Re: [tuning] Re: Rothenberg q

Jason!
Wilson does not limit his principle of MOS to Fifths in that any interval can be used, and
circled around until a two interval pattern in formed. Wilson also explain very basic bedrock
scales that are omitted in Rothenbergs case such as the pentatonics formed out of the
diatonics. That it includes such scales as f a b c e. That these exist historically cannot be
overlooked. Another problem with the Rothenberg (out of just being not understandable to the
average musician) is those scales which he thinks are of importance like the whole tone (and
the other symmetrical scales shows) have had limited historical use. His aim is close but
misses.
Along side MOS is the concept of Constant Structures defined as a tuning system where each
interval occurs always subtended by the same number of steps. This in turn explains many just
scales and even such things as to why and how Partch filled in the large areas of his tunings
with smaller intervals.

Jason_Yust wrote:

> Kraig,
>
> Wilson's diagrams of scales generated by series of equal intervals
> elegantly show, I think, that the series of fifths (approximate 3/2's) are
> special in generating the most stable (in Rothenberg's sense) scales. I
> haven't quite pinpointed the mathematical reason for this but I think it
> follows from the fact that the fifth (actually the fourth) arithmetically
> divides the octave (in the Greek sense).
>
> jason

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Jason Yust wrote,

>Wilson's diagrams of scales generated by series of equal intervals
>elegantly show, I think, that the series of fifths (approximate 3/2's) are
>special in generating the most stable (in Rothenberg's sense) scales. I
>haven't quite pinpointed the mathematical reason for this but I think it
>follows from the fact that the fifth (actually the fourth) arithmetically
>divides the octave (in the Greek sense).

Actually, this latter fact, though acoustically relevant, is not relevant to
the Balzano/Rothenberg properties of scales. These properties are pretty
similar to what Erv Wilson was getting at with his MOS idea, and as you can
see in the Wilson archives and more recent explorations by Carl Lumma, Dave
Keenan, and others, many acoustically unfavorable intervals, and/or
intervals very far from a fifth or fourth, can be used as generators for
scales which look favorable from an MOS/Balzano/Rothenberg point of view.