A parapyth version of MET-24

MET-24 is a scale in 1024edo, with four step sizes. There doesn't seem to be much if anything lost by reducing the number of step sizes to three, and making of it a parapyth temperament Fokker block. Below I present such a Fokker block, in parapyth POTE, which I'm also calling MET-24 unless Margo objects since it seems to be more or less the same scale.

! met24pote.scl
!
MET-24 parapyth temperament Fokker block in POTE tuning
24
!
58.33846
126.99416
185.33261
207.71262
266.05107
288.43108
346.76953
415.42523
473.76369
496.14369
554.48215
623.13785
681.47631
703.85631
762.19476
830.85047
889.18892
911.56892
969.90738
992.28738
1050.62584
1119.28154
1177.62000
1200.00000
!
!! met24trans.scl
!!
!MET-24 2.3.7 transversal
! 24
!!
! 28/27
! 2187/2048
! 567/512
! 9/8
! 7/6
! 32/27
! 896/729
! 81/64
! 21/16
! 4/3
! 112/81
! 729/512
! 189/128
! 3/2
! 14/9
! 6561/4096
! 1701/1024
! 27/16
! 7/4
! 16/9
! 448/243
! 243/128
! 63/32
! 2/1

Hi, Gene!

This is absolutely great, and my one small footnote to this really
fantastic example is that, at least from my perspective, it's
quite close to MET-24 but just about identical to O3!

But MET-24 was your template for a 24-note version of the POTE,
so "met24pote.scl" tells the story just as it happened.

Bravo!

> MET-24 is a scale in 1024edo, with four step sizes. There
> doesn't seem to be much if anything lost by reducing the
> number of step sizes to three, and making of it a parapyth
> temperament Fokker block. Below I present such a Fokker block,
> in parapyth POTE, which I'm also calling MET-24 unless Margo
> objects since it seems to be more or less the same scale.

Looking at this in Scala confirmed that it's taking the general
24-note form of MET-24 and applying it to the POTE, which is
great! So if you associate that general form with MET-24, the
naming certainly fits. The main distinction I might make, as a
long article I posted just before seeing this may explain, is
that O3 has a yet closer generator: 703.871 cents if we take the
average of the 22 usual fifths in the 1024-EDO version.

But if MET-24 was the tuning that gave you idea for this Fokker
block form, then that's the history, and your "MET-24 parapyth
temperament Fokker block in POTE tuning" is exactly correct!

And I agree that reducing the number of step sizes to three is
fine; this also happens when I produce "canonical" or "smooth"
versions of MET-24, O3, etc., without the vagaries of 1024-EDO.
Something I may have just learned is that with the step sizes
reduced to three, I actually have a 24-note Fokker block
temperament -- interesting!

Your POTE version of MET-24 or O3 also illustrates some very
useful choices for optimization that complement those of MET-24
or O3, and show people that they do have a choice: for example,
leaning toward a slightly wider spacing, with considerable
benefit to 9/7 in particular and 2-3-7-9 in general. That's very
valuable, both to show a fine optimization, and how people can do
fine-tuning in slightly different ways within the spirit of the
genre, which this very much expresses!

! met24pote.scl
!
MET-24 parapyth temperament Fokker block in POTE tuning
24
!
58.33846
126.99416
185.33261
207.71262
266.05107
288.43108
346.76953
415.42523
473.76369
496.14369
554.48215
623.13785
681.47631
703.85631
762.19476
830.85047
889.18892
911.56892
969.90738
992.28738
1050.62584
1119.28154
1177.62000
1200.00000

Here's something I found when I ran COMPARE in Scala: a rational
intonation version of O3 from November 2010 that is just about
identical, based on an arithmetic division of the 896/891
undecimal kleisma into 896:895:894:893:892:891. I'll give first
a link and the SHOW SCALE for the cents, then a Scala file.

<http://www.bestII.com/~mschulter/O3-ri24.scl>

|
Rational intonation version of O3 (24), subdivision of 896:891
0: 1/1 0.000 unison, perfect prime
1: 91/88 58.036
2: 1764/1639 127.242
3: 40131/36058 185.277
4: 168/149 207.779
5: 1911/1639 265.814
6: 176/149 288.316
7: 182/149 346.351
8: 567/446 415.566
9: 51597/39248 473.602
10: 297/223 496.103
11: 2457/1784 554.139
12: 14112/9845 623.351
13: 160524/108295 681.387
14: 1344/895 703.888
15: 15288/9845 761.924
16: 15876/9823 831.134
17: 361179/216106 889.170
18: 1512/893 911.671
19: 17199/9823 969.707
20: 1584/893 992.208
21: 1638/893 1050.244
22: 21/11 1119.463 undecimal major seventh
23: 1911/968 1177.499
24: 2/1 1200.000 octave

! O3-ri24.scl
!
Rational intonation version of O3 (24), subdivision of 896:891
24
!
91/88
1764/1639
40131/36058
168/149
1911/1639
176/149
182/149
567/446
51597/39248
297/223
2457/1784
14112/9845
160524/108295
1344/895
15288/9845
15876/9823
361179/216106
1512/893
17199/9823
1584/893
1638/893
21/11
1911/968
2/1

A delightful convergence! Maybe as with Kornerup and the POTE for
meantone, there might be interesting questions as to why an
approach like Kornerup's logarithmic ratio of Phi, or here
dividing 896:891 arithmetically, happens to generate something
close to the POTE.

With warmest congratulations,

Margo