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Strictly proper scales in files section

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

6/7/2006 9:16:17 PM

Some of the strictly proper scales seem quite interesting to me; I've
added a bunch of 22-et scales. The 7 and 8 note ones seem especially
interesting.

🔗Carl Lumma <ekin@lumma.org>

6/7/2006 9:51:05 PM

At 09:16 PM 6/7/2006, you wrote:
>Some of the strictly proper scales seem quite interesting to me; I've
>added a bunch of 22-et scales. The 7 and 8 note ones seem especially
>interesting.

Keep us posted.

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

6/7/2006 11:31:21 PM

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> At 09:16 PM 6/7/2006, you wrote:
> >Some of the strictly proper scales seem quite interesting to me; I've
> >added a bunch of 22-et scales. The 7 and 8 note ones seem especially
> >interesting.
>
> Keep us posted.

I'd be interested in any comments on what is in the files section now.
I just found out that there are 181 7-note strictly proper 31-et
scales, which means I should do some cherry-picking. The first cherry
I picked, on the basis of amount of harmony, turns out to be the
diatonic scale. That's no surprise, and we get the usual suspects such
as harmonic minor and its inverse also.

🔗Herman Miller <hmiller@IO.COM>

6/8/2006 8:18:34 PM

Gene Ward Smith wrote:
> --- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
> >>At 09:16 PM 6/7/2006, you wrote:
>>
>>>Some of the strictly proper scales seem quite interesting to me; I've
>>>added a bunch of 22-et scales. The 7 and 8 note ones seem especially
>>>interesting.
>>
>>Keep us posted.
> > > I'd be interested in any comments on what is in the files section now.
> I just found out that there are 181 7-note strictly proper 31-et
> scales, which means I should do some cherry-picking. The first cherry
> I picked, on the basis of amount of harmony, turns out to be the
> diatonic scale. That's no surprise, and we get the usual suspects such
> as harmonic minor and its inverse also.

It might be useful to show a diagram for each of these scales on the triangular 5-limit grid. For example, the nine 7-note strictly proper scales of 22-ET:

. 7a. 7b. 7c. 7d. 7e.
. (5) (4)
. 7 4 6 3 7 3 7 3 3
. 2 6 3 1 5 2 1 5 2 6 1 5 2 6 4 1 5 2 6
. 1 5 4 4 7 4 7
. (7)
.
. 7f. 7g. 7h. 7i.
. (7) (4) 3 7
. 2 3 (2) 3 7 1 5 6 5 2
. 4 1 5 1 5 6 7 4 3 4 1
. 6 7 4 2 6
. (2) 2

You can get some idea of the harmonic potential of the scales, and see at a glance which familiar scales if any they may resemble (for instance 7d:)

. F#
. D A E B
. C G