Re: Paul on 19 and 31 scale-subsets

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: RE: Scales found within 19 eq and 31 eq
>
> Bob Valentine wrote:
>
> > An alternative that makes less theoretical sense but has a few
> > nice properties comes from saying "what if 31tet had sharps higher
> > than flats", and then building the sequence.
> >

Another way to say it was, take C C# D Eb E F F# G Ab A Bb B and
replace the accidentals with their enharmonic inequivalents(!)
But then I wrote the number sequence wrong, it is

3 2 2 3 3 3 2 2 3 2 3 3
C Db D D# E F Gb G G# A A# B

Beginning to grok the lattice diagrams, I see that the
Fokker/Lumma/Keenan scale would be descrribed as.

3 2 2 3 3 2 3 3 2 2 3 3
C Db D D# E F F# G Ab A A# B

Another one to plug in and spin! This also gets rid of the interesting
9/31 masquerading as both a "major" and as a "minor" third in the
tuning I proposed (D#-Gb, Gb-A#).

Now, those interested in 19 could just plug in '2' and '1' for all these
numbers, right?

(good stuff snipped, I'll look at wafso-just as well, whats a wafso?)

>
> You can get more consonant 7-limit tetrads by using 12 notes out of
> 22-equal. But first, how do you like the 7-limit tetrads in 22-equal?
>

Now that I'm getting facile with my available tuning tables technology,
I'll try two of the 12-of-N that were presented for 22.
2 2 2 2 1 2 2 2 2 2 2 1
and 2 2 2 2 2 1 2 2 2 2 2 1.

I think the issue will be whether I like the triads.

thanks,

Bob Valentine

Bob Valentine wrote,

>Beginning to grok the lattice diagrams, I see that the
>Fokker/Lumma/Keenan scale would be descrribed as.

> 3 2 2 3 3 2 3 3 2 2 3 3
>C Db D D# E F F# G Ab A A# B

>Another one to plug in and spin! This also gets rid of the interesting
>9/31 masquerading as both a "major" and as a "minor" third in the
>tuning I proposed (D#-Gb, Gb-A#).

>Now, those interested in 19 could just plug in '2' and '1' for all these
>numbers, right?

Well, the note names would come out the same, but the maximum error in the
7- (and 9-) limit harmonies would jump from 6.0 cents to 21.5 cents. As the
presence of the 6 consonant 7-limit tetrads is the motivation for the Keenan
scale, it would lose much in the translation.