Semaphoresmic clan
The slendro clan tempers out the slendro diesis, 49/48, a triprime comma with factors of 2, 3 and 7.
Discussed elsewhere are baba, decimal, beep, blacksmith, godzilla, keemun, triforce, superpelog, nautilus, spell and immunity.
Semaphore
Subgroup: 2.3.7
Comma list: 49/48
Sval mapping: [⟨1 0 2], ⟨0 2 1]]
- sval mapping generators: ~2, ~7/4
Gencom mapping: [⟨1 2 0 3], ⟨0 -2 0 -1]]
- gencom: [2 7/6; 49/48]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 949.615
Optimal ET sequence: 5, 14, 19, 24, 67dd, 91dd
Scales: semaphore5, semaphore9, semaphore14
Negri
Negri tempers out the negri comma in the 5-limit, 49/48 and 225/224 in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 to the comma list; this will be discussed below under the title of negra.
Subgroup: 2.3.5
Comma list: 16875/16384
Mapping: [⟨1 2 2], ⟨0 -4 3]]
- mapping generators: ~2, ~16/15
Wedgie: ⟨⟨ 4 -3 -14 ]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 125.7549
Optimal ET sequence: 9, 10, 19, 67c, 86c, 105c
Badness: 0.086856
7-limit
Subgroup: 2.3.5.7
Comma list: 49/48, 225/224
Mapping: [⟨1 2 2 3], ⟨0 -4 3 -2]]
Wedgie: ⟨⟨ 4 -3 2 -14 -8 13 ]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 125.608
Optimal ET sequence: 9, 10, 19, 48d, 67cdd, 86cdd
Badness: 0.026483
2.3.5.7.13 subgroup (negra)
Subgroup: 2.3.5.7.13
Comma list: 49/48, 65/64, 91/90
Sval mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -3]]
Gencom mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3]]
- gencom: [2 14/13; 49/48 65/64 91/90]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 125.567
Optimal ET sequence: 9, 10, 19, 48df, 67cddf, 86cddff
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 49/48, 56/55
Mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -5]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 126.474
Optimal ET sequence: 9, 10, 19
Badness: 0.026190
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 49/48, 56/55, 78/77
Mapping: [⟨1 2 2 3 4 4], ⟨0 -4 3 -2 -5 -3]]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.431
Optimal ET sequence: 9, 10, 19
Badness: 0.017833
Negril
Subgroup: 2.3.5.7.11
Comma list: 49/48, 100/99, 225/224
Mapping: [⟨1 2 2 3 2], ⟨0 -4 3 -2 14]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.767
Optimal ET sequence: 19, 29, 48d, 77cdd
Badness: 0.038679
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90, 875/858
Mapping: [⟨1 2 2 3 2 4], ⟨0 -4 3 -2 14 -3]]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.716
Optimal ET sequence: 19, 29, 48df, 77cddf
Badness: 0.024383
Negric
Subgroup: 2.3.5.7.11
Comma list: 33/32, 49/48, 77/75
Mapping: [⟨1 2 2 3 3], ⟨0 -4 3 -2 4]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 127.039
Badness: 0.030617
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 33/32, 49/48, 65/64, 91/90
Mapping: [⟨1 2 2 3 3 4], ⟨0 -4 3 -2 4 -3]]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 127.039
Badness: 0.020205
Negroni
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 225/224
Mapping: [⟨1 2 2 3 5], ⟨0 -4 3 -2 -15]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.539
Optimal ET sequence: 10, 19e, 29, 77cddee
Badness: 0.035296
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 65/64, 91/90
Mapping: [⟨1 2 2 3 5 4], ⟨0 -4 3 -2 -15 -3]]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.545
Optimal ET sequence: 10, 19e, 29, 77cddeef
Badness: 0.021559
Wilsec
Subgroup: 2.3.5.7.11
Comma list: 49/48, 121/120, 225/224
Mapping: [⟨1 6 -1 5 4], ⟨0 -8 6 -4 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.186
Optimal ET sequence: 9, 20, 29, 38d, 67cdde
Badness: 0.041886
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90, 121/120
Mapping: [⟨1 6 -1 5 4 7], ⟨0 -8 6 -4 -1 -6]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.208
Optimal ET sequence: 9, 20, 29, 38df, 67cddef
Badness: 0.025192
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
Mapping: [⟨1 6 -1 5 4 7 -2], ⟨0 -8 6 -4 -1 -6 11]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.230
Optimal ET sequence: 9, 20g, 29g, 38df, 67cddefg
Badness: 0.021778
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
Mapping: [⟨1 6 -1 5 4 7 -2 7], ⟨0 -8 6 -4 -1 -6 11 -5]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.214
Optimal ET sequence: 9, 20g, 29g, 38df, 67cddefgh
Badness: 0.016828
Nuke
Subgroup: 2.3.5.7
Comma list: 49/48, 3584/3375
Mapping: [⟨1 2 2 3], ⟨0 -6 5 -3]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 80.9538
Optimal ET sequence: 14, 15, 44cd
Badness: 0.129339
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 512/495
Mapping: [⟨1 2 2 3 3], ⟨0 -6 5 -3 7]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 80.8171
Badness: 0.069398
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 77/75, 448/429
Mapping: [⟨1 2 2 3 3 4], ⟨0 -6 5 -3 7 -4]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 81.0243
Optimal ET sequence: 14e, 15, 44cdeff
Badness: 0.048553
Mabila
Subgroup: 2.3.5.7
Comma list: 49/48, 28672/28125
Mapping: [⟨1 6 1 5], ⟨0 -10 3 -5]]
Wedgie: ⟨⟨ 10 -3 5 -28 -20 20 ]]
Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 529.667
Optimal ET sequence: 9, 25, 34
Badness: 0.133638
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 1350/1331
Mapping: [⟨1 6 1 5 7], ⟨0 -10 3 -5 -8]]
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.729
Optimal ET sequence: 9, 25e, 34
Badness: 0.061501
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90, 847/845
Mapping: [⟨1 6 1 5 7 9], ⟨0 -10 3 -5 -8 -12]]
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.763
Optimal ET sequence: 9, 25e, 34
Badness: 0.037270
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
Mapping: [⟨1 6 1 5 7 9 1], ⟨0 -10 3 -5 -8 -12 7]]
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.695
Optimal ET sequence: 9, 25e, 34
Badness: 0.031888
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
Mapping: [⟨1 6 1 5 7 9 1 6], ⟨0 -10 3 -5 -8 -12 7 -4]]
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.736
Optimal ET sequence: 9, 25e, 34
Badness: 0.026981
Hemiripple
Subgroup: 2.3.5.7
Comma list: 49/48, 6561/6250
Mapping: [⟨1 2 3 3], ⟨0 -10 -16 -5]]
Wedgie: ⟨⟨ 10 16 5 2 -20 -33 ]]
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.826
Optimal ET sequence: 23d, 24, 47d, 71bdd
Badness: 0.175113
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 121/120, 567/550
Mapping: [⟨1 2 3 3 4], ⟨0 -10 -16 -5 -13]]
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.826
Optimal ET sequence: 23de, 24, 47de, 71bdde
Badness: 0.066834
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 121/120, 351/350
Mapping: [⟨1 2 3 3 4 4], ⟨0 -10 -16 -5 -13 -7]]
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.635
Optimal ET sequence: 23de, 24, 47de, 71bdde
Badness: 0.046588