a smoother, more melodic bass line. Also, the increasedrhythmic activity in the consequent phrase avoids the parallels,

helps build momentum towards the PAC, and incorporates arhythmic motive from the antecedent. By evaluating these options,students will be better prepared to improve their next attempts,which will be informed by the harmonic, melodic, and rhythmicconsiderations deliberated upon at the alatstage.

In summary, we have provided examples of both melodic andharmonic activities that traverse the six stages of our taxonomy.Although you may nd these specic exercises helpful in your

classroom, it is hoped that the reader will extrapolate from them tocreate ones own activities according to the taxonomy. Put anotherway, we hope the reader aspires to the later stages of learning,

beyond recognition and imitation, and appl, pr, andalatnew exercises uniquely suited to theirteaching needs.


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post-tonalapplIcatIonsofthetaxonomy

The lag between the mind and the ear (or visual vs. aural learning) is most pronounced with post-tonal repertoire, which

many students nd challenging to perform as the resources andtools from their tonal aural-skills classes become less relevant.34Oneof the objectives in our post-tonal aural-skills course is to providestudents with strategies to better familiarize them with 20th-centurymusic and techniques. An effective way to accomplish this goal isto use repeated pitch patterns. These exercises are designed to leadstudents from the familiar (diatonicism) toward the unfamiliar(post-tonal music) in a gradual and systematic fashion.35In addition,

the pitch patterns include sight-singing, transcribing melodies,detecting pitch errors, and improvising melodic fragments.

34 To cite just one example, Karpinskis methodology in hismaalr ear Tra a sht sassumes a four-semester tonal sequenceand does not address post-tonal music.

35 This procedure of starting from a diatonic melody andincrementally changing pitches to create extended chromatic and

then atonal patterns is similar to a technique used in Ronald Herder,Tal/Atal: Prr ear Tra, s a dtat st dat, chrat a Atal m(New York: Continuo Music Press,Inc., 1973).Although the concept of using short pitch patterns thatprogress gradually from the familiar to the less familiar is the same,the conceptual reasoning behind the transformations from one patternto the next is very different. Herders pedagogy is founded on isolatedintervallic relationships, (e.g., he organizes his exercises from smallintervals to large ones), and he recommends deriving dissonances from

projected consonances. In contrast, our transformations are designedto encourage melodic chunking, pitch-class set identication andmanipulation, and the use of anchor pitches. Another distinction isthat Herder begins with a tonal excerpt from music literature and thenbreaks down its diatonicism, while we start with a diatonic patternand move toward the post-tonal excerpt from the literature.


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(a)

(b) Bla Bartk, From the Island of Bali, Mikrokosmosvol. 4, no. 109

?

8

#1

.

?

#2 .

?

#3

.

?

#4

.

?

#5

.

?

#6

.

#7

#8

&

?

8

8

109

Andante,e

.

.

.

j

J

&

?

.

.

.

J

.

&

?

4

4

J

J

J

J

.

J

.

f

p, dolce

Example 5. Pitch pattern exercise

This exercise was designed for a fourth-semester or upper-levelundergraduate course solely devoted to post-tonal music. The goal

of the lesson plan is to help students sing Bartks From the Islandof Bali, which appears in the fourth volume ofmkrk, givenin Example 5(b). Without question, the large leaps, non-functionalmelodic design, and the dissonant clashes between the right andleft hands are challenging to sight-sing. Students are given the


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seven brief pitch patterns shown in Example 5(a). Once again,each successive melody is slightly altered, and through a processof incremental changes the rst pitch pattern gradually morphsinto the opening of Bartks piece. In other words, the repeated

pitch patterns are designed to make the challenge of sight-singingpost-tonal music less daunting by leading a student from thefamiliar (tonal) toward the unfamiliar (post-tonal) in a gradual andsystematic fashion. Below is a detailed discussion of each pitchpattern of Example 5(a) and how it relates to our new taxonomy.

Pitch Pattern #1

The rst pitch pattern is a straightforward, diatonic melodythat begins on scale-degree 5of A minor and descends by stepto the leading tone before concluding on the tonic.

We start diatonically to build associations from familiarterritory.

Pitch Patterns #2 and #3

The lowest two stages of our taxonomyrzandtatoccur when students recall details from previousmelodies and sing the new pitch patterns.

Pitch Pattern #4 This pitch pattern includes a tritone (D4/G#3), which is a

structural element of the piece. Our third learning stage, ptalz, occurs when we

highlight the presence of the tritone (ic6) and the [016] trichord(D4, A3, G#3).

Pitch Pattern #5

This melody, which begins with a chromatic pitch (D#4) and isless tonally stable, is saturated with [016] trichords.

cptalzand applare invoked even more when the studentsare asked to identify and discuss instances of [016].

Pitch Pattern #6

This pitch pattern is the opening phrase for Bartks From theIsland of Bali.

A different kind of ptalzoccurs here with an

orthography switch; D#4 is now notated as Eb4.Although the sixth pitch pattern is the last exercise given, we

now ask the students to appl and pr, thus reaching theupper-level stages of our taxonomy. To begin the applatstage,


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we invite students to transpose the nal pitch pattern by a semitone(T1) and a perfect fourth (T5); these transposition levels are derivedfrom the intervals within the [016] collection, which helps studentsmove from ptalzat toward applat. We also requirestudents to invert this pitch pattern about its initial pitch. Inanticipation of Bartks passage, we have our students transposethe inverted form down four semitones.

Before the students are exposed to Bartks score, we ask thestudents to pr their own pitch patterns, requiring them touse their own versions of [016]. Some students will sing the invertedform while others favor transposed forms of the original. Andsome students will improvise a version of [016] that begins with

the middle pitch of the collection, rather than singing high to lowor low to high. The blank staves of Example 5(a) are provided forstudents to dictate some of their peers improvised melodies. Oncethe students evaluate their own dictations and improvisations,the students then sing The Island of Bali, tying together all thelearning stages by performing the music.

We would like to mention a few points about this particularpitch pattern exercise as it relates to Bartks melody. Notice thatthe opening motive consists of a [0167] tetrachord that highlights aperfect fourth (AD) with neighboring notes. Thus, one may hearthe D as the pitch center for this gesture with AD functioningas scale-degree 5 to 1. (Compare this to the A centricity of the sixpitch patterns presented in Example 5.) We can certainly create adifferent set of pitch patterns that lead toward the left-hand Bartkmelody with D as the pitch center. It can also be argued that thetonal references within Bartks melody stem from the octatoniccollection that is used to organize the pitch material. Thus, another

repeated pitch pattern to consider here is the octatonic scale. As willbe shown in the next example, these repeated pitch patterns can bebased on collections other than diatonic, major and minor scales.


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Once the students were relatively comfortable with exercises thatcontain six or seven pitch patterns, we provided more complicatedversions. Example 7 offers a more complex pitch pattern, and thecomposition from which the exercise is derived is shown in Example7(b). In this exercise, the number of pitch patterns has increased to16. In addition, some of the two-measure motives are left blank fordictation or improvisation, and we use completed pitch patterns forerror detection. This particular pitch pattern exercise is restrictedto major and minor seconds and perfect fourths.36In addition to anintervallic approach to this exercise, we encourage the students tofocus on a number of strategies that might help them sing these post-tonal pitch patterns, such as anchor pitches, a diatonic background

(in this case E major), and compound melodic lines.37

After a few weeks of using our pitch patterns we have foundthat our students were able to quickly advance through an entireexercise. The advantage to using a larger number of pitch patterns(16, 17, even 18) is to give ahstudent within a single class sessionan opportunity to sing or improvise a brief motive in front of their

36 The intervallic impetus for this pitch pattern follows the

pedagogical framework of Lars Edlund,m n: st RaAtal ml(Stockholm: Nordiska musikfrlaget, 1964). At thebeginning of his text, he restricts his focus to major and minor secondsand the perfect fourth. He then introduces the perfect fth followed bymajor and minor thirds, the tritone, minor and major sixths, minor andmajor sevenths, concluding with compound intervals.

37 In addition to an intervallic-based approach and a diatonicframework to learn post-tonal music, Michael Rogers also suggestsusing trichords, recurrent nontonal patterns and modes. Accordingto Rogers, the recurrent nontonal patterns can be memorized,transformed, varied, inverted, displaced by an octave, elided, andcombined in limitless ways to cover most atonal possibilities (140). SeeRogers, Tah Apprah m Thr, 13843. William Thomson,Aa m Ra(Belmont, CA: Wadsworth Publishing Company,Inc., 1969) advocates the need for referring pitches to a contextual[tonal] frameeither a frame that is made explicit by the patterns ofthe melody itself or a frame that is imposed by the reader when themelody does not clearly project its own. (x) For Thomson, using aframework approach to sight sing chromatic and modulating melodiesis more helpful than relying on an intervallic based approach. Thomsonsuggests that for atonal melodies where the tonal framework approach isnot the most appropriate, it is helpful to improvise your own set ofrelationships as a guide to accurate pitch recall. (160)


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peers. As a class, dictation and error detection can be successfullyand quickly implemented. We also found that the students enjoyedhaving the opportunity to improvise their own pitch patterns;oftentimes, the improvisations lead to spirited class discussionsabout what did or did not work. And the students were generallyexcited to nd out which piece each exercise was based on. Becauseof the repeated pitch patterns, the students were able to betterperform the trcomposition that was linked with each exercise.Overall, we were pleased with the engagement, the participation,and the amount and depth of learning that took place when weused these pitch-pattern exercises.

As is obvious from our examples in this essay, many of the

pieces from Bartksmkrkcan easily serve as the foundationfor a number of different pitch patterns. We have successfullyused many songs from Schoenbergs Bk th Ha gar;the post-tonal melodies found inm n; and the chromatic,atonal, and twelve-tone melodies found in the later chapters ofOttmansm r sht s. Designing pitch-pattern exercisesis a matter of identifying the key characteristics of a musicalpassage and composing different motivic and melodic patterns that

incrementally exploit those characteristics.It has been our experience that these pitch-pattern exercises,

both tonal and post-tonal, are effective because they include a lot ofimitation and recall of musical material. Consequently, students usethe lower end of our learning stagesrzand tatfor much of the exercise. Higher stages of learning are invokedonly for new musical events. This isolates the new issue, allowingstudents to focus their attention on ptalzatand applat

only for the new event. In sum, our use of recurrent pitch patternspromotes development of a variety of musical skills by traversingdeliberately through a well-planned progression of learning stages.


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conclusIon

In this article, we have introduced a taxonomy of learning forcollege music classes and demonstrated how it can be used to

design effective aural-skills exercises. We want to stress that thepitch-pattern exercises we describe above are not prescriptions ofwhat needs to happen in an aural skills class. Instead, we offer theseexercises as one possible way to implement and think critically andthoughtfully about our taxonomy. Or to put it another way, weoffer a music learning taxonomy as a pedagogical framework tohelp re-think and re-evaluate the learning process that unfolds in amusic class.

Having demonstrated how our taxonomy can be applied todesign in-class activities, we would also like to encourage somemore global interpretations. Our taxonomy can also be used topromote more in-depth learning for goals spanning a week, amodule or unit, and even an entire semester. We hope our approachwill help us, as instructors, to continually explore and evaluate oureducational goals.

Finally, though our revised taxonomy might be considered

as a pedagogical mold or a set of stair steps on a triangle to getfrom bottom to top, there is a great deal of exibility built into ourframework. We like to think of it as a teaching and learning lthat ends precisely where it beginsimagine the triangle shown inExample 1 wrapping around onto itself to create a kind of spiral.Because each student has his/her own individual strengths andweaknesses, we nd that we constantly traverse the differentstages at different times to address the many different needs of

our students. There is a continuous ebb and ow, which createsa dynamic means of assessing, teaching, evaluating, and, mostimportantly, enhancing student understanding and learning.


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Rifkin Stoecker Music Learning Taxonomy

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Transcript of Rifkin Stoecker Music Learning Taxonomy