Chunking down into N chunks reduces practice required by a factor of Nx where x is the number of possible chunk flavours

Paul Hirsh (@jazzpanflute)

Why do we need full-length scales? Or: why do the scales we practise always need to span an octave? Why do we even need to think of them in that way?

Since all octave-length scales are composed of two chunks called tetrachords, why don’t we just practice those? Especially since most musical phrases fit inside one tetrachord (or pentachord). Taffanel had the idea in his Scale Game, reviewed in an earlier post.

Back in the day, your painting-box of available tetrachords in Western music contained:

2 2 1 major

2 1 2 Dorian aka minor

1 2 2 Phrygian

1 3 1 harmonic aka chromatic

and 2 2 2 Lydian.

This is of course just a small subset of possible interval stacks within the compass of half an octave. By adding the fifth (i.e. topping up the total to 7) we form pentachords. Your scale would then consist of a tetra- sitting atop a penta-chord.

My point is that, stacking any two of just these five elements (or the same one upon itself) creates a possible 25 scales, which when multiplied by the twelve houses means practising 300 instances of scales just to keep your ass covered, which to me seems excessive, and we haven’t even got to the blues yet!

Practising just these tetrachords (or pentachords) reduces the amount of elements you need to practise by a factor of 5! In addition, these elements are half the size.

Or put in broader terms: Just chunking down by a factor of two reduces the practice required by a factor of 2x where x is the number of possible chunks! And we can keep going, chunking on down!

Here is an excerpt from A Love Supreme part 1 where Trane is putting the 3 2 tetrachord through the houses:

For the benefit of the curious, I list here the transpositions that follow (as always, in halfsteps): +6, -7, -1, +14, +1, -7, +5, -4, -4, +9, -6, +3, -7, +7, -10, +14, -5, +2, -5, -5, +2, +2, +1, +1, -3.

(There are prizes if you can see a pattern in that!)

Now my guess is, that 9 out of 10 jazz teachers will call this pattern “pentatonic”, i.e. part of a larger 5-note scale. So they might say, keep practising your pentatonic scales! They can say this on the basis of a figure that uses just three notes!

Moving on, Branford Marsalis wrote a very hip tune called Wolverine, which you should check out on the album Crazy People Music, and which contains this passage:

containing an upward run tracing out these intervals: 1 3 1 3 2 2 2 3. We could of course arbitrarily select the octave from the D to the D and posit a scale (1 3 1 3 2 2), ignoring the fact that the remaining notes, E and G, invalidate the scale hypothesis by not stacking up the octave.

Or we could call the passage a hybrid between the well-known “augmented” scale (1 3) and the wholetone scale (2) straddled by the famed Trane lick a-birthed in Giant Steps 2 2 3.

I read somewhere (it could have been on jazzadvice.com – please add a search box widget guys!) that Michael Brecker’s secret to getting so much done was to only practice stuff he could actually use.

So why are we still whipping ourselves with octave-long scales?

My practice plan for learning a new instrument would begin by learning the smallest chunks in all twelve houses, and then recombining them or stacking them as the fancy takes me. I’m sure that this method would leave nothing uncovered, and would avoid the danger of installing annoying scale habits that we’re all tired of hearing (and of practising).

Not to mention the sweet, smooth learning curve.

In MOVES notation, all numbers in bold represent intervals counted in halfsteps or semitones. Rising and falling intervals are indicated by a + or a – sign. Numbers in parentheses () are interval arrays or scales that stack upon themselves. The term “houses” replaces the idea of keys or tonalities for cases where no identifiable tonal root is expressed.

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