7 Scale Systems you might want to know

[SteveCS]

[2,5} is two half tones, 5 whole tones .

That looks more like an attempt at a major scale, or one of it's modes - they would all be the same using just tone/semitone count and including the octave. The octave is not included in Interval Vector derivation as it is the same pitch class as the tonic (e.g. C0 = C1 = Cn). The Interval Vector for the major scale is 2, 5, 4, 3, 6, 1

 

[IamGroot]

It is not an attempt. It is an accurate summary of the intervals found in a major scale and all its modes.

Your prior answers are focused on music theory. My focus is just mathematical -how many intervals and what size, which is a counting exercise.

 

[mambo4]

Do you thin it's possible to apply math to theory in a fashion that might yield a new, musically usable insight?

 

[Bob_Ross]

Do you thin it's possible to apply math to theory in a fashion that might yield a new, musically usable insight?

Google "the integer model of pitch" and/or "set theory in music". It's already been done, rather extensively, and for almost 100 years.

 

[mambo4]

I know that "apply math to theory" has been done for ages
It's the "musically usable insight" I have less experience with.

I always think back to George Russel's work and consider the actual musical results of all the work he did.
Beauty is in the ear of the beholder and all that, but I was never drawn to the sounds it yieled.

 

[Bob_Ross]

Beauty is in the ear of the beholder and all that, but I was never drawn to the sounds it yielded.

Yeah, I would suggest that liking George Russell's music* -- or any composer's music -- has less to do with whether or not they used math [sic] and more to do with their general sensibilities as an artist.

Have you listened to any music by Anton Webern, Arnold Schoenberg, Charles Wuorinen, Reginald Smith Brindle, Milton Babbitt, Iannis Xenakis, or Donald Martino? Or the later works of Igor Stravinsky? They all used the integer model of pitch to some extent in their works specifically because it allows certain mathematical operations to generate related musical materials. But it's still up to the individual composer to integrate those materials into a musically coherant composition, and everyone's process at that point is different. No one would mistake a Webern piece for a Babbitt piece, even though they both were using serial (ordered) dodecaphonic matrices.


*I would also suggest that George Russell's music has less to do with math per se than it does his own misunderstanding of how math and physics impact our perception of intervals. And I say this as someone who studied with George Russell in the early 1990s.

 

[mambo4]

Have you listened to any music by Anton Webern, Arnold Schoenberg, Charles Wuorinen, Reginald Smith Brindle, Milton Babbitt, Iannis Xenakis, or Donald Martino? Or the later works of Igor Stravinsky?

Nope! Stravinsky is the only one I could name a piece from.
adding these to my playlist, tho.

 

[IamGroot]

Do you thin it's possible to apply math to theory in a fashion that might yield a new, musically usable insight?

Probably not. At least, not with the 12 tone, equal tempered scale system.