Canou scales

This page lists scales of canou temperament, the rank-3 temperament that tempers out the canousma, 4802000/4782969 = [4 -14 3 4⟩.

Canou[9]

sLsLLsLsM

where s = 28/27, M = 10/9, L = 2187/1960~2450/2187.

Unison vectors: 15/14, 245/243, 19683/19600.

7-limit transversal: 28/27, 81/70, 6/5, 980/729, 3/2, 14/9, 243/140, 9/5, 2/1.

In 80edo (a simple, general-purpose tuning): 4, 17, 21, 34, 47, 51, 64, 68, 80.

! canou9-80.scl
! Created using Scale Workshop 1.0.4
!
Canou[9] in 80edo
 9
!
 60.
 255.
 315.
 510.
 705.
 765.
 960.
 1020.
 1200.

In 410edo (an intricate, accurate tuning): 21, 87, 108, 174, 240, 261, 327, 348, 410.

! canou9-410.scl
! Created using Scale Workshop 1.0.4
!
Canou[9] in 410edo
 9
!
 61.4634146341
 254.634146341
 316.097560976
 509.268292683
 702.439024390
 763.902439024
 957.073170732
 1018.53658537
 1200.

Notable modes:

• LLsLsMsLs (major-ish 4th mode)
• LsLsMsLsL (symmetric 5th mode)

Semicanou[10]

This is rank-2; the second generator is not used. Worth documenting anyway.

LsLss-LsLss

where s = 81/77, L = 11/10.

11-limit transversal:

Period 0: 11/10, 81/70~140/121, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 14/9, 18/11, 9/5, 154/81, 2/1.

Canou[14]

sLssLsLssLssMs

where s = 28/27, M = 15/14, L = 175/162.

Unison vectors: 25/24, 245/243, 19683/19600.

7-limit transversal: 28/27, 2187/1960~2450/2187, 81/70, 6/5, 35/27, 980/729, 81/56, 3/2, 14/9, 1225/729, 243/140, 9/5, 27/14, 2/1.

In 80edo: 4, 13, 17, 21, 30, 34, 43, 47, 51, 60, 64, 68, 76, 80.

! canou14-80.scl
! Created using Scale Workshop 1.0.4
!
Canou[14] in 80edo
 14
!
 60.
 195.
 255.
 315.
 450.
 510.
 645.
 705.
 765.
 900.
 960.
 1020.
 1140.
 1200.

In 410edo: 21, 66, 87, 108, 153, 174, 219, 240, 261, 306, 327, 348, 389, 410.

! canou14-410.scl
! Created using Scale Workshop 1.0.4
!
Canou[14] in 410edo
 14
!
 61.4634146341
 193.170731707
 254.634146341
 316.097560976
 447.804878049
 509.268292683
 640.975609756
 702.439024390
 763.902439024
 895.609756098
 957.073170732
 1018.53658537
 1138.53658537
 1200.

Notable modes:

• LsLssLssMssLss (major-ish 5th mode)

Semicanou[14]

LsmsLmm-LsmsLmm

where s = 28/27, m = 81/77, L = 35/33.

11-limit transversal:

Period 0: 35/33, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 3/2, 14/9, 56/33, 243/140~210/121, 9/5, 154/81, 2/1.

13-limit transversal:

Period 0: 35/33, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 3/2, 14/9, 56/33, 243/140~210/121, 9/5, 91/48, 2/1.

In 198edo: 17, 27, 42, 52, 69, 84, 99, 116, 126, 141, 151, 168, 183, 198.

! semicanou14-198.scl
! Created using Scale Workshop 1.0.4
!
Semicanou[14] in 198edo
 14
!
 103.030303030
 163.636363636
 254.545454545
 315.151515152
 418.181818182
 509.090909091
 600.
 703.030303030
 763.636363636
 854.545454545
 915.151515152
 1018.181818182
 1109.090909091
 1200.

Notable modes:

• LmmLsms-LmmLsms (major-ish 5th mode)
• mLsmsLm-mLsmsLm (symmetric 7th mode)

Semicanou[14-a]

This is a variation of semicanou[14].

LsmLsmm-LsmLsmm

where s = 28/27, m = 81/77, L = 35/33.

11-limit transversal:

Period 0: 35/33, 11/10, 81/70~140/121, 27/22, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 3/2, 14/9, 18/11, 243/140~210/121, 9/5, 154/81, 2/1.

13-limit transversal:

Period 0: 35/33, 11/10, 81/70~140/121, 16/13, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 3/2, 14/9, 18/11, 243/140~210/121, 9/5, 91/48, 2/1.

In 198edo: 17, 27, 42, 59, 69, 84, 99, 116, 126, 141, 158, 168, 183, 198.

Semicanou[14-b]

This is the inversion of semicanou[14-a].

sLmsLmm-sLmsLmm

where s = 28/27, m = 81/77, L = 35/33.

11-limit transversal:

Period 0: 28/27, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 22/15, 14/9, 56/33, 243/140~210/121, 9/5, 154/81, 2/1.

13-limit transversal:

Period 0: 28/27, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 22/15, 14/9, 56/33, 243/140~210/121, 9/5, 91/48, 2/1.

In 198edo: 10, 27, 42, 52, 69, 84, 99, 108, 126, 141, 151, 168, 183, 198.

Canou[19]

mLmmmLmmLmmmLmmmsmm

where s = 405/392, m = 28/27, L = 25/24.

Unison vectors: 225/224, 245/243, 19683/19600.

7-limit transversal: 28/27, 175/162, 2187/1960~2450/2187, 81/70, 6/5, 5/4, 35/27, 980/729, 2187/1568~6125/4374, 81/56, 3/2, 14/9, 392/243, 1225/729, 243/140, 9/5, 729/392, 27/14, 2/1.

In 410edo: 21, 45, 66, 87, 108, 132, 153, 174, 198, 219, 240, 261, 285, 306, 327, 348, 368, 389, 410.

! canou14-410.scl
! Created using Scale Workshop 1.0.4
!
Canou[19] in 410edo
 19
!
 61.4634146341
 131.707317073
 193.170731707
 254.634146341
 316.097560976
 386.341463415
 447.804878049
 509.268292683
 579.512195122
 640.975609756
 702.439024390
 763.902439024
 834.146341463
 895.609756098
 957.073170732
 1018.53658537
 1077.07317073
 1138.53658537
 1200.