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Sherlock Holmes, Hercule Poirot, The Hardy Boys, Nancy Drew, Encyclopedia Brown…come on, who doesn’t love a good mystery? Unless, of course, the mystery involves music theory! Point taken. Nevertheless, a good mystery deserves solving, especially when it holds the key to unlocking new musical expression. In today’s Quick Tip, John Proulx is your sidekick in unraveling the mystery of the half-whole diminished scale. This mysterious scale is integral to the improv language of great jazz pianists. So grab a note pad and set aside all presumptions as you gather clues about this most elusive scale. The simplicity of what you’ll discover may be the biggest surprise of all! You’ll learn:

• What is the Half Whole Diminished Scale?
• 3 Half-Whole Diminished Scales
• How to Use Half-Whole Diminished Scales
• Dominant Chord Symbols that Imply the Diminished Scale
• 12 Half-Whole Diminished Scale Exercises
• Appendix—Scale Construction: Asymmetrical vs. Symmetrical

In today’s lesson, John has laid out clues for solving this mystery so clearly that you’ll feel as if you’ve known the truth all along.

Let’s dive in!

Intro to the Half-Whole Diminished Scale

Let’s begin by listening to the sound of the half-whole diminished scale.

What a great sound! Now, let’s investigate how this scale is constructed.

What is the Half-Whole Diminished Scale?

The half-whole diminished scale is an 8-note scale used in jazz improvisation that is constructed of alternating ½ steps and whole steps beginning with a ½ step.

This scale is commonly referred to as the dominant diminished scale by jazz musicians. Also, a few alternative names are sometimes used for this scale, including diminished scale and octatonic scale. However, since there are two varieties of diminished scales (half-whole vs. whole-half), the term “diminished scale” by itself is somewhat ambiguous. Furthermore, although this scale includes 8 notes, it is certainly not the only scale construction to do so. In fact, any 8-note scale is technically an “octatonic scale.” Therefore, the terms dominant diminished and half-whole diminished are most preferable and will be used interchangeably throughout today’s lesson.

The 3 Half-Whole Diminished Scales

For most scales you encounter as a music student, there are 12 unique transpositions—12 major scales, 12 natural minor scales, etc. However, there are only 3 diminished scales (similar to the fact that there is only 1 chromatic scale). Check out the appendix for today’s lesson, Scale Constructions: Asymmetrical vs. Symmetrical, for a more thorough explanation on why there are only 3 diminished scales.

The 3 diminished scales are shown below as half-whole diminished scales starting on the notes C, D♭ and D♮.

In the next section we’ll investigate why jazz musicians are so fond of this interesting scale. But first, be sure to download the lesson sheet PDF and backing tracks for today’s lesson. These resources appear at the bottom of this page after logging in with your membership.

How to Use Half-Whole Diminished Scales

Jazz musician’s like to use half-whole diminished scales when improvising over dominant chords because they contains several alterations (♭9, ♯9, ♯, 11) that add a colorful sound. Check out the following example.

In general, the chord symbol C7 suggests C Mixolydian. However, the half-whole diminished scale has no avoid notes (a.k.a. “weak tones”) over a dominant chord. In fact, it is frequently called the dominant diminished scale for this reason. This scale is especially appropriate for dominant chords with a ♭9 or ♯9. However, because this scale contains the ♮13, it will clash with altered dominants containing the♭13 .

Dominant Chord Symbols that Imply the Diminished Scale

In the previous example, we learned that we can apply the sound of the dominant diminished scale in many circumstances when a regular dominant chord is indicated—for example, C7. However, we also want to be aware of chords symbols that specifically suggest this sound. Let’s examine this chord-scale relationship.

The chord suffix 7(♭9) is most commonly used to imply the dominant diminished sound. Technically speaking, the full chord symbol would be C13(♭9♯9♯11), although you are not likely to see such a symbol in print. Musicians and editors alike prefer chord symbols that represent sounds with the quickest recognition and the smallest footprint. However, all of the following symbols can be used to represent this chord-scale relationship:

Now that you’ve learned all about the half-whole diminished scale and its related chord symbols, let’s play some exercises to familiarize your ears and fingers with this classic jazz sound.

12 Half-Whole Diminished Scale Exercises

If you’re an exceptionally astute investigator, then you likely still have one nagging question. If there are only 3 half-whole diminished scales, then how can I play this sound in all 12 keys? Ah, sheer brilliance! Actually, each of the 3 dominant diminished scales has 4 corresponding dominant chords. In this section, you’ll play a simple scale exercise in all 12 keys to familiarize yourself with these relationships.

This section organizes the scale exercises into groups that sharing a common dominant diminished scale. Don’t worry if this is not immediately clear right now. It will become quite obvious once you set your fingers to play the exercises.

This lesson includes downloadable backing tracks for each exercise in this section. The backing tracks appear at the bottom of this page after logging in with your membership.

Exercises for Scale #1

Each of the exercises in this section use the notes of the C half-whole diminished scale. This scale corresponds the following dominant chords—C7, E♭7, F♯7, A7. In each example, you will play the scale ascending and descending over one of these dominant chords and resolve it in the context of a V7 to I▵7 chord progression.

C7 Resolving to F▵7

E♭7 Resolving to A♭▵7

F#7 Resolving to B▵7

A7 Resolving to D▵7

Great job! In the next section, you’ll play scale exercises for half-whole diminished scale #2.

Exercises for Scale #2

Each of the exercises in this section use the notes of the D♭ half-whole diminished scale. This scale corresponds the following dominant chords—D♭7, E7, G7, B♭7. In each example, you will play the scale ascending and descending over one of these dominant chords and resolve it in the context of a V7 to I▵7 chord progression.

D♭7 Resolving to G♭▵7

E7 Resolving to A▵7

G7 Resolving to C▵7

B♭7 Resolving to E♭▵7

Nice work! In the next section, you’ll play scale exercises for the final half-whole diminished scale.

Exercises for Scale #3

Each of the exercises in this section use the notes of the D half-whole diminished scale. This scale corresponds the following dominant chords—D7, F7, A♭7, B7. In each example, you will play the scale ascending and descending over one of these dominant chords and resolve it in the context of a V7 to I▵7 chord progression.

D7 Resolving to G▵7

F7 Resolving to B♭▵7

A♭7 Resolving to D♭▵7

B7 Resolving to E▵7

Well done! Now that you have played through all the exercises on today’s lesson sheet, be sure to also use the backing tracks to explore improvisation with the half-whole diminished scale.

Conclusion

Congratulations, you have completed today’s lesson and are likely no longer stumped by the perplexities of this mysterious little scale. If you enjoyed today’s lesson, then you’ll love the following resources also:

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Appendix—Scale Construction: Asymmetrical vs. Symmetrical

For most scales you encounter as a music student, there are 12 unique transpositions (ie: 12 major scales, 12 natural minor scales, etc). However, a most deceptive phenomenon behind the mystery of the diminished scale (whether half-whole or whole-half) is that there are only 3. How can this be? Remember, to solve a mystery, you must set aside all presumptions—things are not always as they first appear.

A better question to ask is, “Why are there 12 major scales and 12 minor scales?” The answer—both major and minor scales have an asymmetrical construction. In other words, a major scale does not divide the octave into a consistent pattern of recurring intervals (see below). By contrast, symmetrical scales (also called synthetic scales) have a recurring intervalic pattern. As a result, no one note in a symmetrical scale can be identified as the “tonic.” Without doubt, the most familiar scale is this family is the chromatic scale. The diagram below illustrates the asymmetrical and symmetrical properties of major and chromatic scales respectively. In the diagrams, each square represents a ½ step.

You wouldn’t say that there are 12 chromatic scales, would you? Of course not. Because of its symmetrical construction, there is only one chromatic scale.

Another Common Symmetrical Scale

Before we look at a scale diagram for the half-whole diminished scale, let’s first examine another symmetrical scale. The whole tone scale is a six-note symmetrical scale constructed entirely from whole steps. However, unlike the chromatic scale, there are 2 whole tone scales—one starting on C, and one starting on C#. Consider the following whole tone scale diagrams:

If you were to construct a whole tone scale beginning on the note D, would you obtain a 3rd transposition? No, you would wind up with the exact same notes as the C whole tone scale. The square illustrations above help you visualize this clearly. Therefore, symmetrical scales are also described as scales of limited transpositions. The point is, only asymmetrical scales have 12 transpositions.

Half-Whole Diminished Scales vs. Whole-Half Diminished Scales

Now, let’s consider the similarities and differences between the two types of diminished scales. The diagrams below show both versions.

These diagrams point out that both scales have the same recurring intervalic pattern, however they each begin at a different place in the pattern sequence. In fact, each of the 3 diminished scale can be expressed in two ways. For example, the C half-whole diminished scale can also be written as a B♭ whole-half diminished scale. Since both scales contain the exact same notes, they are essentially the same. This is especially true from a technical perspective—C half-whole diminished and B♭ whole-half diminished are played with the same piano fingering.

The difference between the two types of diminished scales (half-whole vs. whole-half) is their usage. For example, jazz musicians use C half-whole diminished to improvise over C7. However, C whole-half diminished is used over  Cdim7.

While the symmetrical nature of the diminished scale can be confusing, it does have one significant benefit. Since there are only 3 diminished scales, you can quickly learn them all and apply them to your playing!

 

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