RE: [tuning] 20 equal

>Interesting. Never heard of Zweifel.

Check the Tuning Bibliography.

>Did he use the same method of
>pentads, as well?

I don't know.

>(BTW, did you happen to get a chance to actually try these out
>on the ears at all? I'm doubting it as your probably answering on the
>fly from work or something... I myself found the results to indeed be
>pretty interesting.)

Can you create a short MIDI-file or something?

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Paul H. Erlich wrote,

> Check the Tuning Bibliography.

Wow, I must not have been here in quite a while, because it seems to
me like there are about a million more direct links to articles that
are available online and whatnot... What a treasure-trove!:

<ftp://ella.mills.edu/ccm/tuning/papers/bib.html#B>

I couldn't seem to dig up anything on Zweifel's "Generalized Diatonic
and Pentatonic Scales: A Group-Theoretic Approach" (which I'm assuming
must be the article you were referring to) online though.

> Can you create a short MIDI-file or something?

Hopefully I'll get something up at John Starrett's TuningPunk site
eventually.

Dan

Dan,

Your 11-tone mode is the same as Balzano's. Zweifel's generalised
diatonic scale is a mode of it; the only difference is that B is
one step lower (1080 cents). Zweifel uses exactly the same letters
as you. In the paper he gives a number of arguments why he considers
this scale a generalisation of the major mode in 12-tET. The fact that
20=4x5 and 12=3x4 being one of them. Zweifel's notation is also built
into Scala (set notation z20).

Manuel Op de Coul coul@ezh.nl