O3-ri24

Rational intonation version of O3 (24), subdivision of 896:891

Open in Scale Workshop Scala analysis Download scl

Properties

Notes24
Period1200.0 ¢
Just223-limit
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105217.html#105227
Thread2 scales
Tone Tone (¢) Step Step (¢)
91/88 58 91/88 58
1764/1639 127 2016/1937 69
40131/36058 185 91/88 58
168/149 208 1936/1911 23
1911/1639 266 91/88 58
176/149 288 1936/1911 23
182/149 346 91/88 58
567/446 416 12069/11596 69
51597/39248 474 91/88 58
297/223 496 1936/1911 23
2457/1784 554 91/88 58
14112/9845 623 399616/383955 69
160524/108295 681 91/88 58
1344/895 704 1936/1911 23
15288/9845 762 91/88 58
15876/9823 831 24165/23218 69
361179/216106 889 91/88 58
1512/893 912 1936/1911 23
17199/9823 970 91/88 58
1584/893 992 1936/1911 23
1638/893 1050 91/88 58
21/11 1119 893/858 69
1911/968 1177 91/88 58
2/1 1200 1936/1911 23

Similar scales

FileNotesRotationMax diff (¢)
met24pote 24 0 0.4
simplemint24 24 0 0.9
O3-24 24 0 1.7
met24 24 0 2.1
met24-canonical 24 0 2.1
peprmintA 24 6 2.3
peprmint_key1 24 23 2.3
peprmint 24 0 2.3
lin76-34 24 0 2.7
met24-ji3_A 24 6 5.6

Parent scales

FileNotesMax diff (¢)
secor29tolerant 29 10.7
septenarian29 29 11.3
patheq58 58 1.1
Tolerant-Secor-29 29 11.6
cantonpentamint58 58 2.0
htct29b 29 12.6
edo-46 46 7.2
mystery58 58 4.2
17x2_55 34 13.0
edo-58 58 5.4

Child scales

FileNotesMax diff (¢)
14_13-12 12 1.2
ragaldor 7 1.3
met24-slendro10-var_C 5 1.3
met12 12 1.4
met24-oceania_C 5 1.4
kpnobl12 12 1.6
met24-quasi_5-EDO_F 5 1.7
ragaldoj 7 1.9
xen15-chalmers-triadic-reversed-diamond-13-11 7 1.9
xen18-schulter-symmetrical 7 1.9
Mailing list post 
From: Margo Schulter (2012-11-01)
Subject: A parapyth version of MET-24

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
Full thread (2 messages) 
From: genewardsmith (2012-11-01)
Subject: 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
From: Margo Schulter (2012-11-01)
Subject: A parapyth version of MET-24

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

Raw file

! 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
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105217.html#105227
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_90000-106393.json
! topic_id = 105217
! msg_id = 105227