In this post I’d like to review some interesting properties of the familiar major and minor pentatonic scales, and then consider how to create a pentatonic version of the melodic minor scale.

## Major Pentatonic as a Scale Complement

One of the neat the things about the standard major pentatonic scale, which uses degrees {1, 2, 3, 5, 6}, is that it can be seen as the complement of a full 7-note major scale: it contains all the notes that some major scale excludes.  For example, the black keys on the piano – all the notes that are not in C major – form Gb major pentatonic.  In general, if you take all the notes that a major scale excludes, you’ll have the major pentatonic scale rooted at its tritone.  We can visualize this with a clock-style diagram of the octave.  Here, the numbers are not hours but degrees of the major scale, and the red dots represent notes outside the scale.  In the leftmost diagram, the polygon formed by connecting the red dots represents the pentatonic scale rooted at #4 of the parent scale.  Transposing the scale up a semitone (rotating the polygon 30 degrees clockwise) gives the major pentatonic rooted at 5 of the parent scale.  Transposing it down a semitone gives the major pentatonic rooted at 4 of the parent scale.  And transposing it by a tritone (rotating it 180 degrees) gives the pentatonic rooted at 1 of the parent scale.  Notice how the pentatonics rooted at 1, 4, and 5 exist entirely within the parent scale, which is to say that none of the polygon vertices fall on any of the red dots.  The green circle indicates the root of the pentatonic scale, and the dotted line inside the polygon is its axis of symmetry.

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## Major Vs. Minor Pentatonic: Comparing Definitions

If the major pentatonic is built from degrees {1, 2, 3, 5, 6} it’s natural to wonder why we define the minor pentatonic as {1, b3, 4, 5, b7}.  Why not simply flatten 3 and 6 in the major pentatonic formula so that it fits inside a minor scale: {1, 2, b3, 5, b6}?  I don’t know the history of how the major and minor pentatonics evolved in various cultures over time, but I will comment on some abstract reasons why {1, b3, 4, 5, b7} might be more versatile as a scale than {1, 2, b3, 5, b6}.  First of all, it’s convenient to define our minor pentatonic so that it turns out as a mode of our major pentatonic.  This lets us shift from major to relative minor while staying in the same pool of notes.  Indeed C-major pentatonic (C D E G A) and the standard A-minor pentatonic (A C D E G) are modes of each other, or reorderings of the same set of notes.  But if we were to use the formula {1, 2, b3, 5, b6} to get an alternative A-minor pentatonic, it would be A B C E F, which doesn’t fully overlap with C-major pentatonic.  Another notable thing about the standard major and minor pentatonics are that they have no semitones, no tritones, and lots of perfect fourths and fifths, making them very “user-friendly” scales.  The same is not true of {1, 2, b3, 5, b6}, which has two semitones (2-b3 and 5-b6), one tritone (2-b6), and fewer perfect fourths and fifths.  This alternate scale might still be great to make music with, but it lacks the many of the convenient properties of the standard minor pentatonic.

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## Melodic Minor Pentatonic

With these observations in mind, let’s look at the question of how to create a pentatonic scale from the 7-note jazz melodic minor scale.  In sacrificing two notes, we want to preserve as much of the character of melodic minor as possible.  So, which two notes can we afford to lose?  We should probably keep 1 and 5!  To have a minor sound, we need to keep b3.  To have something different from a plain old minor scale, we need to keep at least one of 6 or 7.  Now, as far as I know, there isn’t one universally accepted way to make the remaining choices; that’s to say, the idea of a melodic minor pentatonic hasn’t been standardized in the same way that the major and natural minor pentatonics have been.  I’ve seen melodic minor pentatonic defined alternatively as {1, 2, b3, 5, 6}, as {1, b3, 4, 5, 7}, and as {1, b3, 4, 5, 6}.  What I’d like to do here is explore some interesting qualities of that last definition, {1, b3, 4, 5, 6}.  First of all, it’s the only one of the lot that has no semitones.  In fact it’s a member of one of only three possible pentatonic families with that property (see my post on anhemitonic pentatonics).  Second, it turns out to be a complement of the 7-note melodic minor scale, in the same way that the major pentatonic is a complement of the 7-note major scale!  And third, you can actually transpose the whole thing up a whole-step while remaining inside the 7-note melodic minor parent scale.  To experiment with this, start by playing C-melodic-minor: C D Eb F G A B. Now make up some phrases using {1, b3, 4, 5, 6} or C Eb F G A.  Now transpose your phrases up a whole-step, so you’re using the same {1, b3, 4, 5, 6} pattern rooted at D.  This will give you the notes D F G A B.  The nice thing is that after this whole-step transposition, you’re still playing inside the parent scale of C-melodic minor.  Now try doing that with the other versions of the melodic minor pentatonic and let me know how it works out.

These diagrams show how the {1, b3, 4, 5, 6} pentatonic pattern originates as the complement of a parent melodic minor scale.  If we take the excluded notes of the parent scale (i.e. the red dots) and transpose them down a semitone, we get our {1, b3, 4, 5, 6} pentatonic rooted at 1 of the parent scale.  If we transpose the excluded notes up a semitone, we get the same pentatonic pattern rooted at 2, and still fitting entirely inside the parent.

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## Mix and Match

Notice that {1, b3, 4, 5, 6} is also a subset of the Dorian mode of the major scale, so we could call it a “Dorian pentatonic” as well as a “melodic minor pentatonic.”  There is a difference in how it functions in those two context though.  If you’re thinking of 7-note Dorian as your parent scale, you can only form this pentatonic on the Dorian root: any attempt to transpose it will put you outside the Dorian note set.  However, if you’re thinking of 7-note melodic minor as the parent, then as we just saw, you can transpose this pentatonic between 1 and 2.  It’s also worth noting that the standard minor pentatonic fits inside the full melodic minor scale – you can play it on 2 – but you can’t transpose it anywhere else.  For example, if C-melodic-minor is your parent scale, you can play D minor pentatonic (D F G A C) and remain inside the parent.

In the diagram on the left below, you’ll see how the melodic minor pentatonic (as we’ve defined it) fits inside a major scale.  Here the pentatonic root is at position 2 of the major scale (or at 1 of the major scale’s Dorian mode).  In the diagram on the right, you’ll see how the standard minor pentatonic pattern fits inside a melodic minor scale.  Again, the pentatonic root is positioned at 2.  If we think of the same shape as representing a major pentatonic, its root would positioned at 4 of the enclosing scale.