Tonality Test – 1st Revision

My career clock is ticking. Before I leave the profession (in under 3 months!), I want to find answers to nagging questions. Can my students audiate and identify tonalities in pieces they’ve never heard before — not merely the tonalities of various series of patterns, or teacher-composed songs, or even great folk songs like “Go Down Moses”? Can students transfer their tonal audiation skills? Can they identify the tonality of complex, multifaceted works that, we hope, they’ll encounter later in life?

To answer these questions, I re-administered (and then re-wrote) my Tonality Test. You can find this revised version at the bottom of this post.

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Some Details About the Tonality Pre-Test Results

Back in September and October of 2023 — after students had heard and sung many songs and tonal patterns in major and minor, but before they had sung patterns in various series — they took the test as a pre-test. (You can find details about that original version here.) The most important descriptive statistic is that the obtained mean of 19.18 was very close to the chance score of 20 — exactly where I wanted it to be. The pre-test, in other words, did its job: It showed me that my students had no clue how to aurally discriminate between major and minor tonalities.

Back then, I wrote the following year-long goal:

Throughout the year, I’ll teach my tonal audiation exercises; then I’ll administer the test again; and finally I’ll revise it by removing the lousy items, those with poor discrimination values. I’ll also remove many of the 18th century items, especially most of the Handel excerpts, which I love, but seem to me now to be too much of a good thing.

Did things turn out that way? Keep reading to find out.

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Tonality Post-Test: Descriptive Statistics

During the third week in March, 2024, students (n = 172) in 4th, 5th, and 6th grades at the Stephen Decatur School in Philadelphia took the Tonality Test as a post-test.

Students filled in their answers using a google form shown, in part, in Figure 1.

FIGURE 1. Sample of the google test form

The obtained post-test mean was 29.2, very close the theoretical mean of 30. The obtained standard deviation was 4.57, greater than its theoretical counterpart (3.33). These numbers tell me that the original 40-item test was a bit too hard for its intended population (upper elementary students): too many kids scored between the chance score of 20 and the theoretical mean of 30; and not enough kids scored between 30 and 40 (the highest possible score).

In Figure 2, you’ll see information about each test item: the item’s number, name, difficulty level, discrimination value, tonality, and genre. Very easy items (those with difficulty levels of 90% or higher) are highlighted in blue; very difficult items (those with difficulty levels below 60% are highlighted in red).

FIGURE 2: Information about each item.

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Item Analysis: A Brief Tutorial

My two goals: shorten the test and simplify it. A handy way to kill those two birds with one stone is to eliminate some of the very difficult items.

If you look at the top row in Figure 2, you’ll see the initials Df and Ds. They stand for Item Difficulty and Item Discrimination. Let me give you a brief tutorial about what these terms mean and how I calculated the numbers in each column.

After students submitted their answers, I ordered their scores from lowest to highest; then I separated the lowest 27 percent and the highest 27 percent, a practice recommended by Robert Ebel in his book Measuring Educational Achievement (1965).  Twenty-seven percent of 172 is 46.4. In other words, I made use of 46 of the lowest google forms and 46 of the highest google forms, giving me 92 google forms in all to play with.

To calculate item difficulty, I did the following:

I added the number of correct responses from the lowest 27% to the number of correct responses from the highest 27%.  Then I divided that sum by the total number of google forms, in this case, 92.

The equation looks like this:

Let me show you how this works in real life. As an example, I’ll use a rejected item, Johann Christian Bach’s Concerto, Op. I. No. 6. In the high scoring group, 45 students answered the item correctly; in the low scoring group, 41 students answered the item correctly.  I added 45 to 41, got 86; then I divided 86 by 92, the total number of google forms I investigated.  The result was .93, meaning that the J. C. Bach excerpt is a very easy test item.

With the numbers plugged in, the equation looks like this:

Calculating item discrimination was a bit trickier. First, I subtracted the low scorers who got it right (41) from the high scorers who got it right (45), and then divided that number (4) by half the number of test papers I’m working with (46).  The result is .09, which means Item #1, though it’s a positively discriminating item, doesn’t show a clear distinction between the high and low achievers.

The equation looks like this:

With the number plugged in, the equation looks like this:

Some readers may catch that the formulas I use to calculate difficulty and discrimination are slightly different from those recommended by Gordon (2012) and Walters (2010), my esteemed professors at Temple University. They don’t follow the 27% rule. According to Ebel (1965), 27% is the best compromise between two contradictory ideals: You want the high scorers and low scorers to represent the sample as a whole; but you also want the two subgroups to be as different from each other as possible. If I were to use only small groups of low and high scorers, the number of test forms might be too small to represent the sample as a whole; if, on the other hand, I use all the test forms — the top and bottom 50% — the high and low scoring groups would not differ enough to offer up revealing data. The Goldilocks ideal, according to Ebel (1965, p. 349), is the top and bottom 27% because it “provides the best compromise between two desirable but inconsistent outcomes: 1) to make the extreme groups as large as possible, and 2) to make the extreme groups as different as possible.”¹

Anyway, item discrimination basically works like this: If most of the high scoring kids get an item right, while most low scoring students get it wrong, that’s a good thing. It means the test item is doing what it’s supposed to do — draw a line between those students who “get” tonality and those who don’t. On the other hand, if most of the high scoring students get an item wrong, while most of the low scoring kids get that same item right, that spells trouble: The test item is not doing one of its main jobs, which is to differentiate between high and low achievers.

I decided ahead of time that if test items fall in the range of difficulty from 50 percent to 90 percent, I will retain them.  If they fall outside that range, I’ll discard them (or at least most of them).  And I wanted only positively discriminating items with a value of at least .20, with most of the items greater than .40. 

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If you look at the bottom of Figure 2, you’ll see the 6 items I removed from the revised version of the test. I suppose I could have kept the J.C.Bach Concerto item, and I might have (despite its low discrimination value) if I had another easy instrumental chamber example in minor. But no such luck. Let me say that items on the extreme ends of difficulty (very easy or very hard) often have low discrimination values.

TO BE CONTINUED…

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Tonality Test – 1st Revision

1. Beethoven – Symphony No. 6, Pastoral, 1st mvmt

2. Haydn – Symphony No. 95, III. Menuet

3. Aviva Duo – B’Arvot Hanegev

4. Vivaldi – Four Seasons, “Spring” – 1st mvmt

5. Handel – Israel in Egypt, He Smote All the First-born of Egypt

6. Haydn – String Quartet Op. 76_3, – 2nd mvnt.

7. Mendelssohn – Piano Trio No. 1, Op. 49 Ist mvmt

8. Southern Jubillee Singers – Above My Head, I Hear The Music In The Air

9. Tchaikovsky_ Violin Concerto In D, 3rd mvmt

10. Bach- Orchestral Suite No.2, Rondeau

11. The Armstrong Family – How Can I Keep from Singing

12. Bach – Violin Partita #3, Gavotte En Rondo

13. Alfred Deller – Hey, Ho, The Wind and the Rain

14. Mozart – Requiem Mass, III. Dies Irae

15. Beethoven – Ecossaises, WoO 83

16. Chasidic Cappella – Modim Anachnu Loch

17. Bach – Concerto No. 2, BWV 593_ Ist mvmt

18. The Weavers – Yerakina

19. Mendelssohn – Song without words. 67, No. 2 (Arr. Violin_Piano)

20. Sweet Honey in the Rock – Silvie

21. Mozart – Symphony No. 25, 1st mvmt

22. John Denver – Matthew

23. Nielsen, Carl – Quintet for Winds, Op. 43, 4th mvmt

24. Handel_ Parnasso In Festa, Del Nume Lieo

25. Telemann – St Mark Passion, Lieblich’s Wort aus Jesu Munde

26. Chopin – Prelude #10 (performed by my piano teacher, Marian Filar)

27. Buddy Holly – Everyday

28. Vivaldi – Concerto, RV 108 for Guitar, Bassoon, and Strings, 3rd. mvmt

29. Chad Mitchell Trio – Dona Dona

30. Herb Alpert – Zorba the Greek

31. Edelweiss from The Sound of Music (Performed by members of the Vienna Boys Choir)

32. Handel – Imeneo – Consolami mio bene

33. Bach – Brandenburg Concerto #4, 1st mvmt.

34. Beethoven – Symphony No. 5, Ist mvmt.

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1. To be fair, Ebel didn’t come up with the 27% rule. Truman L. Kelley first introduced it in his 1939 (!) article “The Selection of Upper and Lower Groups for the Validation of Test Items.” ↩︎

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Ebel, Robert L. 1965. Measuring Educational Achievement. Englewood Cliffs, New Jersey: Prentice Hall.

Gordon, Edwin. 2012. Learning Sequences in Music: Skill, Content, and Patterns. Chicago: GIA. 

Kelley, T. L. 1939. “The selection of upper and lower groups for the validation of test items.” Journal of Educational Psychology, 30(1), 17–24

Walters, Darrel L.  2010.  A concise guide to assessing skill and knowledge. Chicago: GIA.

Why Rote Songs Are Not Enough

            In his notorious debate with Gordon, Bennett Reimer (1994) was right, sort of. He chastised Gordon for focusing too heavily on songs and patterns to the almost total exclusion of—how shall I describe them?—masterpieces. He was wrong to suggest that MLT must work this way, but I think he discerned a disturbing trend. All MLTers agree that functional, contextual patterns are the indispensible “part” of whole-part-whole. But rote songs? In at least one respect, I’m different from my MLT colleagues. I never drank the rote song Kool-Aid.

            Darrel Walters described functional tonal and rhythm patterns as the “vitamins” of musical content. His comparison is apt as far as it goes, but let’s push it along. Patterns are vitamin pills; Beethoven Symphonies are nutritious meals, exquisitely prepared. What about teacher-composed songs and chants? I think of them as meal replacement bars. They provide temporary nutrition, vitamins, fiber; they’re better than nothing, and they fill you up on long road trips. But human-made, synthesized nutrition bars cannot, in the long term, replace real, natural food. Let’s not pretend they can.

            And the same is true for teacher-composed songs.

            I don’t believe my students have adequately learned to audiate minor tonality just because they’ve learned functional patterns along with a few rinky-dink rote songs in the minor mode I made up in my car while driving to work. 

            Like this one …

 

   Tchaikovsky was one of the greatest melodists of all time. But you’d never know it by listening to my bastardization of his melody from Swan Lake. So that you may compare the two, here is Tchaikovsky’s melody in its original form:

            On the plus side, my tune checks all the boxes: The range (from C sharp to B natural) is narrow enough that kindergarten through 2nd grade children can sing the song easily while they rock front and back; the phrase structure is a serviceable parallel period in the minor mode.

            And what was my “inspiration”? I needed a front-and-back rocking song in minor/triple. It’s that simple. So I thought about it for 5 minutes, remembered this tune by Tchaikovsky, simplified it (by removing the exquisite hemiola rhythms in the woodwinds), threw in some descriptive lyrics, and there you have it. Yes, the “Front and Back” song serves educational purposes—tonal, metric, kinesthetic—and serves them well. And yet for all that, my tune (in contrast to Tchaikovsky’s) is rinky-dink rubbish.

TRADITIONAL MLTer: I’m assuming, Eric, that you’ve composed many songs for your students, especially those in Kindergarten. Do you really want to call your compositions “rinky-dink?” Why put yourself down that way? And why are you so skeptical about the value of rote songs? Simply sing the “Front and Back” song with students while engaging with them in the movement activity; then teach functional patterns in the context of minor, and then return to the rote song by asking students to sing the resting tone. There’s your whole-part-whole process. Students are audiating the minor mode. A job well done. Finished.

            To which I respond with a full-throated no! My students have not arrived at the final whole, just because they can name the tonality of my song or sing its resting tone. Despite the MLT predilection to isolate musical elements from each other, tonality does not exist in a vacuum. How we audiate patterns in major tonality (in Beethoven’s Pastoral Symphony, for instance) is pushed and pulled by the musical elements that surround those patterns.

            Let me show you what I mean. What follows is a deep dive into the development section of Beethoven’s Pastoral Symphony, 1st movement. Before we go toe to toe with Beethoven, I want to clarify a few things: We can’t expect our pre-school or lower elementary students to understand a Beethoven Symphony with the same depth that high school or college students can bring to it; but surely, we don’t expect our students to remain at the acculturation stage of preparatory audiation. As students emerge from babble, and understand music better, they need greater musical “nourishment” than rote songs and patterns can provide. In my units on Genre, tempo, vocal register, and Dynamics, you can find dozens of sound files and lessons that take elementary students far beyond acculturation. Eventually—as you’ll see in the next section—students will be able to audiate complex musical ambiguities not found in short, monophonic rote songs.

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Bernstein Analyzes Beethoven

            In his lecture series, The Unanswered Question, Bernstein (1976) discussed the following 24-bar passage from Beethoven’s Pastoral Symphony, 1st movement, mm. 151-174.

FIGURE 1. Beethoven’s Pastoral Symphony, 1st movement, measure 151-174

            No one can explain musical ambiguity in Beethoven as well as Bernstein, so I will yield the floor to him (with a few abridgments). Before I let Bernstein go on at length, I must mention two things: First, Bernstein’s descriptions, though fascinating, are a bit hard to follow, so I’ve created Tables 1 and 2 below to help clarify his analysis. Second, in his discussion, Bernstein refers to the following repetitive motive (shown in Figure 2) as the “jaunty” motive.

FIGURE 2: The “Jaunty” Motive

   Bernstein (1976, pp. 179-84) wrote:

What are we to say of the long strings of unvaried repetition [in this] development section? The profuse repetition could be a metaphor for the profuse repetition of Nature herself, the infinite reduplication of species. But [this is] not the kind of metaphor we are seeking. What is the musical metaphor to be discovered in that famous long passage of literal repeats? We will look at measures 151-174, the first 24 bars in a larger 92 bar structure. What is their metaphorical meaning—not in terms of jonquils and daisies, but of notes and rhythms? We know that the notes come from the “jaunty” motive, transposed to B-flat major, and played 4 times by the 1st violins. This is then literally repeated by the 2nd violins, doubled by [an oboe or flute] an octave higher. That makes 8 bars. The 8-bar segment is repeated and re-repeated with the same alternations of 1st violins as against 2nd violins plus a high woodwind; and it’s played 3 times in all—3 times 8 bars making 24 bars. That’s one way of looking at this episode, from an orchestral point of view. We perceive one of Beethoven’s intentions via his instrumental texture, the alternating high and low registers, and the 24-bar crescendo to a climax.

    In Table 1, I show what the 24 bars reveal from an orchestral point of view:

Table 1.

 

            Bernstein (1976, pp. 184-86) goes on to say that listeners may hear (audiate, in other words) this same passage in a completely different way.

Now let’s view the same 24 bars harmonically, and we find a very different story. Four bars of B-flat in the 1st violins, as before, repeated as before in the 2nd violins with the higher woodwind octave. Again [we hear] the 1st violins—that’s now 12 bars. And now a sudden switch of key to D major (bar 163) for 12 more bars. We’re still following the same instrumental pattern, mind you, but in this new key of D, which is maintained for 2 more repeats, finally [we arrive at the] climax. This has been a totally different construction of those same 24 bars—2 x 12: twelve bars in B-flat and 12 bars in D. Not at all 3 x 8, as we saw at first. In other words, there are 2 different substructures functioning simultaneously within the span of 24 bars. One substructure is the orchestral texture, 3 x 8; and the other is the harmonic rhythm, 2 x 12. And the simultaneous contradiction of the two creates one glorious ambiguity…out of what seemed to be merely 24 stupefying repetitions.

 

            In Table 2 below, I offer a side-by-side description of the 2 ways to audiate Beethoven’s 24-bar passage.

Table 2:

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Audiating Both/And and Not Merely Either/Or

            What did Bernstein and Beethoven reveal? Two things. First, a single phrase of music may embody different phrase structures. And second (and even more important for this discussion), conflicting musical elements can be equally true, and mutually supportive. Could it be that great works of music, works that have moved people across cultures and centuries, hold our interest because of the push and pull of built-in ambiguities? I believe so. But, I hear you asking, what about works of music that do not have conflicting elements? Can a single element in a piece of music be ambiguous? Can a monophonic melody be, for instance, tonally ambiguous?

Let’s have some fun with the “Star-Spangled Banner.” Is the opening melody (minus the harmony) in the major or lydian mode?

        Yes, I concede: You can reasonably audiate this melody in either major or lydian. But notice that the ambiguity in this case is either/or. Never would a musician audiate the “Star-Spangled Banner” in major and lydian at the same time. You choose one tonality to audiate, reject the other, and stick with your choice.

            In contrast, the Bernstein/Beethoven example above is a both/and ambiguity, and by that I mean the following: 1) orchestration and keyality are equally valid ways to understand Beethoven’s phrase structure; 2) those two elements, though they seem to conflict, are interactive; and 3) their interaction is aesthetically gripping precisely because they vie for our attention.

            How does all this fit with Gordon’s stages of audiation? At Gordon’s 4th stage of audiation, we reassess our first impressions of the tonality, keyality, meter, and form of a piece of music—but when we do so, we focus on one element at a time. At stage 5, we compare one piece with another, but we still focus on a single element, tonality perhaps. One glaring omission in Gordon’s theories is that he never accounted for musical elements working in tandem. Could there be a stage of audiation, one that Gordon did not consider, in which we audiate two or more elements that conflict with each other, but are equally compelling and, on a deep level, mutually supportive (as in the Beethoven example above)? I think so, and I’ll write more about it soon in a future blog post: Form, Flux, and a New Stage of Audiation.)

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Conclusion

           And now I can loop back around to why rote songs are not enough. Rote songs serve music education in the short-term (like a protein meal-replacement bar), but they’re inadequate for our students’ musical “nutrition” in the long-term. It’s not just because Beethoven’s Pastoral Symphony is a masterpiece, while Bluestine’s “Front and Back” song is a far cry from one. Beethoven surrounded his major tonality with keyality, form, timbre, texture, phrasing, dynamics, rhythm patterns, tempo, and meter. And those elements may conflict with each other, the way orchestration and harmonic rhythm were in conflict in the passage Bernstein analyzed; and such conflict—orchestration telling us one thing, harmonic rhythm telling us something else— is what makes a piece worthy of serious study.

            In teacher-composed songs there are rarely either/or conflicts, and never both/and conflicts. My composed songs—typically short, monophonic melodies—feature musical elements that neither contradict each other, nor develop over long periods of time. Under these conditions (and restrictions), conflicts and ambiguities simply cannot arise.

            And if students never grapple with musical ambiguities, they will never deeply understand the final whole of whole-part-whole. What’s more, our students will not learn to understand pieces beyond Stage 4 and 5 of audiation. Instead, they will be trapped in a musical world where elements develop in isolation, never in tandem. To sum up, if we expose our students to nothing but patterns and short songs, we stunt their musical growth, and forfeit the key music education goal of teaching students to audiate multifaceted works.

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Bernstein, L.  (1976).  The unanswered question:  Six talks at Harvard.  Cambridge, Massachusetts:  Harvard University Press.

Reimer, Bennett and Gordon, Edwin. (1994).  “The Reimer/Gordon Debate on Music Learning:  Complementary or Contradictory Views?”  MENC National Biennial In-service Conference in Cincinnati, Ohio.  Audio Tape Stock #3004, ISBN 1-56545-052-3

A Brief Introduction to Beat-Function Syllables

A colleague recently asked me about “Gordon syllables.”

“I get that they’re beat-function syllables,” she said. “But how do you perform them? What do they actually sound like?”

Here is a brief audio clip during which I perform rhythm patterns in duple and triple meters with beat-function syllables. I don’t go into much explanation about how they work. I mostly just perform.

In the last few years, MLTers have uploaded many excellent videos on Youtube showing how to perform patterns with these syllables. Each MLTer seems to have their own performing style. I first heard these syllables performed back in 1986 by Roger Dean, former chair of the Music Education Department of Temple University; and no one, in my opinion, has ever performed patterns with rhythm syllables as musically! At any rate, here is my way of performing patterns with beat-function syllables.

Tonality Test – Original Version

It’s been a busy first month of school. What can I do to unwind, relax, clear my head?  The answer is all too clear: Write a tonality test.  It’s finished, at least in its initial form.  In final form, the test will be much shorter.  (It’s 18 minutes long, even with no verbal instructions.)

I constructed this test to see how well students can aurally discriminate between major and minor tonalities in pieces they have not heard before. I call it the “original” version, but that’s not quite accurate. I edited most of the sound files a few years ago, and was all set to administer the test to students back in early 2020 when Covid struck. The early draft of the test was 23 minutes long — too long for upper-elementary students to sit through with full attention. I spent several hours today editing the musical examples, shaving off roughly 5 seconds from each test item. I also replaced a few items that seemed questionable (a folk song in minor that featured too many dorian touches), or redundant (a Handel chorus stylistically similar to another choral test item.)

Please take a moment to listen to each example.  I’ve included commentary after the music, and I intend to write more extensive commentary after I wake up from a long, deep sleep.

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1 Bach, Johann Christian – Concerto, Op. I. No. 6

2 Hamilton – “My Shot”

3 Haydn – Symphony No. 95, III. Minuet

4 Scarlatti – Sonata In C, Longo 104

5 Chad Mitchell Trio – “Dona Dona”

6 Tchaikovsky – Violin Concerto In D, 3rd mvmt

7 Chasidic Cappella – Modim Anachnu Loch

8 Vivaldi – 4 Seasons, “Spring” – 1st mvmt

9 Sweet Honey in the Rock – “Silvie”

10 Bach- Orchestral Suite No.2, Rondeau

11 Beethoven – Ecossaises, WoO 83

12 The Weavers – “Yerakina”

13 Bach – Concerto No. 2, BWV 593_ Ist mvmt

14 Handel – Imeneo – “Consolami mio bene”

15 Nielsen, Carl – Quintet for Winds, Op. 43, 4th mvmt

16 Gould, Morton – Holocaust Miniseries 1978 (opening theme)

17 Handel – Parnasso In Festa, “Del Nume Lieo”

18 Bach – Brandenburg Concerto #4, 1st mvmt.

19 Aviva Duo – “B’Arvot Hanegev”

20 Beethoven – Symphony No. 6, “Pastoral”, 1st mvmt

21 Mozart – Requiem Mass, III. Dies Irae

22 Haydn – String Quartet Op. 76_3, – 2nd mvnt.

23 Telemann – St Mark Passion – “Lieblich’s Wort aus Jesu Munde”

24 Mendelssohn – Piano Trio No. 1, 1st mvmt

25 Bach – Violin Partita #3, Gavotte En Rondo

26 Handel – Israel in Egypt, “He Smote All the First-born of Egypt”

27 Herb Alpert – “Zorba the Greek”

28 Alfred Deller – “Hey, Ho, the wind and the rain”

29 Handel: Keyboard Suite #3, Presto

30 “Edelweiss” from The Sound of Music

31 Southern Jubillee Singers – “Above My Head, I Hear The Music In The Air”

32 Mozart – Symphony No. 25, 1st mvmt

33 The Armstrong Family – “How Can I Keep from Singing”

34 Handel – Belshazzar, Acts 3 “And War and Slavery Be No More”

35 Vivaldi – Concerto, RV 108 for Guitar, Bassoon, String Orchestra, 3rd. mvmt

36 John Denver – “Matthew”

37 Mendelssohn – Song without words. 67, No. 2 (Arr. Violin_Piano)

38 Chopin – Prelude #10

39 Buddy Holly – “Everyday”

40 Beethoven – Symphony No. 5, 1st mvmt.

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You’ll notice in Figure 1 below that each test item has 2 options: Major tonality or minor tonality. 

FIGURE 1.

I rigged it so that if students pattern-mark (major… major… major, or minor… minor… minor, or major… minor… major… minor… major, etc.), they would score a chance score of 20. If you take a look at Figure 2 below, you’ll see 20 items in major and 20 items in minor. I never placed more than 2 major or 2 minor items back to back, and I deliberately ordered the items so the genres would continually change throughout the test. You won’t see or hear, for instance, two folk songs in a row.

FIGURE 2.

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About the Music

The test contains—I hope you’ll agree—music of great stylistic variety; but achieving that wasn’t easy!  I tried to choose items that were musically engaging in their meter, tempo, dynamics, style, articulation, timbre, and texture.  But quite a lot of music was closed off to me: Much Renaissance and early Baroque music is sort of major-ish, but the harmonies dance around the resting tone without that push-to-the-dominant quality.

Let me go into this a bit.  I’m not knocking the importance of teaching kids to audiate other modes; I’m just saying that major and minor are qualitatively different from other modes.  In dorian, for instance, you have the tonic, subtonic, and major subdominant with its raised 6th; but somehow… there’s no push to arrive at 3rd base, which, in turn, urges you on to home plate. And it’s precisely this lead up to the dominant, not the dominant-tonic resolution, that sets the major and minor modes apart from the others.

Anyway, where was I? Oh yes, much music was closed off to me. Medieval?  Renaissance?  Forget about it.  My test items start with the late Baroque—with Bach, Handel, Telemann, Vivaldi, and Scarlatti. And even with these guys, I faced the scourge of every tonality test designer: the dreaded Picardy Third! The test is, to a great extent, an aural cross-section of the 18th century (with too much Handel, as I said above).

By the time we get into the 19th century, passed Haydn, Mozart, and Beethoven, new problems creep in.  True, the Chopin prelude and the Mendelssohn Song Without Words are explicitly in the minor mode.  But so much of 19th century music features dense chromaticism and frequent modulations. 

Let me interrupt myself again just to offer this opinion that when you arrange Chopin’s incomparably gorgeous piano music for other instruments, the results are always terrible.  His melodies suggest a bel canto singer, or a violin, or often a cello, but when you transcribe his music — in short, when you make explicit what’s implicit — you only butcher it.  Mendelssohn is the opposite.  His piano writing, to me, always cries out to be transcribed for chamber instruments.  So I hope this violin/piano version of his F sharp minor Song Without Words (item #37) will not offend anyone.

But getting back to the test… What’s a test writer to do with all these restrictions?  Seek out folk music, naturally.  Jewish, African American, Greek.  I included some great stuff, music I’ve listened to and been devoted to my whole life.

These musical excerpts go a long way in dispelling the myth that music in the major mode is always fast and happy, and music in the minor mode is always sluggish and sad. I deliberately included buoyant minor mode music (such as the Vivaldi item #35), and slow, heart-rending major mode music (such as items 28 and 33).

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The purpose of this test is to see how well students can aurally discriminate between major and minor tonalities in pieces they have not heard before. I have already administered the test to students (n = 299) as a pre-test.

FIGURE 3.

As you can see in Figure 3, the obtained mean of 19.18 is very close to the chance score of 20 — exactly where I want it to be!

My plan: Throughout the year, I’ll teach my tonal audiation exercises; then I’ll administer the test again; and finally I’ll revise it by removing the lousy items, those with poor discrimination values. I’ll also remove many of the 18th century items, especially most of the Handel excerpts, which I love, but seem to me now to be too much of a good thing.

Please check back in around May 2024 for more data.

A Disorganized Rant About Music Literacy

I’m reading a very interesting facebook thread right now about music literacy. Here is my response to some of the ideas on that thread.

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Dr. Gordon wasn’t perfect. He made several notable mistakes, usually when he swung too far in the opposite direction of a problem. Teaching students to recognize symbols, and calling that reading, is a problem; naming notes by use of gimmicks such as “Every good boy does fine,” and calling that reading, is a problem. Gordon sought to fix these deficiencies in music education, which he described as “decoding” notation, but his solutions, in my opinion, were less than stellar.

By the way, Gordon was wrong in calling note-naming “decoding.” Decoding is a good thing; decoding is the same as notational audiation. What Gordon objected to was recoding, which Goodman (1968) described as “sounding out” print, but not attending to meaning. Gordon also objected to symbolic recognition — merely naming symbols but not sounding out or understanding their meaning. I agree with these sentiments. But Gordon should not have used the word decoding: When you decode a coded message, you understand it; and when you paraphrase the meaning of a coded message, you understand it deeply.

Decoding is the good guy; symbolic recognition is the bad guy.

And what about recoding — the ability to convert notation to sound? Recoding is a good guy too, but it’s incomplete. Recoding notation — “sounding it out,” in other words — means nothing if students don’t understand the syntax of what they’re reading. Recoding is like reliability in test design: it’s necessary but not sufficient.

The psycholinguist Frank Smith (1994) pointed out something similar in language reading: just being able to sound out words, or recognize whole words, does not mean you understand the word, the sentence, the paragraph, the piece. But in his denunciation of phonics, Smith went too far. More than 100 experimental, randomized-controlled studies over the past 100 years have shown that phonics is indispensable for beginning readers. Chall’s (1996a) exhaustive book Learning to Read: the Great Debate, in which she reviewed 87 studies from 1912 to 1967, should have settled the matter. Her 1996 updated edition of that book should really have settled the matter. The meta-analysis put out by the National Reading Panel (2000) should have put the final nail in the whole-word/whole language coffin. But no. In every generation, people keep reinventing anti-phonics nonsense.

I’m not saying phonics is enough. In her brilliant book Stages of Reading Development, Chall (1996b) theorized that phonics is both a level of learning (with many sub-levels) and one of 6 stages of reading development. Her theory, as I see it, may be applied to music reading as well: symbolic association is a level of learning and a stage of music reading development.

Composite synthesis, by the way, is not a level of learning, but is, in my opinion, a stage of music reading development. In my book (2000), I think I got that wrong. But that’s for another blogpost.

I once asked Dr. Gordon who he thought his most important influences were, outside of music, when he constructed his skill-learning sequence. He unhesitatingly said that the two thinkers who influenced his skill-learning sequence most were Frank Smith and Robert Gagne — which struck me as odd because Frank Smith trashed the very idea of sequential learning. I resisted the temptation at that moment to say to Gordon that his thinking was at its best when he learned from Gagne, and at its worst when he followed Frank Smith down the rabbit hole of anti-phonics.

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Do We “Bring Meaning” To Notation?

Frank Smith and Kenneth Goodman, two prominent psycholinguists in the 1970s and 1980s, held the wrong-headed opinion that we “bring meaning” to notation — an idea MLTers are saddled with to this day. In a New York Times Interview from 1973, journalist Edward Fiske asked Goodman the following question: If the sentence is “The boy jumped on the pony and rode off,” and a student reads it as “The boy jumped on the horse and rode off,” should the teacher correct him? No, the teacher should not correct him, according to Goodman. The student brought basically the correct meaning to the sentence. And that’s good enough.

Except it’s not good enough! A horse is not a pony!

And this is the problem I have with the “bringing meaning to notation” business: accuracy is devalued.

Skilled readers bring to notation not meaning but understanding. Of course such understanding may vary from one music reader to another, especially when it comes to phrasing, style, and general interpretation. And if the music is tonally and metrically ambiguous, the meaning of the notation gets even murkier. But even in such a case, there are limits to how valid your interpretation can be.

Don’t get me wrong. I love Gordon’s idea that we audiate the essentialness of a piece of music; I love the idea that we may disagree about which pitches and durations are essential. In fact, I’m writing a blogpost now called, “The Most Ignored But Essential Part of MLT is … Essentialness.”

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Sounding Out Notation

Gordon seemed to suggest — he never said it outright — that students who have learned to read and audiate familiar patterns can look at music notation, familiar or not, and then audiate the essential pitches and durations effortlessly. But there’s an intermediate step he never talked or wrote about: Before you can decide what pitches and durations are essential in a notated piece of music, you must “sound out” every, every, every notated pitch and duration.

Maybe you doubt this. If so, think about regular, non-notational audiation for just a minute. You hear a piece; then you go to work, sorting out the essential pitches and durations; with those building blocks, you form patterns, you audiate a resting tone and macro and micro beats, then you audiate tonality and meter, and so on. You can do this because you have all the pitches and durations to work with.

As I see it, notational audiation works basically the same way, but with one important addition: To read and understand music, you must sound out the notation, that is, you must convert written notes into sound. (The music may be outwardly or inwardly heard; it doesn’t matter.) Once you’ve sounded out the written pitches and durations — all of them, essential or not — then, and only then, can you audiate the notation accurately. In short, music readers cannot bypass sound to get to meaning.

TRADITIONAL MLTer: We don’t bypass sound. We teach students to read/sing familiar patterns; and then they can read/sing unfamiliar patterns.”

ME: But can they? Are students really able to read/sing unfamiliar patterns after singing whole, familiar patterns at sight? What tools have you given them?

TRADITIONAL MLTer: Once they learn to read familiar tonic and dominant patterns in major, then they can notationally audiate unfamiliar patterns with the same functions.

ME: Yes, students can audiate the unfamiliar patterns they see, but only if someone else reads the patterns for them. The question before the house is, What skills do MLT-trained students have to get the notes off the page before they audiate the music they’re reading? None. MLT fails to provide students with crucial recoding skills.

TRADITIONAL MLTer: For students to read unfamiliar music successfully, they don’t have to learn to recode directly. Students will do this naturally. ‘Sounding out’ notes is not a skill we need to teach.”

The traditional MLTer may have a point. Perhaps recoding is not a skill we must teach our students directly; maybe students will pick it up on their own.

I built my dissertation study on the notion that students must have the tools to sound out unfamiliar written music (recode it, in other words) before they can audiate it. This was the central question of my study: Can students teach themselves to convert written notes to the pitches those notes represent, or must they be taught to do so directly? If you’re interested in learning more about this, please read the post Music/Language Analogies Part 6: Phonemes and Morphemes found here.

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Coda: A Few More Thoughts About “Bringing Meaning”

To finish this post, I’ll rant a bit more about “bringing” meaning to notation. Let’s say you’re reading a piece by Mozart, who has written an unambiguous IV-V-I progression; and let’s say you “bring” the meaning to it that Mozart actually wrote a ii-V-I progression. Sure, you can do that. Hell, it’s a free country, so therefore, you can “bring” any meaning you damn well please.

But let me say with all the strength I can muster that you have a responsibility — to Mozart, to yourself, to the art of music — to read music accurately. And how do you do this? By bringing recoding skill to the notes Mozart wrote. And once you recode Mozart’s notation, you can take the next crucial step: you can audiate (in other words, decode) the notation.

And what about bringing meaning? Mozart’s notation is so saturated with meaning that to bring meaning to it is not only unnecessary but arrogant. We can only humbly take meaning from it, by bringing understanding to it.

The phrase “bring meaning to notation” suggests that it’s ok to bring any meaning you want to what you see — a ii-V-I instead of a IV-V-I progression. But you pay a price for bringing the wrong meaning to Mozart’s notation; and the price you pay is that you’re wrong. Despite what Goodman said in his New York Times interview, there’s nothing good to be said about being wrong.

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Bluestine, E.  (2000).  The ways children learn music:  An introduction and practical guide to music learning theory.  Chicago:  GIA.

Chall, J. S.  (1996a).  Learning to read:  The great debate (3^rd ed.).  New York:  McGraw-Hill.

Chall, J. S.  (1996b).  Stages of reading development (2^nd ed.).  New York:  McGraw-Hill.

Fiske, Edward B. “Approach to Reading Rethought” (interview with Kenneth Goodman). New York Times, July 9, 1973.

Goodman, K.  (1968).  The psycholinguistic nature of the reading process.  In K. Goodman (Ed.), The psycholinguistic nature of the reading process (pp. 15–26).  Detroit:  Wayne State University Press.

National Reading Panel (NRP).  (2000).  Report of the National Reading Panel:  Teaching children to read:  An evidence-based assessment of the scientific research literature on reading and its implications for reading instruction: Reports of the subgroups.  Rockville, MD:  National Institute of Child Health and Human Development Clearinghouse.

Smith, F.  (1994).  Understanding reading:  A psycholinguistic analysis of reading and learning to read.  Hillsdale:  Lawrence Erlbaum Associates.

Meter Test — Second Revision

Here is the latest version of a Meter Discrimination listening test I began writing many years ago. I constructed this test before Covid, administered it once, threw out poorly discriminating items, revised it, shortened it, administered to a new group, got decent difficulty and discrimination numbers, shortened it some more, reordered the items to spread the difficult items around; and in 2020, I was all set to administer it again to a new group of students so I could obtain reliability estimates. Then Covid struck.

I’m using the test this year with my 4th graders to fulfill a Philadelphia School District requirement: their SPM (Student Performance Measure). To meet my school districts expectations, I must treat the test as a criterion-reference test (basically a pass/fail mastery test). Actually, it’s more a test of my teaching than of my students’ learning. Here is how it works (and now, I’m quoting from the Philadelphia School District SPM template):

To achieve an Educator Effectiveness rating of Distinguished, 80% of students will score a 19 or above on the post‐test assessment.

To achieve an Educator Effectiveness rating of Proficient, 70‐79% of students will score 19 or above on the post‐test assessment.

To achieve an Educator Effectiveness rating of Needs Improvement, 60‐69% of students will score 19 or above on the post‐test assessment.

To achieve an Educator Effectiveness rating of Failing, less than 60% of students will score 19 or above on the post‐test assessment.

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Here are the test item sound files:

1. Bizet – Carmen – Overture

2. Schubert – German Dance in B-flat, D. 783 #7

3. The Beatles – Norwegian Wood

4. Scarlatti – Sonata in G Major, K. 455 (synthesizer)

5. Bernstein – West Side Story – I Feel Pretty

6. Prokofiev – Classical Symphony, 3rd mvmt

7. Seal – Kiss from a Rose

8. Beethoven – Symphony #9, 4th mvmt

9. The Del-Vikings – Come Go with Me

10. Johann Strauss – Tales from the Vienna Woods

11. Verdi – Rigoletto_ La donna è mobile

12. Mozart – Eine Kleine Nachtmusik 1st mvmt

13. James Taylor – Sweet Baby James

14. Johann Strauss – Blue Danube Waltz

15. Handel – Parnasso In Festa – Chorus

16. Haydn – Symphony #103, Drumroll– III. Menuet

17. Verdi – Il Trovatore – Anvil Chorus

18. Bach – Toccata In D, BWV 912

19. Billy Joel – Piano Man

20. Banjo solo – Cherokee Shuffle

21. Handel – Brockes Passion – Gott selbst der Brunnquell

22. Bizet – Carmen Suite No. 1_ VI. Les toréadors

23. Smetana – Bartered Bride – Act 1, Scene 1

24. Molly Mason & Jay Ungar – The Lovers’ Waltz

25. Bizet – Carmen Suite No. 1- IV. Seguidilla

26. The Marcels – Blue Moon

27. Handel – Water Music, Suite #2 – Minuet

28. Gotye – Somebody That I Used to Know

29. Saint-Saëns – Carnival of the Animals – Fossils

30. Kelly Clarkson – Breakaway

31. Saint-Saëns- Samson et Dalila – Bacchanale

32. Rankin Family – Mo Shall al dhekh

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Please take a look at FIGURE 1 below. 

FIGURE 1

You’ll see that I present item analyses for all items except 22 and 24. For this revised version of the test, I replaced those items with different musical examples by the same composer/performers (Bizet and Mason & Ungar respectively). I ordered the items with 4 factors in mind: meter, genre, item difficulty, and item discrimination. Let me go into this in greater detail.

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Technical Matters

—In this 2nd revised version, the meter test consists of 32 items, 16 in duple meter and 16 in triple meter. I threw out 8 test items (4 in duple meter and 4 in triple meter) from the original test because of their poor discrimination values.

—I shortened the test items.  Each item is now between 25 and 30 seconds long.  Most are exactly 27 seconds long. (Incidentally, I have no way of knowing, yet, if shortening the items will have any effect on how students respond to them.)

—No more than 2 duple examples appear consecutively, and no more than 2 triple examples appear consecutively.  If students circle duple or triple only, or if they consistently alternate their responses, they will receive a chance score of 16.

—The revised test has 15 vocal items (shown in bold print) and 17 instrumental items. You’ll notice that pieces similar in style and genre are not lumped together.  No two vocal items appear consecutively; in a few instances, two instrumental items appear consecutively (#1 and #2; #24 and #25).  This was inevitable.  Still, I made sure the back-to-back instrumental items are stylistically different from each other.

—The 4 very difficult items (shown in green font) are those with difficulty levels at 60% or lower).  I deliberately spaced them apart, so students will not face the daunting task of answering many difficult items in a row.

—The 3 very easy items (shown in red font) are those with a difficulty level of 90%.  I deliberately spaced them apart so kids, while taking the test, will get a periodic breather.

— I learned in a previous administration of the test that half the test items have difficulty levels at or above 75%, while half have difficulty levels below 75%.  If you look at the item difficulty levels, you may think the items were randomly scattered, so that the varied difficulty levels happened by chance. Actually, to make sure items varied in difficulty levels throughout the test, I arranged them by following this procedure: I divided the 32 items into four 8-item groups based on item difficulty. I then made sure each 8-item group had 4 above-average items and 4 below-average items. These groups then became items 1-8, 9-16, 17-24, and 25-32.

—Based on a previous administration of the test, all 32 items are positively discriminating, and only 3 have discrimination values lower than .2. (This does not include the new items 22 and 24.)

In Figure 2 below, you’ll see the format of the test.

FIGURE 2.

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Final Technical Points and Some Personal Reflection

In September 2023, I administered this Meter Test as a pre-test to 4th grade students (n = 103) at the Stephen Decatur School in Philadelphia. As shown in Figure 3, the obtained pre-test mean of 15.07 is encouragingly low, and in fact, is a full point lower than the chance score of 16. The standard deviation (not shown in Figure 3 but calculated separately by use of an excel spreadsheet) is 3.68, which means the scores were all over the map, and basically the kids had no clue what they were doing. Which is exactly what a pretest should reveal!

FIGURE 3.

I just listened to the whole test all the way through, and I’m happy with the sum of its parts.  I got rid of some of the gentler items, so the revised test sounds a bit more raucous than the original version; and because the items are shorter, the whole test moves at a faster pace. (From start to finish, the test clocks in at 14 minutes.) But I’m glad it still has moments of humor, like the “Blue Moon” example that kids love, and Glenn Gould’s positively goofy performance of the Bach Toccata.

In May 2024, following 7 months of instruction in musical meter discrimination, I will administer the test again. My predictions are that the same group of students who took the pretest will obtain the theoretical mean of 24 and a theoretical standard deviation of 2.67. After I calculate the mean and standard deviation, I will analyze each item to determine difficulty levels and discrimination values; and finally, I will obtain test-retest and Kuder-Richardson 20 reliability estimates.

And now, we come to the hard part: waiting. Will the items retain their varied difficulty levels and their high discrimination values?  And what about the reliability of the test?  Will students’ scores be relatively stable over time?  And will the test show a high degree of internal consistency?  By next May, I should have the answers.  As Willy Wonka said, “The suspense is terrible.  I hope it’ll last.”

Folk Dances My Students Will Learn During the 2023-2024 School Year

            Here is a spread sheet with the folk dances I plan to teach this year. I’ll be using the John Feierabend Move It! Video series with my 1^st graders, and Phyllis Weikart’s video series with my older students.

            If you’re familiar with Phyllis Weikart’s fantastic video series Beginning Folk Dances, you’ll notice I follow her sequence closely, at least in a broad sense. I’ve chosen 39 of her dances. The 40th dance is Cotton-Eyed Joe, which is not one of hers, but is too much fun to leave out. Some of her dances are easier than she claims; others (such as Troika) are far more difficult. But her basic sequence holds up quite well: students in 2nd grade begin learning simple locomotor and non-locomotor movements; by 6th grade, they learn the Cherkessiya, Grapevine, Schottische, Yemenite, and some other steps.

            I tend to favor the circle and line dances, but I avoid the mixers. If the dance patterns are so complex that I can’t figure them out, I avoid them. (If I can’t get it, my 3rd graders won’t get it either.)

            It takes about 4 or 5 lessons for kids to learn each dance well. Each grade, 2^nd grade through 6^th, will learn 8 dances.

            Just to show you that elementary school students can learn these dances, I have included 2 videos of my 4th grade students performing Armenian Misirlou and Amos Moses.

Armenian Misirlou:

Amos Moses:

Whole-Part-Whole: Its Meandering Path To Prominence

Introduction

            A few days ago, Eric Rasmussen and Beau Taillefer uploaded an Audiation in the Wild podcast episode called Whole-part-whole and Chaining. They start the podcast with Beau casting a wide net.

BEAU: Eric, maybe you can help me out. I forget who contributed the idea of whole-part-whole to Music Learning Theory, because I don’t believe it was Gordon himself.

ERIC: You know, I’m not a hundred percent sure.

            Gentlemen, you’ve come to the right place. Please let me add my impartial perspective.

            The whole-part-whole learning process in general education is, of course, far older than Gordon’s Music Learning Theory. It’s basic to learning, a foundation of good teaching, and it works like this: You introduce kids to a “whole” of something, just to give them a quick, drive-by view; then you dig into the “parts,” by relating those parts, somehow, to the “whole” the kids started with; and finally, you come back to the same whole the kids started with, but now they understand it with greater sophistication.

            But this post isn’t about general education, or even the wide field of music education. It’s about the whole-part-whole learning process in MLT. So let’s return to the question: Who first contributed the idea of whole-part-whole to MLT? The answer is simple.

            I did.

            Which is mostly not true, but it contains a grain of truth. Actually, it was Darrel Walters — which, as attributions go, has a lot more truth behind it. But to make this claim credible, I must go deeply into MLT history.

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What is the Whole-Part-Whole Process?

            Our subject today is the whole-part-whole approach to learning. What is it? How does it work? Was it always built into MLT? And if not, when did it first infiltrate the MLT universe? In the 1st edition of my book (1995, p. 14), I described it this way:

WHOLE #1: Students learn a rote song, or they listen to a piece of music.

PART: Students hear and then sing or chant patterns (though not necessarily the same patterns found in the piece they’re studying).

WHOLE #2: Students return to the piece with a greater understanding of its structure.

            I mentioned in my book that no one ever wrote about the whole-part-whole process as eloquently (and now I’ll add the word lucidly) as Darrel Walters (1988, 1989, 1992). He described the 3 steps as 1) Introduction, 2) Application, and 3) Reinforcement.

            Later in this post, I’ll have more to say about Walters’s insights into whole-part-whole. For now, I’d like to zoom ahead to 2023 to show you how MLTers write about whole-part-whole today. 

            The next time you visit the GIML website, take a look at the passage about the Whole-Part Whole learning process. Here’s how you can find it: 1) Log on to the GIML website homepage; 2) hover over the words “Music Learning Theory” at the top; 3) then click on the word “Methodology” in the dropdown menu; 4) finally, scroll down. Just after the section called “Sequence,” and before the section called “Other Central Principles,” you’ll find a section about the Whole/Part/Whole Curriculum. Here is what you’ll find (in condensed form):

The Whole/Part/Whole approach (sometimes called Synthesis/Analysis/Synthesis) is a common way in education to organize students’ experience with content. The first whole stage (Synthesis) is an introduction, an overview that establishes basic familiarity with what the topic is about. The second stage (Analysis) consists of detailed study of the parts of the topic. On returning to the whole (the second Synthesis) students have a more sophisticated understanding of how the parts fit together to form a unified whole. 

Music Learning Theory provides an elegant Whole/Part/Whole approach to developing audiation. Songs and music literature are the “whole” part of the music curriculum. These are taught during classroom activities. Tonal and rhythm patterns are the “part” part, and are taught during learning sequence activities. Although learning sequence activities are the heart of Music Learning Theory, where theory is applied directly to music teaching practice, the main objective is to enhance the teacher’s ability to help students understand the music they study in classroom activities.

            Reading this makes me smile. In 2023, MLTers venerate whole-part-whole — along with audiation, aptitude, sequential learning, tonal and rhythm syntax, and early childhood development — as one of the pillars that holds up the MLT citadel. 

            I’m proud to say, with no trace of facetiousness, that I deserve a healthy-sized chunk of credit for this.

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 A Time Before Whole-Part-Whole: A Bit of MLT History

           Let’s take a trip back in time to 1968 when Gordon wrote his monograph How children Learn When They Learn Music. It’s a great read! So many MLT ideas — in early gestation — are in this book. Even then, Gordon was laser-focused on teaching children to understand tonality and meter. He had firmly decided on a beat-function syllable system and moveable DO with LA-based minor as verbal associations. He understood that children must have aural/oral training (though he didn’t call it that) before they learn to read and write music notation. He denounced music theory as an aid to help children understand music. He even included a section on teaching harmony and part-singing! 

            But back in 1968, Gordon had only rudimentary thoughts about how to teach students based on their levels of aptitude. He had not yet begun the pattern difficulty studies. He endorsed the vague skill-learning sequence of sound-before-sight, but he put forth no clear way to combine skills with content. Even the term “audiation” would not make its way into the world for another 8 years. 

            And he made no mention of the whole-part-whole process, which doesn’t surprise me: without patterns as the middle “part” of whole-part-whole, why would Gordon bring it up, or even think about it?

            Skip ahead a few years to 1971. Gordon expanded his 1968 book into the more scholarly and imposing book The Psychology of Music Teaching. Three new things stand out: First, he inserted long, detailed reference sections at the end of each chapter. Second, he added chapters on the history, nature, and use of music aptitude tests. And third — the most exciting — he showed, tentatively, how music teachers can apply Gagné’s (1965) general learning theory to music. Here, in chapter 4 of The Psychology of Music Teaching, we glimpse for the first time, Gordon’s brilliant mind in overdrive. 

            But he makes no mention of the whole-part-whole process. 

            And now we move ahead 5 years. It’s 1976, and Gordon is about to become the world’s foremost thinker in music education. In 1976, he coined the term “audiation,” and he wrote the 1^st edition of Learning Sequence and Patterns in Music. And MLT was born. Gordon had replaced most of Gagné’s terms with his own:

            Verbal association remained Verbal Association.

            Chaining and Multiple-discrimination learning became Partial Synthesis.

            Concept learning became Generalization.

            Problem solving became Creativity.

            Principle learning became Theoretical Understanding.

            What about the aural/oral level? Is it rooted in Gagné’s principles as well. It seems to be an offshoot of stimulus-response learning. But no. It has no precedent in general learning theory, and is in fact, one of Gordon’s most inspired ideas. I’ll say more about this in a future blog post.

Anyway, it’s 1976/1977, and most of our MLT “old friends” have arrived. Gordon presented us with 3 learning hierarchies — skills, rhythm content, and tonal content. He explained how to combine skills with content. We see what a curriculum might look like, with sequential and comprehensive objectives.

            And how do patterns fit into all this? The first of Gordon’s pattern difficulty studies (1974) had already been published; another (1976b) was hot off the presses; and a third (1978) was nearing publication. Some patterns, it turned out, are easy to audiate; others are more difficult. What if music teachers linked students’ aptitude, somehow, with the audiation difficulty level of tonal and rhythm patterns? Students with low music aptitude could, then, perform the easy patterns and not grow frustrated; students with average and high music aptitude could perform the more difficult patterns and not grow bored. It was — and is — a novel and intriguing way to meet the individual needs of music students; and in a few years, Gordon would come up with a precise (perhaps too precise) way to do just that.

            What’s missing, still, is the whole-part-whole process. How many sentences does Gordon (1976a/1977) devote to it?

            None.

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The Turning Point

            Three years go by; it’s now 1980. Gordon has greatly expanded his book, and he writes about the whole-part-whole process for the first time. Here is what he has to say, his full treatment of this vitally important subject (1980, pp. 136-137):

In simplification, learning takes place in three steps: one gains a vague impression of the totality of a piece of literature, then specifically studies patterns, and finally interprets the piece of literature with precision.

            That’s it.            

            This is how the whole-part-whole process, a fundamental idea in education, entered the MLT universe — in two unremarkable sentences that most readers probably sped passed. Back in 1980, did Gordon’s students realize, did Gordon himself realize, these sentences marked a watershed moment in Music Learning Theory?

            I invite you to take your copy of the 1980 edition off your shelf (and I hope you all own a copy because it is, along with the one from 1988, the most interesting edition) and study pages 136-137. I think you’ll agree with me that Gordon neither precedes nor follows the 2 sentences quoted above with anything about whole-part-whole. These sentences stand alone.

            How did whole-part-whole, a throw-away idea in 1980, evolve into one of the most important principles in MLT today? Give me just a bit more time, and I’ll explain.

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The Most Important Gordon Lecture Ever!

            Four more years go by, and Gordon writes the 1984 edition of Learning Sequences in Music. He is putting the finishing touches on his first set of call-and-response exercises. And these exercises will forever be saddled with the grotesque, pompous, academically inflated name — “learning sequence activities,” a term every bit as ugly to my ears as that syrupy melody MLTers still use: So la so fa mi re ti do, which causes my ears to bleed every time I hear it.

            Anyway, where was I? Ah yes, it’s 1984 and Dr. Gordon is probably facing questions from students and colleagues about how pattern instruction relates to real music. He can give whole-part-whole short shrift no longer. Here is what he had to say (1984, p. 201):

In summary, learning takes place in three stages: 1) A student gains a vague impression of the tonality and meter of a piece of literature the [sic] he hears and performs, 2) He studies tonal patterns and rhythm patterns in that tonality and meter, but not necessarily the tonal patterns and rhythm patterns found in that piece of literature, and 3) Finally he is able to interpret that piece of literature with syntactical meaning.

            And that’s all he had to say about whole-part-whole in 1984. Or rather, it would be all he had to say, if not for a lecture he delivered at the 1984 Music Educators’ National Conference in Chicago. This lecture, to me, contains some of his greatest moments, mainly because the angry, snarky audience members simply would not let him off the hook. They challenged him; and he fought his way back. (If you can track it down, listen to the early childhood music lecture he gave at that same conference. The audience was noticeably hostile, but Gordon stood his ground.)

            At one point, during a lecture (1984b) called “The basis of music learning theory,” Gordon was asked about how parts and wholes relate to each other in music instruction. And he was ready. Here is an audio clip of his answer from that 1984 lecture:

            My hunch is, had the question not been raised, Gordon would not have brought up whole-part-whole in his lecture at all. And yet pattern instruction is pointless — pointless — unless those patterns (and the skills we connect to them) relate to real music. And by “real music,” I mean more than just rote songs; I mean the music of Beethoven and Bach and Gershwin and Art Tatum and Bobby McFerrin.

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Darrel Walters Expounds on Whole-Part-Whole

            We now move ahead to 1986. Gordon writes the first edition of Jump Right In: The General Music Series; and soon after, Darrel Walters (1988) writes a booklet called “Coordinating Classroom Activities and Learning Sequence Activities.” Walters, who was then a newly hired Temple University professor, had deep insight into MLT, and a clear and direct prose style.

            In his 20-page booklet (a length worthy of the topic, finally), Walters (1988) offered numerous examples of how to create and teach lessons that reinforce phrases, songs, and larger pieces of music — the final “whole” of the process. He suggested, for example, that teachers “illustrate form in a song being performed by demonstrating repetitions and sequences of tonal patterns.” (p. 13) He then applied this broad suggestion to each of Gordon’s skill levels. At the partial synthesis level, for instance, teachers can “explain the musical form by singing salient tonal patterns from repeated and contrasting sections, using tonal syllables, and label the form.” (p. 14)

            For the first time, MLT teachers saw how Step 3, the final “whole,” — the payoff — could work at each skill level; in fact, MLT teachers today can still gain insight from this booklet. Referring to it a year later, Walters (1989, p. 152) wrote the following:

The booklet … describes step-by-step techniques that the teacher can apply to the reinforcement of learning at Step III.

            Clearly, Gordon thought highly of the booklet Walters had written, and indeed, he seemed particularly fond of the specific reinforcement activities Walters had created: Gordon reworded them slightly, and then included them in the 1988 edition of Learning Sequences in Music.

            In short, no writer on MLT deserves more credit for shining a spotlight on the whole-part-whole process than Darrel Walters.

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My Contribution

            We are near the end of our journey. Let’s move ahead 6 years to the summer of 1994. I began writing my book in May and finished writing it by the 3rd week in August. An early task in the process was deciding on the topics and order of the chapters. The book needed a decent-sized introduction that spelled out for the reader what was to come. And I knew that the audiation chapter had to follow the introduction. And of course, chapters on aptitude, tonal syntax, and rhythm syntax had to appear soon after.

            But I kept thinking about Gordon’s 1984 MENC lecture, and about that questioner who wouldn’t let Gordon off the hook about parts and wholes. One of my goals in writing the book was to clear up misunderstandings about MLT: No, audiation is not the same as inner-hearing; no, MLT is not a method; and no, Gordon most certainly does not advocate a learning approach that moves from part to part to part to part, with a final “whole” seemingly never in sight.

            The task of bringing the whole-part-whole process to prominence was nearly complete, thanks to Walters who had done most of the heavy lifting. But one thing was missing: To show that whole-part-whole was incontrovertibly vital to MLT, I needed to devote to it an entire chapter — not a perfunctory afterthought buried in the middle of a textbook, and not even a skillfully written booklet — but a chapter, early on, up front, and in plain sight.

            Whole-part-whole was MLT bedrock, and I wanted to make bloody sure the world knew it.

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Coda

            In the whole-part-whole chapter in my book (1995), I mentioned, almost in passing, that my lessons are built on a whole-part-whole approach in many respects. In their podcast (which I mentioned at the beginning of this post, and which started me on this tirade if you recall), Beau and Eric talk mostly about whole-part-whole as an approach to practicing music. This shows just how versatile the process is.

            To finish this long post, I’ll let Walters (1988, p. 20) have the final word:

The activities suggested in the preceding pages … should not be the primary focus for one who has read this document. It is more important that teachers understand and appreciate the concept of the whole-part-whole approach to learning, that they remain continuously sensitive to the value of reinforcement in learning, and that they find as many ways as possible to capitalize on its power on behalf of students.

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Bluestine, Eric. 1995. The Ways Children Learn Music: An introduction and Practical guide to music learning theory (1st edition). Chicago: GIA 

Gagne, Robert M.  1965.  The Conditions of Learning.  New York:  Holt, Rinehart and Winston.

Gordon, Edwin. 1968. (Re-issued in 2014 in its original form). How Children Learn When They Learn Music. Chicago: GIA. 

Gordon, Edwin. 1971. The Psychology of Music Teaching. Englewood Cliffs: Prentice Hall.

Gordon, Edwin. 1974. “Toward the Development of a Taxonomy of Tonal Patterns and Rhythm Patterns: Evidence of Difficulty Level and Growth Rate.” Experimental Research in the Psychology of Music: Studies in the Psychology of Music IX (1974): pp. 39-232.

Gordon, Edwin. 1976a. Learning Sequence and Patterns in Music. Chicago: GIA.

Gordon, Edwin. 1976b. Tonal and Rhythm Patterns: An Objective Analysis. Albany: State University of New York Press.

Gordon, Edwin. 1977. Learning Sequence and Patterns in Music (revised edition). Chicago: GIA. 

Gordon, Edwin. 1978. A Factor Analytic Description of Tonal and Rhythm Patterns and Objective Evidence of Pattern Difficulty Level and Growth Rate. Chicago: GIA.

Gordon, Edwin. 1980. Learning Sequences in Music: Skill, Content, and Patterns. Chicago: GIA. 

Gordon, Edwin. 1984a. Learning Sequences in Music: Skill, Content, and Patterns. Chicago: GIA. 

Gordon, Edwin. 1984b. “The Basis of Music Learning Theory.” [audiocassette]. Music Educator’s National Conference [MENC], International Audio Stats Educational Services: Los Angeles, Calif. [OCC Number / Unique Identifier: 12019891]

Gordon, Edwin E. and Woods, David G.  1986. Jump Right In: The Music Curriculum.  Chicago:  G.I.A.

Gordon, Edwin. 1988. Learning Sequences in Music: Skill, Content, and Patterns. Chicago: GIA. 

Gordon, Edwin. 2012. Learning Sequences in Music: Skill, Content, and Patterns. Chicago: GIA. 

Taillefer, Beau and Rasmussen, Eric: https://audiation-in-the-wild.simplecast.com/

Walters, Darrel L. 1988. “Coordinating Classroom Activities and Learning Sequence Activities.”  Chicago:  G.I.A. 

Walters, Darrel L.  1989. “Coordinating Learning Sequence Activities and Classroom Activities.”  In D. L. Walters and C. C. Taggart (Eds.), Readings in Music Learning Theory.  Chicago:  G.I.A. 

Walters, Darrel L.  1992. “Sequencing For Efficient Learning.”  In R. Colwell (Ed.), Handbook Of Research On Music Teaching And Learning.  New York:  Schirmer Books.

Music/Language Analogies Part 5: A Story with a Happy Ending

            Back in 2007, I completed my doctoral study. I wanted to find out the best way to teach tonal music reading to elementary school students. These kids (the subjects who took part in my study) had already learned to audiate and perform tonic, dominant, and cadential patterns in major and minor tonalities. They had moved nicely through the pre-notation skill levels (aural/oral, verbal association, and partial synthesis). They were, at least based on the principles of MLT, ready to read tonal patterns. My task was to see how best to teach them to do that.

            In the proposal (and also in my later dissertation), I inserted the following quote from Gordon’s  Learning Sequences in Music (2003, p. 111):

In symbolic association, students learn to read tonal patterns and rhythm patterns as entire patterns.  That is, individual pitches and durations are not given consideration, just as in the Chinese language, for example, which has no alphabet, logographs are read and written as complete words, and individual characters are not given consideration.

            Rarely, back then, did I disagree with Dr. Gordon—and even today, I’m with him a solid 80% of the time—but for me, this quote was a red flag.  Whole patterns for beginning readers?  Where was the research to support such a statement?  When I was writing my dissertation, I came across an extensive literature review by Jeanne Chall (1996a) and a meta-analysis put out by the National Reading Panel (2000); these reports showed the indispensable value of systematic phonics instruction. Chall subtitled her book “The Great Debate.” For me, the debate was settled: children don’t simply read whole words, at least not at first. I went on to read Chall’s brilliant book Stages of Reading Development (1996b), in which she spelled out the role of phonics in children’s education.

            Gordon’s blanket statement about reading only whole patterns made no sense to me.  A decade earlier, in the first edition of The Ways Children Learn Music (1995), I had written about my doubts.  Even back then, I wanted, someday, to conduct a study to investigate the role of whole patterns in music reading instruction.  But I wasn’t sure how best to go about it.

            I ended up, 12 years later, completing an experimental study in which I compared 4 groups of beginning music readers.  All 4 groups learned to read (that is, to sing at sight) familiar tonal patterns. One group read whole patterns only; a second group read individual pitches within patterns only; a third group learned to read whole patterns, followed by individual pitches within patterns; and a fourth group learned to read individual pitches within patterns, followed by whole patterns.  A classic design:  one group learned A; another learned B; a third learned A before B; and a fourth learned B before A.

            At the end of the treatment period, I administered to all subjects a test of sight-reading and a test of sight-singing, each of which I designed.

            When the dust settled, when all the statistics were in, I found no significant differences among the groups.

            I concluded that no one method of teaching tonal music reading used in my study was superior to any other.  And there you have it.  Years of work went out with a whimper, not a bang.

            But that’s not the end of my story.  To design the study, I had to think and think and think. And because I knew that non-MLTers would be reading my dissertation, I really had to spell things out. I wrote a 58-page introductory chapter in which I laid out, in copious detail, why I believed the study was necessary.  No easy task:  I had to explain Gordon’s MLT, and then explain how I was breaking from Gordon’s MLT.  This was not a good way to make friends.  (For those of you who have a doctoral defense in your future, here’s a word of caution:  If you don’t already have a thick skin, you’re in trouble!)

            In my introduction, I included a long section about music/language analogies.  Mostly, I focused on the analogies Gordon typically made to explain (and sometimes defend) his thinking.  I also wrote about a few analogies I came up with that helped to explain what I was doing and thinking.  One committee member questioned whether such philosophical writing belonged in a quantitative study.  Here is that written exchange.  The committee member’s comments are below in italics; my response follows in bold print:

Keep in mind that this is a doctoral study, not a position paper.  Your design and procedures, even your rationale can be explained without recourse to analogies and other diversions.  If you must include them, then I suggest you read linguistics research, and you’ll find others who have considered the relation of language and music.  Reporting their work will strengthen your proposal.

I agree that citing the work of others who have compared music with language strengthens the proposal. After conducting literature searches (through ERIC, Dissertation Abstracts, etc.), I can say with a high degree of certainty that no one has compared whole tonal patterns to free morphemes; nor has anyone compared pitches within patterns to inflectional bound morphemes.

Let me emphasize that this section—The Nature of Music/Language Analogies—is nothing more than philosophical speculation. The question I have wrestled with is, Does this section belong in a quantitative study?  After much reflection, I have chosen to retain it for two reasons:

First, I want to make it clear to the readers of this proposal (and ultimately to those who will read the dissertation) that my study is not simply a comparison between 1) Gordon’s whole-pattern approach and 2) the “traditional” approach of teaching students to read one note at a time without regard for syntax.  The linchpin of my study is that it is possible to teach students to read individual pitches without jeopardizing their audiation of functional patterns in a tonal context.  I cannot “prove” the validity of this teaching approach by comparing music with language.  All I can do is use music/linguistic analogies to help readers to better understand what I am doing.

Second, this section reveals the thought processes out of which the design and procedures of my study were constructed.  In a sense, the teaching methods and the music/language analogies “grew up” together. The new teaching approach I have been trying with my students (teaching students to read notes within patterns) gained precision as I began to think of pitches as morphemes rather than phonemes; and as the analogies grew more precise—as I began to understand that whole patterns are analogous to free morphemes, and that pitches within patterns are analogous to inflectional bound morphemes—my teaching improved.

            I told you earlier that my story had a happy ending, so here it is:  individual pitches without context are analogous to phonemes in language; whole patterns are analogous not to words, but to free morphemes; and pitches within patterns—this is the clincher!—are analogous not to letters, and not to phonemes, but to inflectional bound morphemes. And it was this analogy that sparked a creative breakthrough: I figured out how to teach students to read individual pitches in a way that maintained tonal syntax.

            The End

            Wasn’t that a nice story?  Maybe you think it cries out for a sequel, and so it does.  In the next blogpost, Part 6, I’ll explain all those intimidating linguistic terms. And I’ll show you how to teach students to read tonal notation one note at a time — while still audiating the tonal context.

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Bluestine, E. (2007). A Comparative Study of Four Approaches to Teaching Tonal Music Reading to a Select Group of Students in Third, Fourth, and Fifth Grade, Unpublished doctoral dissertation, Temple University.

Bluestine, E (1995). The Ways Children Learn Music: An introduction and practical guide to music learning theory (1st edition). Chicago: GIA.

Chall, J. (1996a). Learning to read: The great debate (revised, with a new foreword). New York: McGraw-Hill.

Chall, J. (1996b). Stages of reading development (2nd ed.). Fort Worth, TX: Harcourt-Brace.

Gordon, E. E.  (2003).  Learning sequences in music:  Skill, content, and patterns.  Chicago:  GIA.

National Reading Panel (NRP).  (2000).  Report of the National Reading Panel:  Teaching children to read:  An evidence-based assessment of the scientific research literature on reading and its implications for reading instruction: Reports of the subgroups.  Rockville, MD:  National Institute of Child Health and Human Development Clearinghouse.

A Guide For Music Student Teachers

            Many, many, many years ago I had the worst student teacher in the world—at least in my world. This person (who will remain nameless, ageless, and genderless for the remainder of this blog post) could do nothing right. This person could not match pitch; this person displayed poor rhythm, had only meager piano skills; this person yelled at students frequently, always “ran out” of songs and activities to teach, taught music notation to my kindergarten students, and informal guidance activities to my 6^th graders. Worst of all, the students’ singing was worse at the end of the period than it was at the beginning!

            And this person argued with me, telling me that the poorly taught lesson I just observed was only my opinion. According to this person, the lesson went beautifully. That was all that mattered. Besides, how could I criticize the lesson when I offered this person no guidance?

            “I’ve been giving you guidance left and right!  What more do you want?” I said, thoroughly exasperated.

            “I want you to put it in writing,” this person told me.  “Then I’ll know exactly what you want.”

            “Okay, fine.  I’ll put it in writing.”

            So I did.  I drew up a set of guidelines. Here they are, my bite-sized nuggets of advice to student teachers.

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General Guidelines for Student Teachers

• Be a self-starter.  (Don’t wait to be told.)
• Always dress and conduct yourself professionally.
• Make your presence felt.  (Avoid being “the person in the back of the room.”)
• Plan at least ten activities per period for kindergarten and first grade students; plan at least five activities for older students.
• Before you teach an activity, clear it with me.
• Before you teach, run the lesson through your mind from start to finish several times.
• Before you teach, make sure your materials are close at hand.
• At an early point in the period, take role and mark absent students.
• As you finish an activity, mentally prepare yourself for the next one.
• Stick to your general plan.  (In other words, don’t wing it.)
• While you teach, walk around the room often.
• Insist that students quiet down completely before you or they talk or perform.
• Show what you want students to do.
• Be firm with students, yet positive.
• If I ask you to change your lesson, change accordingly without arguing.
• Continually add activities to your repertoire.  (Never tell me you have run out of things to teach.)
• Budget class time.  This one may be the hardest guideline to follow.  If you decide ahead of time that an activity will last 10 minutes, then move on to a new activity at the 10-minute mark.  Stick to your timetable!  You can always return to the activity at the end of class if you have time.

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Music Guidelines for Student Teachers

• If you sing or chant inaccurately, fix your mistake immediately.
• Listen to students’ verbal and musical responses.  If they are out of tune, or out of tempo, don’t let it slide.  Sweat the small stuff.  Help them get back on track.
• Make use of the achievement record sheet by asking the high achievers to perform, one at a time, for the others.  Have kids teach other kids.
• Never accept poor musical performances from the high achievers.
• Piano accompaniments to rote songs should have a definite rhythmic profile, thinly textured harmony, and just a bit less melody than the kids need.  Translation:  Don’t bang out melody with thick, rhythmically boring chords underneath!
• Play the piano more softly than you sing; play much more softly than the class sings.
• Practice, practice, practice those piano accompaniments until you can stand up, play the piano, sing, and watch the class at the same time.
• For a change of pace, move out from behind the piano and sing a cappella.  A cappella singing is important, not just during LSAs, but during rote song activities too.
• Use visual aids when appropriate.  (But avoid visual aids—such as overly ornate diagrams—that are more distracting than helpful.)
• Every lesson must include movement, even if the movement is as seemingly insignificant as the tapping of micro beats.
• Involve the kids in several “stations” around the room.  (Make your lessons interesting to look at.)
• If music is not “hanging in the air” at any given time, ask yourself why not.
• A music lesson is successful if the kids sound better at the end of class than they did at the beginning of class.