Wednesday, February 15, 2006

Wednesday Question: The Octatonic Scale

I think Wednesday will be a better day than Friday for the weekly question. On Friday's I'm usually trying to get stuff done before the weekend: grading quizzes and homework, preparing next week's lectures, looking at materials for next week's committee meetings, etc. So I don't have time to blog until later at night, when I'm at home without access to my books or other research tools beyond Google and my own brain. Thus, a switch to Wednesday, as long as it doesn't interfere with my running.

Today's question is about the octatonic scale. As the name implies, this scale has eight different pitch classes, one more than the typical major or minor scale. It is constructed by alternating half steps and whole steps, and requires that one pitch name gets repeated. An example would be: C Db Eb E F# G A Bb. In this case the E is repeated as both a flat and natural. Because the scale can be divided into halves that contain identical intervals, it is called symmetric. Major and minor scales are not symmetric, pointing clearly to the tonic note due to irregular patterns of intervals (Whole - Whole - Half - Whole - Whole - Whole - Half for ascending major). The two half steps are significant landmarks, separated by an unequal number of whole steps (2 versus 3). Thus a half step heard in a piece of music based on the major scale helps us to locate where we are on the scale, in relation to tonic. The octatonic scale does not have significant landmarks, so it does not locate tonic notes well. See my previous post on this.

Another feature of the octatonic scales symmetry is the fact that only three unique collections exist, compared to twelve for the diatonic scales. If we transpose the above octatonic scale up by a half step, we get C# D E F G Ab Bb B. Another half step gives us D Eb F F# G# A B C. Each of these three scales are unique in the collection of notes. But another half step transposition gives Eb E F# G A Bb C Db, which is a reordering of the first scale. Enharmonic spellings, such as switching Eb with D#, don't matter with the octatonic scale which is fundamentally based on the equal tempered system.

The octatonic scale is used in jazz improvisation, called the diminished scale because the form starting with a whole step will spell a diminished seventh chord: C D Eb F Gb Ab A B. The first, third and fifth notes of the scale are the C diminished triad, and the A added makes an A fully-diminished seventh chord.

20th century art composers use the octatonic scale to provide a logical organization of pitches that doesn't evoke tonality but does have an aura of familiarity. There are debates as to how significant the scale is to Stravinsky's music, with claims ranging from the Petroushka chord (C major and F# major together) as a subset of the octatonic scale to Pieter van den Toorn's claims that it abounds in all of Stravinsky's music.[1] Other composers who have used obvious forms of the octatonic scale include Bela Bartok, Claude Debussy, and Olivier Messiaen (who called it one of his modes of limited transposition).

[1] P.C. van den Toorn: The Music of Igor Stravinsky (New Haven, CT, 1983)


Michael J. West said...

Is the octatonic scale used as a mode in jazz improvisation? I.e., would a jazz solo that uses the octatonic be considered modal jazz?

I'm quite curious. I don't suppose that you have an example of a diminished-scale jazz piece?

Skwid said...

Apostrophe abuse, apostrophe abuse! Fridays, anyone?

Although technical music stuff at this level blows my little mind, I still find it strangely compelling.

Scott Spiegelberg said...

Michael, octatonic scales would not be used for modal jazz. That genre pretty strictly uses the modal diatonic scales, though sometimes modified. The strict diatonic modes are Ionian, Dorian, Phrygian, Lydian, Mixolydian, and Aeolean. Jazzers will sometimes use a Lydian-Mixolydian hybrid. Octatonic scales are used more with traditional changes, as a great way of blowing over a diminished chord or an altered chord. As for examples, they would be in the improv, not so much in the melodies. I did compose a piece in college that was based on the octatonic scale, which was successful. I treated a descending form as the skeleton for my melody.

Skwid, I even debated that apostrophe briefly, before deciding it wasn't worth checking. I'm glad you like the topic. Now you know how I feel when you and the others go into high realms of CS and IT.

Tim Rutherford-Johnson said...

Ah, the octatonic scale, my favourite of all scales. A neat trick for all church organists: take four major triads a minor third apart (eg C-Eb-F#-A), and just improvise harmonies overlapping these trids. Bingo - instant Messiaen!

Scott Spiegelberg said...

Tim, as long as you use additive rhythm or a good isorhythmic pattern as well. Of course, I know plenty of congregations that would not appreciate instant Messiaen, much less the real thing.