Whole-Tone Harmony Part I

Imagine your instrument lost exactly half of its notes, and specifically every alternate one. It might make sense to say you now had an instrument turned not in 12-TET but in 6-TET. In a society that only had such instruments, which harmonies would be available to them?

For the moment my purpose is just to list all the chords and see what we get. By "chord" here I just mean "more than one note that can be sounded together". For ease of use I'll label the chords with note-names from C Whole Tone (C-D-E-F#-G#-A#) and also numerically (choosing one of the notes as the 1 and expressing the chord as something related to tonal harmony where possible).

We'll deal with the unique 5-note chord first, C-D-E-F#-G#, a cluster of whole tones with one missing. We could call this the "5-W cluster", where W stands for whole tone.

The smallest chords are the dyads (two notes), and we have only three of these:

  • The major second or "2-W cluster": C-D (1-2)
  • The major third: C-E (1-3)
  • The tritone: C-F# (1-b5)

Continuing after the tritone just gives us the other two in inversion. But these are not enough on their own to build a harmonic language, so we'll pass on from them.

This does, however, tell us that we can obtain three 4-note chords, which come from deleting each of the dyads in turn:

  • The "4-W cluster": E-F#-G#-A# (1-2-3-b5)
  • The augmented add 9: D-F#-G#-A# (1-3-#5-9)
  • The 7b5: D-E-G#-A# (1-3-b5-b7)

This leaves four three-note chords:

  • The "3-W cluster": C-D-E
  • The "sus 2 b5": C-D-F#
  • The "sus 4 b5": C-D-G#
  • The augmented triad: C-E-G# (1-3-#5)

Unless someone tells me I missed one, this is the complete roll-call: 10 chords, of which three are mere dyads. So only seven chords that are really worthy of the name.

I think we could divide these seven into two pairs and an odd one out:

  • The two clusters: 4-W and 5-W
  • The two augmented chords: the augmented add 9 and augmented triad itself.
  • The two suspensions: the sus 2 b5 and sus 4 b5.
  • The dominant 7b5.

Schoenberg -- in chapter 20 of the harmony book -- suggests that the whole-tone scale may have arisen in Western music either from appoggiaturas to the augmented triad (augmented add 9) or from altered dominants (7b5), so these two may have historical precedence. They're also probably the most useful in a modern tonal setting such as jazz or film music.

The clusters are, I think, easy to play and hear but hard to say much about; they're clusters, they sound good but they need a context to make any sense. They're much less rough than semitone clusters, of course. I tend to use them as colours, usually under or above a melody note to give it that hard, bright, Messiaen-like "shimmer".

On an acoustic piano you can even silently depress the cluster, hold the middle pedal and then play to get a "whole tone reverb" kind of effect, a technique that many mid-century composers experimented with. That also works nicely on Pianoteq; no other software piano can do this as far as I know. (You can get a similar effect from a convolution reverb with a custom-made impulse response but that's nowhere near as flexible in performance.) You can do this with any chord, of course, but these "W-clusters" work particularly well to my ears.

That leaves those weird "suspensions", which have Forte number 3-8A ("sus 2 b5") and 3-8B ("sus 4 b5"). In common practice harmony the first of these would be called the "Italian sixth". There it functions like a rootless V-of-V dominant chord; C-D-F# "wants" to resolve to C#7, which resolves to F# major.

The other ("sus 4 b5") has no tonal interpretation I'm aware of. These two are inversions of each other -- hence the "A" and "B" designations -- which means they're sometimes treated as equivalent in atonal practice. But the major and minor triads are related in the same way, so this sense of equivalence is far from universal.

Those two chords are certainly interesting but overall this analysis suggests that whole-tone harmony is pretty impoverished. Not only are there only a few available chords but all of them (except perhaps the clusters) have a strongly dominant character, giving progressions of chords in this harmonic system their famous "directionless" or "floating" sound. I'm not aware of any music that's been written entirely in this harmony (i.e. effectively in 6-TET) other than pedagogical demonstrations or exercises. Schoenberg agrees; writing in this way would, he thinks, "bring about an emasculation of expression, erasing all individuality".

Three possibilities seem to present themselves. The first is that we can use whole-tone harmony sparingly as a seasoning for harmony in some other system. This is very commonly done. In a tonal setting it appears as a way to prolong the dominant chord before a resolution (Scriabin's Poem of Ecstasy being the supreme example of that). The second possibility is to remain in whole-tone harmony but season it with additional notes. That will be the subject of the next post.

The third is worthy of a short note for now and a follow-up later: combining the whole-tone scale with its complement, the other whole-tone scale. Of course, this produces the total chromatic. But it may be that combining chords from these two disjoint harmonic systems may produce more movement and variety. When improvising I tend to automatically do this, shifting between the two whole-tone scales as a way to keep the overall sound consistent while relieving the sameness of the single scale that can lead to boredom. As I said, I'll come back to this; I want to creep up on it by simpler means first.