The Half-Whole Harmonic and Melodic Minor Scales

The Half-Whole (or Whole-Half) Diminished scale has eight notes. What happens if we delete one? It turns out there are only two ways to do this, but each produces a seven-note scale with a full complement of modes.

C Half-Whole is C-Db-D#-E-F#-G-A-Bb. Dropping the Bb or the A are the two possibilities -- because of the symmetry of the scale, dropping any of the other notes just creates modes of these two.

Dropping Bb gives us 1-b2-b3-b4-b5-bb6-bb7, which I call Ultra Locrian bb7, although that name doesn't actually make a lot of sense. More interestingly its modes include a couple of melakatas, one of which is the "Hungarian Minor" that's related to those Hungarian pentatonics I explored a while ago. The easiest of its modes to find might be Harmonic Minor b5. I'm inclined, therefore, to call this "Half-Whole Harmonic Minor".

Dropping A instead gives us 1-b2-b3-b4-b5-bb6-b7, which is a mode of Melodic Minor with a b5 (note the similarity with Harmonic Minor b5). Of course, I'm tempted to call this "Half-Whole Melodic Minor". This scale group doesn't contain any melakatas, making it a bit more exotic.

I'm inclined to think of these in terms of the Forte 4-3 they both contain. Half-Whole Harmonic Minor is formed from 4-3 plus the "Phrygian trichord" of 1-b2-b3. Half-Whole Melodic Minor is formed from 4-3 plus the "minor-major trichord" of 1-b3-7, a minor-major seventh with no fifth. If you find this viewpoint useful, a little experimentation will show how to fit the two parts together in the right way; leaving a whole tone between the top of the 4-3 and the bottom of the trichord does the trick.

Yet another way to think of these is to notice each has one minor third interval: so just play the ordinary octatonic scale but remember where the minor third is. This might be useful for the more visual players; I can imagine using it at the keyboard more than on guitar but your mileage may vary.

On guitar I'd be looking for combinations of the diminished, half-diminished, dominant and minor arpeggios that can be found in the parent scale, since these are easy to "see" and usually cohere well with other things that are going on in the music, so they help us to "ease into" the new sound.

Perhaps these are the absolute simplest ways to find these scales, at least on guitar:

  • Half-Whole Harmonic Minor is a minor triad (or m6 chord) at the root and a m7 chord at the b5
  • Half-Whole Melodic Minor is a minor triad (or m7 chord) at the root and a dominant 7 chord at the b5

We should have a look at the modes of these scales, since they're pretty easy to find and play. In each case, a mode will be either Half-Whole or Whole-Half with one note omitted. Don't underestimate the fruitfulness of skipping a note! These might not be things you want to pour deep theoretical study into but they contain many melodic ideas that you might not find any other way.

In each case, the modes fall into two groups -- those that come from dropping a note from the Half-Whole scale, 1-b2-b3-b4-b5-5-6-b7 and those that come from dropping a note from the Whole-Half scale, 1-2-b3-4-b5-b6-6-7.

Modes of "Half-Whole Harmonic Minor"

Those that come from dropping a note from the Half-Whole scale:

  • Dropping b7 gives 1-b2-b3-b4-b5-5-6 -- Ultra Locrian bb7. Minor 6 chord at the root.
  • Dropping 5 gives 1-b2-b3-b4-b5-6-b7 -- Super Locrian Natural 6
  • Dropping b4 gives 1-b2-b3-#4-5-6-b7 -- Shadvidamargini. Minor 7 at the root.
  • Dropping b2 gives 1-#2-3-#4-5-6-b7 -- Nasike Bhushani. Dominant 7 at the root.

Those that come from dropping a note from the Whole-Half scale -- none of these contain any of the common seventh chords at the root, which makes them quite intriguing:

  • Dropping b3 gives 1-2-#3-#4-#5-6-7 -- Lydian Augmented Sus 4. A suspended major 7 sound.
  • Dropping b5 gives 1-2-b3-4-#5-6-7 -- Augmented Minor
  • Dropping 6 gives 1-2-b3-4-b5-b6-7 -- Harmonic Minor b5

Modes of "Half-Whole Melodic Minor"

Those that come from dropping a note from the Half-Whole scale:

  • Dropping 6 gives 1-b2-b3-b4-b5-bb6-b7 -- Super Locrian bb6. Dominant 7 chord at the root.
  • Dropping b5 gives 1-b2-b3-b4-5-6-b7 -- Natakapriya b4. Minor 7 chord at the root.
  • Dropping b3 gives 1-b2-3-#4-5-6-b7 -- Ramapriya. Dominant 7 chord at the root.

Those that come from dropping a note from the Whole-Half scale -- no minor or major triads at the root for any of these, in fact all four contain a fully diminished seventh chord at the root instead:

  • Dropping 7 gives 1-2-b3-4-b5-b6-bb7 -- Jhankaradhvani b5
  • Dropping b6 gives 1-2-b3-4-b5-6-7 -- Melodic Minor b5
  • Dropping 4 gives 1-2-b3-#4-#5-6-7 -- Lydian Minor #5
  • Dropping 2 gives 1-#2-#3-#4-#5-6-7 -- Susdim Major

Incidentally, Lydian Minor #5 is unaccountably called "Lydian b5" in the book. Sorry about that; there are a few odd scale names like that, but unfortunately I no longer have the technology set up to update it so they're left as an exercise for the sharp-eyed reader.