The Half-Hole Hypermode

There are only three octatonic ("half-whole") diminished scales, and two have reasonably well-known applications over everyday chords. What about the third?

The term "octatonic scale", favoured by many writers int he classical tradition, has two demerits: it is inaccurate (there are many octatonic scales that aren't this) and it's imprecise (it names two quite different scales). So I will use the more jazzy terms "Half-Whole" and "Whole-Half" here.

The Half-Whole Diminished scale is constructed by an alternating sequence of semitones and tones, beginning with the former. This yields the chord tones 1 b2 b3 3 #4 5 6 b7. Thus it contains the 1 3 5 b7 of a dominant chord, plus the alterations b9, #9 and #11. This is the usual jazz application of this scale: as melodic material on a dominant chord with an altered 9 but unaltered 5.

The Whole-Half Diminished comes from the opposite alternation: whole tone followed by semitone. This produces the chord tones 1 2 b3 4 b5 b6 bb7 7. Thus it contains the notes of the familiar "fully" diminished chord, 1 b3 b5 bb7, along with some interesting colour tones (7, 9, 11, b13). This is its most common application. Personally I also enjoy it as a mild outside sound on a minor chord, particularly if it has a m6 or "minor major 7" quality.

The "other" one is the diminished hypermode, which comes is built from the same alternation but beginning with a whole tone that encloses the root. The chord tones are b2 2 3 4 5 b6 b7 7. It has no obvious tonal application; although it contains the 3 5 and b7 of a dominant chord it also contains the 7, 9 and 11, which together are not very happy bedfellows in conventional classical or jazz harmony. Similarly, the textbooks wouldn't recommend this as a sound on a major 7 chord (though I think that's a more convincing possibility).

Lately I've been listening hard to the way non-functional harmony is used in early 20th century classical music that isn't yet atonal. One thing I noticed it that you often hear a dominant chord with the tonic note already incorporated in it -- in the simplest case, for example, G7/C (G7 over a C bass note). This creates an odd sense of the cadence already having happened -- it "spoils" the ii-V-I in favour of something more ambiguous.

If you do this with the whole tone scale you get things like Scriabin's famous "Extase" chord. In my terms this comes from the "whole-tone hypermode" b2 b3 4 5 6 7, i.e. the whole-tone scale shifted by a semitone. This is the whole tone scale that belongs to the dominant chord, but we're thinking of it "suspended" over the tonic. If you put the tonic back in you get 1 b2 b3 4 5 6 7, which is usually called the Neapolitan scale.

Something very similar happens with the half-whole diminished scale suspended over a tonic, which you can hear in Debussy and Stravinsky as well as Scriabin. I derived some miscellaneous fingerings for those kinds of chord here, but without the tonic present.

Since it already has eight notes, adding a ninth (the tonic) gets us very close to the total chromatic, so that considering this as a nine-note scale might not be very productive. I'd prefer to just think of it as a hypermode, floating above the tonic whether the latter happens to be there or not.

Note that Neapolitan is a "minor scale" in the sense that is contains b3 and doesn't contain 3; it's a good sound on a normal minor chord. The Half-Whole Hypermode isn't, because it contains the 3; it's more like a "major scale", but so dissonant that it's probably best not to think of it that way.

Also notice how both of these symmetrical scales in their normal dominant uses imply a natural 5th but altered 9th, in contrast to the crude jazz pedagogy that recognises only two dominants, the "altered" and the "non-functioning" or "Lydian dominant". In fact people have known for a long time that precisely which alterations are present can be crucial to getting the harmony right, and that real life may be more complicated than they let on in college.