Slendro clan
The slendro clan tempers out the slendro diesis, 49/48, a triprime comma with factors of 2, 3 and 7.
Semaphore
- Main article: Semaphore and godzilla
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 (CTE): ~2 = 1\1, ~7/4 = 952.2948
Optimal ET sequence: 5, 14, 19, 24, 67dd, 91dd, 115ddd
Scales: semaphore5, semaphore9, semaphore14
Overview to extensions
The second comma of the comma list defines which 7-limit family member we are looking at.
Godzilla adds 81/80. Immunity adds 2240/2187. Superpelog adds 135/128. Beep adds 21/20. Baba adds 16/15. These all use the same nominal generator as semaphore, though some of them are of very low accuracy.
Decimal adds 25/24, splitting the octave in two. Negri adds 225/224, splitting the hemifourth in two. Triforce adds 128/125, splitting the octave in three. Keemun adds 126/125, splitting the hemitwelfth in three. Nautilus adds 250/243, splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds 648/625 with a 1/4-octave period. Blacksmith adds 28/27, splitting the octave in five. Spell adds 3125/3072, splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Finally, mabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five.
Discussed elsewhere are
- Beep (+21/20) → Bug family
- Immunity (+2240/2187) → Immunity family
- Decimal (+25/24) → Dicot family
- Triforce (+128/125) → Augmented family
- Keemun (+126/125) → Kleismic family
- Nautilus (+250/243) → Porcupine family
- Hemidim (+648/625) → Dimipent family
- Blacksmith (+28/27) → Limmic temperaments
- Spell (+3125/3072) → Hemimean clan
Considered below are godzilla, superpelog, negri, nuke, mabila, and hemiripple.
Godzilla
- Main article: Semaphore and godzilla
Godzilla tempers out 81/80, equating 9/8 and 10/9, so it finds the prime 5 at a stack of four fifths, as does any temperament in the meantone family. 19edo is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. Mos scales are of 5, 9, or 14 notes.
Subgroup: 2.3.5.7
Comma list: 49/48, 81/80
Mapping: [⟨1 0 -4 2], ⟨0 2 8 1]]
- mapping generators: ~2, ~7/4
Wedgie: ⟨⟨2 8 1 8 -4 -20]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 948.7959
- 7- and 9-odd-limit diamond monotone: ~7/4 = [942.857, 960.000] (1\14 to 4\5)
- 7- and 9-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]
Optimal ET sequence: 5, 14c, 19
Badness: 0.026747
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 49/48, 81/80
Mapping: [⟨1 0 -4 2 -6], ⟨0 2 8 1 12]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 947.4563
Tuning ranges:
- 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
- 11-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]
Optimal ET sequence: 14c, 19, 33cd
Badness: 0.028947
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 49/48, 78/77, 81/80
Mapping: [⟨1 0 -4 2 -6 -5], ⟨0 2 8 1 12 11]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 947.8877
Tuning ranges:
- 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
- 13- and 15-odd-limit diamond tradeoff: ~7/4 = [910.890, 968.826]
Optimal ET sequence: 14cf, 19, 33cdff
Badness: 0.022503
Semafour
Subgroup: 2.3.5.7.11
Comma list: 33/32, 49/48, 55/54
Mapping: [⟨1 0 -4 2 5], ⟨0 2 8 1 -2]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 948.2089
Optimal ET sequence: 14c, 19e, 33cdee, 52cdeee
Badness: 0.028510
Varan
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 81/80
Mapping: [⟨1 0 -4 2 -10], ⟨0 2 8 1 17]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 949.6160
Optimal ET sequence: 19e, 24, 43de
Badness: 0.039647
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 77/75, 81/80
Mapping: [⟨1 0 -4 2 -10 -5], ⟨0 2 8 1 17 11]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 949.5255
Optimal ET sequence: 19e, 24, 43de
Badness: 0.025676
Baragon
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 81/80
Mapping: [⟨1 0 -4 2 9], ⟨0 2 8 1 -7]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 949.0311
Optimal ET sequence: 5, 19, 24
Badness: 0.035673
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 81/80, 91/90
Mapping: [⟨1 0 -4 2 9 -5], ⟨0 2 8 1 -7 11]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 949.0670
Optimal ET sequence: 5, 19, 24
Badness: 0.026703
Helayo
- For the 5-limit version of this temperament see High badness temperaments #Hogzilla.
Subgroup: 2.3.5.7
Comma list: 49/48, 3645/3584
Mapping: [⟨1 0 11 2], ⟨0 2 -11 1]]
Wedgie: ⟨⟨2 -6 1 -14 -4 19]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 947.0969
Optimal ET sequence: 5c, 14, 19
Badness: 0.0791
- Music
Superpelog
Subgroup: 2.3.5.7
Comma list: 49/48, 135/128
Mapping: [⟨1 0 7 2], ⟨0 2 -6 1]]
Wedgie: ⟨⟨2 -6 1 -14 -4 19]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 939.0297
Optimal ET sequence: 9, 14c, 23d, 37bcd, 60bbccdd
Badness: 0.058216
11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 49/48
Mapping: [⟨1 0 7 2 5], ⟨0 2 -6 1 -2]]
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 938.4673
Optimal ET sequence: 9, 14c, 23de, 37bcde
Badness: 0.028535
- Music
- Mindaugas Rex Lithuaniae by Chris Vaisvil (blog) (superpelog[9] in 23edo tuning)
Baba
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 973.296
Wedgie: ⟨⟨2 -2 1 -8 -4 8]]
Optimal ET sequence: 5, 11b, 16bc
Badness: 0.044321
11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 49/45
Mapping: [⟨1 0 4 2 1], ⟨0 2 -2 1 3]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 978.164
Optimal ET sequence: 5, 11b, 16bc, 27bbcc
Badness: 0.036538
Negri
- Main article: 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
- See also: Mabila family
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
- See also: Ripple family #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