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Family relationships

🔗Gene Ward Smith <gwsmith@svpal.org>

3/4/2005 11:46:37 PM

I took the 71 11-limit temperaments I posted comma sequences for, and
broke them up by family relationships; here are the families as
defined by comma sequences which have more than one member on that list.

16/15

[1, -1, 3, 4, -4, 2, 3, 10, 13, 1]
[16/15, 28/27, 55/54]

[1, -1, 3, -4, -4, 2, -10, 10, -6, -22]
[16/15, 28/27, 100/99]

[2, -2, -2, 0, -8, -9, -7, 1, 7, 7]
[16/15, 50/49, 77/75]

135/128

[1, -3, -4, -1, -7, -9, -5, -1, 8, 11]
[135/128, 21/20, 33/32]

[2, -6, 1, -2, -14, -4, -10, 19, 16, -9]
[135/128, 49/48, 33/32]

25/24

[4, 2, 2, -4, -6, -8, -20, -1, -16, -18]
[25/24, 49/48, 33/32]

[4, 2, 2, 10, -6, -8, 2, -1, 16, 21]
[25/24, 49/48, 45/44]

[2, 1, 6, 5, -3, 4, 1, 11, 8, -7]
[25/24, 28/27, 45/44]

[2, 1, -4, 5, -3, -12, 1, -12, 8, 28]
[25/24, 64/63, 45/44]

250/243

[3, 5, -6, 4, 1, -18, -4, -28, -8, 32]
[250/243, 64/63, 55/54]

[3, 5, 9, 4, 1, 6, -4, 7, -8, -20]
[250/243, 28/27, 55/54]

128/125

[3, 0, -6, -6, -7, -18, -20, -14, -14, 4]
[128/125, 64/63, 100/99]

[6, 0, 3, 3, -14, -12, -16, 7, 7, -2]
[128/125, 49/48, 77/75]

81/80

[1, 4, 10, 18, 4, 13, 25, 12, 28, 16]
[81/80, 126/125, 3168/3125]

[1, 4, 10, -13, 4, 13, -24, 12, -44, -71]
[81/80, 126/125, 4125/4096]

[1, 4, 10, 6, 4, 13, 6, 12, 0, -18]
[81/80, 126/125, 45/44]

[1, 4, -2, -6, 4, -6, -13, -16, -28, -10]
[81/80, 36/35, 288/275]

[1, 4, -2, -1, 4, -6, -5, -16, -16, 4]
[81/80, 36/35, 33/32]

[1, 4, 3, -1, 4, 2, -5, -4, -16, -13]
[81/80, 21/20, 33/32]

[2, 8, 8, 12, 8, 7, 12, -4, 0, 6]
[81/80, 50/49, 45/44]

[3, 12, -1, -8, 12, -10, -23, -36, -60, -19]
[81/80, 1029/1024, 385/384]

2048/2025

[2, -4, -4, -12, -11, -12, -26, 2, -14, -20]
[2048/2025, 64/63, 100/99]

[2, -4, -4, 0, -11, -12, -7, 2, 14, 14]
[2048/2025, 64/63, 45/44]

[2, -4, -4, 10, -11, -12, 9, 2, 37, 42]
[2048/2025, 64/63, 55/54]

[2, -4, -16, -24, -11, -31, -45, -26, -42, -12]
[2048/2025, 126/125, 3168/3125]

[6, -12, 10, -14, -33, -1, -43, 57, 9, -74]
[2048/2025, 1728/1715, 540/539]

15625/15552

[6, 5, 3, -2, -6, -12, -24, -7, -22, -16]
[15625/15552, 126/125, 100/99]

[6, 5, 22, -21, -6, 18, -54, 37, -66, -135]
[15625/15552, 225/224, 4125/4096]

[18, 15, -6, 9, -18, -60, -48, -56, -31, 46]
[15625/15552, 1029/1024, 385/384]

[24, 20, 16, -12, -24, -42, -102, -19, -97, -89]
[15625/15552, 2401/2400, 385/384]

32805/32768

[1, -8, -14, -18, -15, -25, -32, -10, -14, -2]
[32805/32768, 225/224, 100/99]

[1, -8, -14, 23, -15, -25, 33, -10, 81, 113]
[32805/32768, 225/224, 2200/2187]

[2, -16, -40, -60, -30, -69, -102, -48, -84, -30]
[32805/32768, 3136/3125, 5632/5625]

[3, -24, -1, 28, -45, -10, 34, 65, 148, 82]
[32805/32768, 1029/1024, 385/384]

🔗Carl Lumma <ekin@lumma.org>

3/5/2005 1:23:19 PM

This looks useful...

-Carl

>I took the 71 11-limit temperaments I posted comma sequences for, and
>broke them up by family relationships; here are the families as
>defined by comma sequences which have more than one member on that list.
>
>
>16/15
>
>[1, -1, 3, 4, -4, 2, 3, 10, 13, 1]
>[16/15, 28/27, 55/54]
>
>[1, -1, 3, -4, -4, 2, -10, 10, -6, -22]
>[16/15, 28/27, 100/99]
>
>[2, -2, -2, 0, -8, -9, -7, 1, 7, 7]
>[16/15, 50/49, 77/75]
>
>
>135/128
>
>[1, -3, -4, -1, -7, -9, -5, -1, 8, 11]
>[135/128, 21/20, 33/32]
>
>[2, -6, 1, -2, -14, -4, -10, 19, 16, -9]
>[135/128, 49/48, 33/32]
>
>
>25/24
>
>[4, 2, 2, -4, -6, -8, -20, -1, -16, -18]
>[25/24, 49/48, 33/32]
>
>[4, 2, 2, 10, -6, -8, 2, -1, 16, 21]
>[25/24, 49/48, 45/44]
>
>[2, 1, 6, 5, -3, 4, 1, 11, 8, -7]
>[25/24, 28/27, 45/44]
>
>[2, 1, -4, 5, -3, -12, 1, -12, 8, 28]
>[25/24, 64/63, 45/44]
>
>
>250/243
>
>[3, 5, -6, 4, 1, -18, -4, -28, -8, 32]
>[250/243, 64/63, 55/54]
>
>[3, 5, 9, 4, 1, 6, -4, 7, -8, -20]
>[250/243, 28/27, 55/54]
>
>
>128/125
>
>[3, 0, -6, -6, -7, -18, -20, -14, -14, 4]
>[128/125, 64/63, 100/99]
>
>[6, 0, 3, 3, -14, -12, -16, 7, 7, -2]
>[128/125, 49/48, 77/75]
>
>
>81/80
>
>[1, 4, 10, 18, 4, 13, 25, 12, 28, 16]
>[81/80, 126/125, 3168/3125]
>
>[1, 4, 10, -13, 4, 13, -24, 12, -44, -71]
>[81/80, 126/125, 4125/4096]
>
>[1, 4, 10, 6, 4, 13, 6, 12, 0, -18]
>[81/80, 126/125, 45/44]
>
>[1, 4, -2, -6, 4, -6, -13, -16, -28, -10]
>[81/80, 36/35, 288/275]
>
>[1, 4, -2, -1, 4, -6, -5, -16, -16, 4]
>[81/80, 36/35, 33/32]
>
>[1, 4, 3, -1, 4, 2, -5, -4, -16, -13]
>[81/80, 21/20, 33/32]
>
>[2, 8, 8, 12, 8, 7, 12, -4, 0, 6]
>[81/80, 50/49, 45/44]
>
>[3, 12, -1, -8, 12, -10, -23, -36, -60, -19]
>[81/80, 1029/1024, 385/384]
>
>
>2048/2025
>
>[2, -4, -4, -12, -11, -12, -26, 2, -14, -20]
>[2048/2025, 64/63, 100/99]
>
>[2, -4, -4, 0, -11, -12, -7, 2, 14, 14]
>[2048/2025, 64/63, 45/44]
>
>[2, -4, -4, 10, -11, -12, 9, 2, 37, 42]
>[2048/2025, 64/63, 55/54]
>
>[2, -4, -16, -24, -11, -31, -45, -26, -42, -12]
>[2048/2025, 126/125, 3168/3125]
>
>[6, -12, 10, -14, -33, -1, -43, 57, 9, -74]
>[2048/2025, 1728/1715, 540/539]
>
>
>15625/15552
>
>[6, 5, 3, -2, -6, -12, -24, -7, -22, -16]
>[15625/15552, 126/125, 100/99]
>
>[6, 5, 22, -21, -6, 18, -54, 37, -66, -135]
>[15625/15552, 225/224, 4125/4096]
>
>[18, 15, -6, 9, -18, -60, -48, -56, -31, 46]
>[15625/15552, 1029/1024, 385/384]
>
>[24, 20, 16, -12, -24, -42, -102, -19, -97, -89]
>[15625/15552, 2401/2400, 385/384]
>
>
>32805/32768
>
>[1, -8, -14, -18, -15, -25, -32, -10, -14, -2]
>[32805/32768, 225/224, 100/99]
>
>[1, -8, -14, 23, -15, -25, 33, -10, 81, 113]
>[32805/32768, 225/224, 2200/2187]
>
>[2, -16, -40, -60, -30, -69, -102, -48, -84, -30]
>[32805/32768, 3136/3125, 5632/5625]
>
>[3, -24, -1, 28, -45, -10, 34, 65, 148, 82]
>[32805/32768, 1029/1024, 385/384]
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