Just a Couple of Just Scales

Hello, all, and submitted for your inspection and comment a "just
major" and "just minor" 12-tone, 7-limit scale:

C 1
C# 21/20
D 9/8
Eb 25/21
E 5/4
F 4/3
F# 7/5
G 3/2
G# 63/40
A 5/3
Bb 25/14
B 15/8
C' 2

C 1
Db 15/14
D 9/8
Eb 25/21
E 5/4
F 4/3
Gb 10/7
G 3/2
Ab 100/63
A 5/3
Bb 25/14
B 15/8
C' 2

Each of the above scales contain the diatonic semitones 15/14, 16/15
and 200/189 and a 21/20 chromatic semitone. The scales contain the
familiar 4:5:6 and 10:12:15 triads as well as triads that are close to
their 12-TET brethren. Don't know if these scales are useful musically.

ham_45242 wrote:

> The scales contain the
> familiar 4:5:6 and 10:12:15 triads as well as triads that are close to
> their 12-TET brethren. Don't know if these scales are useful musically.

They certainly are. If you také a "meantone-like" approach and consider 1/1 as C, then the first scale can be understood as a chain of differently sized fifths from Eb to G# and the second scale as a chain from Gb to B. If you have a copy of Manuel's scale archive, there you can find three scales of mine which also used 7-limit intervals in this "meantone-like" way. The files are "parizek_7lmtd1.scl" (Eb to G# if 1/1 is D), "parizek_7lqmtd2.scl" (the same), and "parizek_ji1.scl" (Eb to G# if 1/1 is Eb).

Petr

ham_45242 wrote:
> Hello, all, and submitted for your inspection and comment a "just
> major" and "just minor" 12-tone, 7-limit scale:
>
> C 1
> C# 21/20
> D 9/8
> Eb 25/21
> E 5/4
> F 4/3
> F# 7/5
> G 3/2
> G# 63/40
> A 5/3
> Bb 25/14
> B 15/8
> C' 2
>
>
> C 1
> Db 15/14
> D 9/8
> Eb 25/21
> E 5/4
> F 4/3
> Gb 10/7
> G 3/2
> Ab 100/63
> A 5/3
> Bb 25/14
> B 15/8
> C' 2
>
> Each of the above scales contain the diatonic semitones 15/14, 16/15
> and 200/189 and a 21/20 chromatic semitone. The scales contain the
> familiar 4:5:6 and 10:12:15 triads as well as triads that are close to
> their 12-TET brethren. Don't know if these scales are useful musically.
> That has quite a few intervals in common with my own 11-limit JI arsenal. A partial set for a combined major and minor would contain 25 ratios in 17 pitch classes (and I assign 1/1 and 2/1 to D/Re/Yegah-Neva to keep everything symmetrical):

D - 1/1
D# - 21/20 or 28/27
Eb - 16/15
E - 9/8 or 10/9
F - 6/5 or 32/27
F# - 5/4
Gb - 9/7 or 14/11
G - 4/3
G# - 7/5
Ab - 10/7
A - 3/2
A# - 14/9 or 11/7
Bb - 8/5
B - 5/3 or 27/16
C - 16/9 or 9/5
C# - 15/8
Db - 40/21 or 27/14
D - 2/1

It's part of a "modified Partch set" derived from a rationalized 41-out-of-72-edo Miracle ("studloco") temperament, 41 ratios in 31 pitch classes plus 11/10 and 20/11 for a total of 43 ratios. The above scale also includes a couple of 11-versus-7 "faux Pythagorean" ratios, 14/11 and 11/7.

Anyway, I don't like to use ratios with three-digit numerators and denominators, since they don't really fit into the 72-equal mold, and I can accept fifths and fourths that are a septimal kleisma or similar interval out of tune for my own needs. It is definitely good to have on hand those 25-vs.-7 "meantone" ratios such as the 28/25 major second and 25/21 minor third.

For the record, I'm not at all a hardcore JI composer; I'm mostly a specialist in 31-, 41-, 53- and 72-equal temperament right now. ~D.