Octatonic scales & the diminished 7th

[Joe_Campbell]

I've been learning about octatonic scales, and I came across an interesting bit of information: that any octatonic scale can be broken into two diminished 7th chords, as long as those chords are not enharmonic equivalents.

However, it occurred to me that since all divisions in dim. 7th chords are equal, is it arbitrary which root is picked for either chord? Or is there a grammatically 'correct' root for either chord (i.e. the simplest?). I also noticed that since notation can be personal preference for octatonic scales (like where to place the chromatic unison), does this have any bearing on the above 'problem' as well?

edit - fixed an incorrect word

[karlhenning]

You are millimeters away from Messiaen's observation in classifying the octatonic scale as one of his "modes of limited transposition."

[Joe_Campbell]

I remember hearing about that. The whole tone is also one, no? I'm guessing the octatonic scale must be 3 semitones removed before it repeats itself?

[greg]

it's all right here, btw:

http://en.wikipedia.org/wiki/Modes_of_limited_transposition

I've been learning about octatonic scales, and I came across an interesting bit of information: that any octatonic scale can be broken into two diminished 7th chords, as long as those chords are not enharmonic equivalents.

However, it occurred to me that since all divisions in dim. 7th chords are equal, is it arbitrary which root is picked for either chord? Or is there a grammatically 'correct' root for either chord (i.e. the simplest?). I also noticed that since notation can be personal preference for octatonic scales (like where to place the chromatic semitone), does this have any bearing on the above 'problem' as well?

So...... where did you read about octatonic scales in the first place? I can't think of any book that actually explains them- all i have is a guitar/keyboard book of scales with a few of the 8-tone scales.

[karlhenning]

I remember hearing about that. The whole tone is also one, no?

Yes, indeed.

I'm guessing the octatonic scale must be 3 semitones removed before it repeats itself?

Correct;  or put another way, there are a total of three distinct transpositions of the octatonic scale.

[Joe_Campbell]

So...... where did you read about octatonic scales in the first place? I can't think of any book that actually explains them- all i have is a guitar/keyboard book of scales with a few of the 8-tone scales.

Theory and rudiments introductory. I had to learn about the octatonic scale as well as pentatonic, whole tone, blues, etc...I also had to learn the all the modes (e.g. Phrygian)...those are tricky!

FWIW, does anyone have an answer for my first question? Is there a 'correct' diminished chord to 'choose' when ripping apart an octatonic scale?

BTW, thanks for the info, Karl

[karlhenning]

FWIW, does anyone have an answer for my first question? Is there a 'correct' diminished chord to 'choose' when ripping apart an octatonic scale?

Spelling likely depends on context . . . and legibility will be the rule.

[greg]

Spelling likely depends on context . . . and legibility will be the rule.

That's what i'd say. If it looks right, you should be able to get away with it.

[lukeottevanger]

[cough] the locus classicus of triads and diminished sevenths derived from an octatonic context...[/cough]  0:) 0:) 0:)

[Joe_Campbell]

[cough] the locus classicus of triads and diminished sevenths derived from an octatonic context...[/cough]  0:) 0:) 0:)

Hmm...I'd love to try and play that. You don't have a pdf floating around do you?

[lukeottevanger]

Esnips seem to have changed the way they lay things out, but I think there's a download button underneath the image. The piece comes from a set of children's pieces I wrote in 2003 (more Kinderszenen than Album for the Young). You can find links to all the scores and recordings of these pieces and many others in the first post of 'my' thread.

BTW, the gaps at the top of the scores to these children's pieces are supposed to contain a picture which never made it to the PDFs, though the 'deluxe edition' (i.e. the one I could crank out at home) does have them.