User:TallKite/Catalog of seven-limit rank two temperaments with Color names

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(The original version of this page is here: Catalog of seven-limit rank two temperaments.)

Below is a complete listing of all 179 7-limit rank-two temperaments with TE complexity less than 20 and TE badness less than 0.06, obtained by the method discussed here. The TE error is multiplied by 1200 so that it can be thought of as cents, and the badness is multiplied by 1000. Some "Junk" temperaments of very low complexity are listed below the main list, which is ordered by increasing complexity.

Temperament list

THIS LIST IS SORTABLE, so you can sort by name or by pergen, and look up a specific temperament. Rules for choosing comma sets: prime limit strictly ascends, no torsion allowed, primes excluded because of downward inheritances are not allowed in other commas, and double-odd-limit is minimized. See: Color Notation/Temperament names.

  • Color name column: alternatives or objections are bolded
  • Pergen column: all double-splits are false doubles unless otherwise noted. Mapping for 5/4 and 7/4 is indicated.
  • Commas column: ratios are grouped by prime limit with actual commas (","), and sorted within prime-limit by double odd limit.
  • Cm = Complexity = corresponds roughly to the odd limit of the commas
  • Err = Error = corresponds roughly to the cents discrepancy from JI
  • Bad = Badness = a combination of complexity and error
  • The final column is the wedgie, made invisible to make the table fit on the screen well. Eventually this column will be deleted.

Many temperaments list three commas. The comma not used in the color name is in parentheses. This comma usually came from the original page, which listed only the two lowest-odd-limit commas. It's listed here just as some extra info for the reader. If this comma is a lower odd limit, but was excluded to avoid torsion or allow a downward inheritance, it is bolded.

Name Color Name Pergen Commas Mapping Cm Err Bad Wedgie
Ternary 3-edo & Yo + za (P8/3, ^1) 32/27, 10/9 (16/15) 3 5 7 0
0 0 0 1
0.770 58.026 28.673 <<0 0 3 0 5 7]]
Dicot Yoyo & Ruyo (P8, P5/2) 25/24, 15/14 (36/35) 1 1 2 2
0 2 1 3
0.818 35.781 19.935 <<2 1 3 -3 -1 4]]
Mother Gubi & Zogu (P8, P5) 16/15, 21/20 (64/63) 1 0 4 6
0 1 -1 -2
0.835 41.553 24.152 <<1 -1 -2 -4 -6 -2]]
Brutus Yo & Zogugu (P8, P5) 10/9, 28/25 (56/45) 1 0 -1 -4
0 1 2 4
0.859 86.798 53.389 <<1 2 4 1 4 4]]
Geryon Yoyo & Rubi (P8, P5/2) 25/24, 8/7 (25/21) 1 1 2 3
0 2 1 0
0.863 82.117 51.009 <<2 1 0 -3 -6 -3]]
Antaeus 2-edo & Zoyo (P8/2, ^1) 9/8, 35/32 (36/35) 2 3 0 10
0 0 1 -1
0.887 57.236 37.537 <<0 2 -2 3 -3 -10]]
Beep Gugu & Zogu (P8, P4/2) 27/25, 21/20 (36/35) 1 0 0 2
0 2 3 1
0.917 26.605 18.638 <<2 3 1 0 -4 -6]]
Father Gubi & Zo (P8, P5) 16/15, 28/27 (36/35) 1 0 4 -2
0 1 -1 3
0.954 28.092 21.312 <<1 -1 3 -4 2 10]]
Flat Yoyo & Zogu (P8, P5/2) 25/24, 21/20 (35/32) 1 1 2 3
0 2 1 -1
0.969 32.444 25.381 <<2 1 -1 -3 -7 -5]]
Quad 2-edo & Yoyo + za

(4-edo + za?)

(P8/4, ^1) 9/8, 25/24 (27/25) 4 6 9 0
0 0 0 1
0.979 57.541 45.991 <<0 0 4 0 6 9]]
Phlegyas Yo & Zoyo (P8, P5) 10/9, 35/32 (64/63) 1 0 -1 6
0 1 2 -2
0.991 62.667 51.293 <<1 2 -2 1 -6 -10]]
Malacoda Yoyobi & Ruyo (P8, P4/2) 75/64, 15/14 (35/32) 1 0 3 2
0 2 -1 1
0.997 44.954 37.207 <<2 -1 1 -6 -4 5]]
Sharptone Gu & Zogu (P8, P5) 81/80, 21/20 (28/27) 1 0 -4 -2
0 1 4 3
1.022 28.544 24.848 <<1 4 3 4 2 -4]]
Ugolino Gugu & Ruyo (P8, P4/2) 27/25, 15/14 (126/125) 1 0 0 -1
0 2 3 5
1.068 46.010 43.758 <<2 3 5 0 2 3]]
Charon Yo & Biruyo (P8/2, P5) 10/9, 50/49 (49/45) 2 0 -2 -1
0 1 2 2
1.082 57.767 56.404 <<2 4 4 2 1 -2]]
Nessus Yo & Zozo (P8, P4/2) 10/9, 49/48 (160/147) 1 0 -1 2
0 2 4 1
1.133 55.258 59.070 <<2 4 1 2 -4 -9]]
Penta Trigubi & Zogugu (P8, P5/3) 144/125, 28/25 (36/35) 1 1 2 2
0 3 2 4
1.163 41.597 46.882 <<3 2 4 -4 -2 4]]
Medusa Layobi & Ruyo (P8, P5) 135/128, 15/14 (64/63) 1 0 7 6
0 1 -3 -2
1.182 36.664 42.712 <<1 -3 -2 -7 -6 4]]
Plutus Gu & Ruyo (P8, P5) 81/80, 15/14

(200/189 243/224)

1 0 -4 -5
0 1 4 5
1.224 36.293 45.275 <<1 4 5 4 5 0]]
Sodium Gugubi & Zogu (P8, P5/2) 243/200, 21/20 (54/49) 1 1 1 2
0 2 5 3
1.241 43.494 55.814 <<2 5 3 3 -1 -7]]
Mite Gugu & Zogugu (P8, P4/2) 27/25, 28/25 (28/27) 1 0 0 -2
0 2 3 6
1.257 41.576 54.770 <<2 3 6 0 4 6]]
Baba Gubi & Zozo (P8, P4/2) 16/15, 49/48 (49/45) 1 0 42
0 2 -2 1
1.258 33.587 44.321 <<2 -2 1 -8 -4 8]]
Quint 5-edo & Gubi + za (P8/5, ^1) 256/243, 16/15 (27/25) 5 8 12 0
0 0 0 1
1.278 35.517 48.312 <<0 0 5 0 8 12]]
Sharp Yoyo & Zo (P8, P5/2) 25/24, 28/27 (225/224) 1 1 2 1
0 2 1 6
1.333 19.537 28.942 <<2 1 6 -3 4 11]]
Walid Gubi & Biruyo

(best Sarurubi ext.?)

(P8/2, P5) 16/15, 50/49 (160/147)

(512/441 = srr#2)

2 0 8 9
0 1 -1 -1
1.395 30.187 48.978 <<2 -2 -2 -8 -9 1]]
Pelogic Layobi & Zogu (P8, P5) 135/128, 21/20 (225/224) 1 0 7 9
0 1 -3 -4
1.404 23.529 38.661 <<1 -3 -4 -7 -9 -1]]
Oxygen Triyo & Zogu (P8, P4/3) 250/243, 21/20 (175/162) 1 2 3 3
0 -3 -5 -2
1.412 36.009 59.866 <<3 5 2 1 -5 -9]]
Wallaby Layobi & Zo (P8, P5) 135/128, 28/27 (35/32) 1 0 7-2
0 1 -3 3
1.433 34.157 58.468 <<1 -3 3 -7 2 15]]
Dominant Gu & Rugu (P8, P5) 81/80, 36/35 (64/63) 1 0 -4 6
0 1 4 -2
1.466 11.550 20.690 <<1 4 -2 4 -6 -16]]
Pater Gubi & Zotrigu (P8, P5) 16/15, 126/125 (189/100) 1 0 4 11
0 1 -1 -5
1.469 29.457 53.001 <<1 -1 -5 -4 -11 -9]]
Diminished Quadgu & Rugu (P8/4, P5) 648/625, 36/35 (50/49) 4 0 3 5
0 1 1 1
1.494 12.047 22.401 <<4 4 4 -3 -5 -2]]
Decimal Yoyo & Zozo (P8/2, P4/2)

true double

25/24, 49/48 (50/49) 2 0 3 4
0 2 1 1
1.502 15.075 28.334 <<4 2 2 -6 -8 -1]]
Blacksmith 5-edo (& Zo) + ya (P8/5, ^1) 256/243, 28/27 (49/48) 5 8 0 14
0 0 1 0
1.526 13.210 25.640 <<0 5 0 8 0 -14]]
Hystrix Triyo & Rugu (P8, P4/3) 250/243, 36/35 (160/147) 1 2 3 3
0 -3 -5 -1
1.543 22.654 44.944 <<3 5 1 1 -7 -12]]
Dichotic Yoyo & Ru (P8, P5/2) 25/24, 64/63 (200/189) 1 1 2 4
0 2 1 -4
1.588 17.871 37.565 <<2 1 -4 -3 -12 -12]]
Octokaidecal Sayoyo & Zo

(Zo & Biruyo?)

(P8/2, P5) 800/729, 28/27 (50/49)

(800/729 is too obscure?)

2 0 -5 -4
0 1 3 3
1.618 16.849 36.747 <<2 6 6 5 4 -3]]
Fluorine Lagubi & Zogu (P8, P5) 729/640, 21/20 (243/224) 1 0 -7 -5
0 1 6 5
1.618 25.482 55.623 <<1 6 5 7 5 -5]]
August Trigu & Rugu (P8/3, P5) 128/125, 36/35 (225/224) 3 0 7 -1
0 1 0 2
1.655 11.594 26.459 <<3 0 6 -7 1 14]]
Deflated Trigu & Zogu (P8/3, P5) 128/125, 21/20 (525/512) 3 0 7 13
0 1 0 -1
1.734 23.590 59.079 <<3 0 -3 -7 -13 -7]]
Jamesbond 7-edo (& Gu) + za (P8/7, ^1) 2187/2048, (25/24) 81/80

Yoyo creates torsion

7 11 16 0
0 0 0 1
1.749 16.364 41.714 <<0 0 7 0 11 16]]
Armodue Layobi & Rugu (P8, P5) 135/128, 36/35 (243/224) 1 0 7 -5
0 1 -3 5
1.804 18.075 49.038 <<1 -3 5 -7 5 20]]
Opossum Triyo & Zo (P8, P4/3) 250/243, 28/27 (126/125) 1 2 3 4
0 -3 -5 -9
1.895 13.586 40.650 <<3 5 9 1 6 7]]
Pajara Sagugu & Ru (P8/2, P5)

vM3, m7

2048/2025, (50/49) 64/63

Biruyo creates torsion

2 0 11 12
0 1 -2 -2
1.953 6.301 20.033 <<2 -4 -4 -11 -12 2]]
Progression Quingubi & Rugu (P8, P5/5)

^^m3, vvM7

[7 3 -5], 36/35 (392/375) 1 1 2 2
0 5 3 7
1.976 14.868 48.356 <<5 3 7 -7 -3 8]]
Sidi Yoyo & Zozoyo (P8, P11/4)

vM3, \m7

25/24, 245/243 (405/392) ([-3 9 0 -4]) not best ext. of Squares 1 3 3 6
0 -4 -2 -9
2.074 15.794 56.586 <<4 2 9 -6 3 15]]
Godzilla (Gu &) Zozo (P8, P4/2)

M3, vm7

81/80, 49/48 (245/243) 1 0 -4 2
0 2 8 1
2.181 6.748 26.747 <<2 8 1 8 -4 -20]]
Meantone Gu (& Zotrigu) (P8, P5)

M3, vm7 = A6

81/80, 126/125 (225/224) 1 0 -4 -13
0 1 4 10
2.205 3.384 13.707 <<1 4 10 4 13 12]]
Injera Gu & Biruyo (P8/2, P5)

M3, vm7

81/80, 50/49 (405/392)

not best ya ext. of Laruru

2 0 -8 -7
0 1 4 4
2.205 7.686 31.130 <<2 8 8 8 7 -4]]
Inflated Trigu & Zo (P8/3, P5)

vM3, M6

128/125, 28/27 (875/864) 3 0 7 -6
0 1 0 3
2.224 13.279 54.729 <<3 0 9 -7 6 21]]
Negri Laquadyo & Ruyoyo (P8, P4/4) [-14 3 4], (49/48) 225/224

Zozo creates torsion

1 2 2 3
0 -4 3 -2
2.245 6.308 26.483 <<4 -3 2 -14 -8 13]]
Keemun Tribiyo & Zotrigu (P8, P12/6) [-6 -5 6], (49/48) 126/125

Zozo creates torsion

1 0 1 2
0 6 5 3
2.280 6.326 27.408 <<6 5 3 -6 -12 -7]]
Superpelog Layobi & Zozo (P8, P4/2)

m3, vm7

135/128, 49/48 (405/392) 1 0 7 2
0 2 -6 1
2.316 13.029 58.216 <<2 -6 1 -14 -4 19]]
Augene Trigu & Ru (P8/3, P5)

vM3, m7

128/125, 64/63 (126/125) 3 0 7 18
0 1 0 -2
2.336 5.456 24.816 <<3 0 -6 -7 -18 -14]]
Ripple Quingu & Rugu (P8, P4/5) [-1 8 -5], 36/35 (2560/2401) 1 2 3 3
0 -5 -8 -2
2.454 11.901 59.735 <<5 8 2 1 -11 -18]]
Triforce Trigu & Zozo (P8/3, P4/2)

vM3, \m7

128/125, 49/48 (392/375) 3 0 7 6
0 2 0 1
2.529 10.318 54.988 <<6 0 3 -14 -12 7]]
Schism Layo & Ru (P8, P5)

vM3 = d4, m7

[-15 8 1], 64/63 (360/343) 1 0 15 6
0 1 -8 -2
2.544 10.503 56.648 <<1 -8 -2 -15 -6 18]]
Hexe Trigu & Biruyo (P8/6, P5)

vvM3, ^m7

128/125, 50/49 (3136/3125)

not best ya ext. of Satribiru

6 0 14 17
0 1 0 0
2.689 9.578 57.730 <<6 0 0 -14 -17 0]]
Hedgehog Triyo & Biruyo (P8/2, P4/3)

vM3, \m7

250/243, 50/49 (245/243)

not best ya ext. of Latribiru

2 1 1 2
0 3 5 5
2.784 6.810 43.983 <<6 10 10 2 -1 -5]]
Porcupine Triyo (& Ru) (P8, P4/3)

vM3, m7

250/243, 64/63 (875/864) 1 2 3 2
0 -3 -5 6
2.819 6.200 41.057 <<3 5 -6 1 -18 -28]]
Superpyth Sayo (& Ru) (P8, P5)

vM3 = A2, m7

[12 -9 1], 64/63 (245/243) 1 0 -12 6
0 1 9 -2
2.874 4.695 32.318 <<1 9 -2 12 -6 -30]]
Doublewide Quadbiyo & Zotriyo (P8/2, Wm7/8) [-9 -6 8], (50/49) 875/864 = zy3

Biruyo creates torsion

2 1 3 4
0 4 3 3
2.928 6.082 43.462 <<8 6 6 -9 -13 -3]]
Magic Laquinyo & Ruyoyo (P8, P12/5) [-10 -1 5], 225/224 (245/243) 1 0 2 -1
0 5 1 12
2.937 2.631 18.918 <<5 1 12 -10 5 25]]
Nautilus Triyo & Zozo (P8, P4/6) 250/243, 49/48 (4000/3969) 1 2 3 3
0 -6 -10 -3
2.943 7.955 57.420 <<6 10 3 2 -12 -21]]
Flattone Gu & Lazoyoyo (P8, P5) 81/80, 525/512 (875/864) 1 0 -4 17
0 1 4 -9
2.987 5.186 38.553 <<1 4 -9 4 -17 -32]]
Catler 12-edo (& Gu) + za (P8/12, ^1) [-19 12], 81/80 (128/125) 12 19 28 0
0 0 0 1
3.026 6.590 50.297 <<0 0 12 0 19 28]]
Sensi Sepgu & Zotrigu (P8, WWP5/7) [2 9 -7], 126/125 (245/243) 1 6 8 11
0 -7 -9 -13
3.080 3.242 25.622 <<7 9 13 -2 1 5]]
Beatles Sasa-Gugu & Ru (P8, P5/2) [19 -9 -2], 64/63 (686/675) 1 1 5 4
0 2 -9 -4
3.125 5.636 45.872 <<2 -9 -4 -19 -12 16]]
Liese (Gu &) Latriru (P8, P11/3) 81/80, (686/675) (1029/1000)

[-9 11 0 -3] (downward ext.)

1 0 -4 -3
0 3 12 11
3.211 5.435 46.706 <<3 12 11 12 9 -8]]
Muggles Laquinyo & Zotrigu (P8, P12/5) [-10 -1 5], 126/125 (525/512) 1 0 2 5
0 5 1 -7
3.261 6.343 56.206 <<5 1 -7 -10 -25 -19]]
Triton Latriyo & Ruyoyo (P8, P11/3) [-18 7 3], 225/224 (1029/1000) 1 0 6 7
0 3 -7 -8
3.342 6.365 59.245 <<3 -7 -8 -18 -21 1]]
Porky Triyo & Ruyoyo (P8, P4/3) 250/243, 225/224

(2240/2187 = szg)

1 2 3 5
0 -3 -5 -16
3.362 5.774 54.389 <<3 5 16 1 17 23]]
Mothra Gu & Latrizo (P8, P5/3) 81/80, 1029/1024

(1728/1715 = r3g)

1 1 0 3
0 3 12 -1
3.573 3.491 37.146 <<3 12 -1 12 -10 -36]]
Orwell Lasepyo & Ruyoyo (P8, P12/7) [-21 3 7], 225/224

(1728/1715 = r3g)

1 0 3 1
0 7 -3 8
3.685 1.832 20.735 <<7 -3 8 -21 -7 27]]
Myna Quinbigu & Zotrigu (P8, WWP5/10) [9 9 -10], 126/125

(1728/1715 = r3g)

1 9 9 8
0 -10 -9 -7
3.731 2.331 27.044 <<10 9 7 -9 -17 -9]]
Garibaldi Layo & Ruyoyo (P8, P5) [-15 8 1], 225/224

(3125/3087 = r3y5)

1 0 15 25
0 1 -8 -14
3.823 1.778 21.644 <<1 -8 -14 -15 -25 -10]]
Miracle Lala-tribiyo & Ruyoyo

(Latrizo & Ruyoyo?)

(P8, P5/6) [-25 7 6], 225/224 (1029/1024)

Lala-tribiyo is too obscure?

1 1 3 3
0 6 -7 -2
3.991 1.261 16.742 <<6 -7 -2 -25 -20 15]]
Squares (Gu &) Laquadru (P8, P11/4) 81/80, (2401/2400 = z4gg)

[-3 9 0 -4] (downward ext.)

1 3 8 6
0 -4 -16 -9
4.022 3.412 45.993 <<4 16 9 16 3 -24]]
Valentine Satritrigu & Zotrigu

(Latrizo & Zotrigu?)

(P8, P5/9) [13 5 -9], 126/125 (1029/1024)

Satritrigu is too obscure?

1 1 2 3
0 9 5 -3
4.210 2.103 31.056 <<9 5 -3 -13 -30 -21]]
Diaschismic Sagugu & Zotrigu (P8/2, P5) 2048/2025, 126/125

(5120/5103 = sry)

2 0 11 31
0 1 -2 -8
4.290 2.472 37.914 <<2 -4 -16 -11 -31 -26]]
Mohajira Gu & Sarurutrigu (P8, P5/2) 81/80, 6144/6125

(not called best ext. of Lala-ruru)

1 1 0 6
0 2 8 -11
4.368 3.504 55.714 <<2 8 -11 8 -23 -48]]
Nusecond Legu & Zotrigu (P8, P11/11) [5 13 -11], 126/125

(2430/2401 = z4y)

1 3 4 5
0 -11 -13 -17
4.454 3.048 50.389 <<11 13 17 -5 -4 3]]
Octacot Saquadyo & Zozoyo (P8, P5/8) [5 -9 4], 245/243 (2400/2401)

(not best ya ext of Squares)

1 1 1 2
0 8 18 11
4.551 1.961 33.845 <<8 18 11 10 -5 -25]]
Würschmidt Saquadbigu & Ruyoyo (P8, WWP5/8) [17 1 -8], 225/224

(8748/8575 = r3gg)

1 7 3 15
0 -8 -1 -18
4.578 2.908 50.776 <<8 1 18 -17 6 39]]
Superkleismic Tritriyo & Zotriyo (P8, WWP4/9) [-5 -10 9], 875/864 (1029/1024) 1 4 5 2
0 -9 -10 3
4.620 2.695 47.932 <<9 10 -3 -5 -30 -35]]
Catakleismic Tribiyo & Ruyoyo (P8, P12/6) [-6 -5 6], 225/224

(4375/4374 = zy4)

1 0 1 -3
0 6 5 22
4.684 1.176 21.501 <<6 5 22 -6 18 37]]
Alicorn Laquadbigu & Zotrigu (P8, P4/8) [-2 13 -8], 126/125

(10976/10935 = sz3g)

1 2 3 4
0 -8 -13 -23
4.847 2.090 40.913 <<8 13 23 2 14 17]]
Rodan Sasa-triyo & Saruyo

(Latrizo & Zozoyo?)

(P8, P5/3) [20 -17 3], (245/243 1029/1024)

5120/5103 (Sasa-triyo is too remote?)

1 1 -1 3
0 3 17 -1
5.012 1.773 37.112 <<3 17 -1 20 -10 -50]]
Shrutar Sagugu & Zozoyo (P8/2, M2/4) 2048/2025, 245/243

([11 -14 0 4])

2 1 9 -2
0 2 -4 7
5.101 2.185 47.377 <<4 -8 14 -22 11 55]]
Tritonic Lala-quinyo & Ruyoyo (P8, WWP4/5) [-29 11 5], 225/224

(50421/50000 = z5g5)

1 4 -3 -3
0 -5 11 12
5.291 2.039 47.578 <<5 -11 -12 -29 -33 3]]
Quartonic Saleyo & Zoquadyo (P8, P4/11) [3 -18 11], (1728/1715 = r3g)

(4000/3969 = rry3) 4375/4374

1 2 3 3
0 -11 -18 -5
5.395 1.758 42.632 <<11 18 5 3 -23 -39]]
Clyde Tribiyo & Zozoyo (P8, W4P4/12) [-6 -5 6], 245/243

(3136/3125 = zzg5)

1 6 6 12
0 -12 -10 -25
5.610 1.802 47.261 <<12 10 25 -12 6 30]]
Septimin Lala-leyo & Ruyoyo (P8, WWP4/11) [-35 6 11], 225/224

(84035/82944 = z5y)

1 4 1 5
0 -11 6 -10
5.874 1.896 54.502 <<11 -6 10 -35 -15 40]]
Echidna Sagugu & Triru-agu (P8/2, P4/3) 2048/2025, 1728/1715

(not a best ext)

2 1 9 2
0 3 -6 5
5.925 1.984 58.033 <<6 -12 10 -33 -1 57]]
Compton 12-edo & Ruyoyo (P8/12, ^1) [-19 12], 225/224

(250047/250000)

12 19 0 -22
0 0 1 2
5.927 1.219 35.686 <<0 12 24 19 38 22]]
Bidia (Sagugu &) Trisa-quadru (P8/4, P5) 2048/2025, (3136/3125 = zzg5)

[43 -20 0 -4] (downward ext.)

4 0 22 43
0 1 -2 -5
5.940 1.921 56.474 <<4 -8 -20 -22 -43 -24]]
Wizard Lala-quadtriyo & Ruyoyo (P8, WM9/12) [-31 2 12], 225/224

(118098/117649 = Lr6)

2 1 5 2
0 6 -1 10
6.372 1.207 40.846 <<12 -2 20 -31 -2 52]]
Buzzard Sasa-quadyo & Saruyo (P8, P12/4) [24 -21 4], (1728/1715 = r3g)

5120/5103 (torsion)

1 0 -6 4
0 4 21 -3
6.420 1.396 47.963 <<4 21 -3 24 -16 -66]]
Semisept Sasa-segu & Saru-atribigu (P8, W6P5/17) [30 6 -17], (1728/1715 = r3g)

(3136/3125 = zzg5) [12 3 -6 -1]

1 12 6 12
0 -17 -6 -15
6.499 1.434 50.472 <<17 6 15 -30 -24 18]]
Hemiwürschmidt Saquadbigu & Zozoquingu (P8, WWP5/16) [17 1 -8], (2401/2400 = z4gg)

3136/3125 (torsion)

1 15 4 7
0 -16 -2 -5
6.598 0.560 20.307 <<16 2 5 -34 -37 6]]
Hemikleismic Tribiyo & Rurutriyo (P8, P12/12) [-6 -5 6], 4000/3969

(6144/6125 = rrg3)

1 0 1 4
0 12 10 -9
6.704 1.390 52.054 <<12 10 -9 -12 -48 -49]]
Sensei Sepgu & Ruyoyo (P8, WWP5/7) 78732/78125, 225/224 1 6 8 23
0 -7 -9 -32
6.706 1.580 59.218 <<7 9 32 -2 31 49]]
Hemififths Trisa-Yoyo & Saruyo (P8, P5/2) [35 -25 2], (2401/2400 = z4gg)

5120/5103 (torsion)

1 1 -5 -1
0 2 25 13
6.812 0.575 22.243 <<2 25 13 35 15 -40]]
Pluto Trisa-sepyo & Sazoyoyo (P8, W3P4/7) [25 -26 7], ([5 -4 3 -2] [5 -7 -1 3]) [10 -11 2 1] (torsion) 1 5 15 15
0 -7 -26 -25
7.022 1.400 57.514 <<7 26 25 25 20 -15]]
Amity Saquinyo & Zoquadyo (P8, P11/5) [9 -13 5], 4375/4374

(5120/5103 = sry)

1 3 6 -2
0 -5 -13 17
7.127 0.559 23.649 <<5 13 -17 9 -41 -76]]
Merman Trila-sepyo & Ruyoyo (P8, W3P4/7) [-40 15 7], 225/224 (2500000/2470629 = r7y7) 1 5 -5 -5
0 -7 15 16
7.243 1.260 55.078 <<7 -15 -16 -40 -45 5]]
Parakleismic Thegu & Zoquadyo (P8, W3P4/13) [8 14 -13], (3136/3125 = zzg5)

4375/4374 (torsion)

1 5 6 12
0 -13 -14 -35
7.343 0.610 27.431 <<13 14 35 -8 19 42]]
Slender Trila-theyo & Ruyoyo (P8, P4/13) [-46 10 13], 225/224 (589824/588245 = sr6g) 1 2 2 3
0 -13 10 -6
7.359 1.261 56.934 <<13 -10 6 -46 -27 42]]
Hemithirds Sasa-quintrigu & Zozoquingu (P8, WWP4/15) [38 -2 -15], (1029/1024 = Lz3 3136/3125 = zzg5) [-15 1 -5 1] (torsion) 1 4 2 2
0 -15 2 5
7.385 0.974 44.284 <<15 -2 -5 -38 -50 -6]]
Unidec Laquadtrigu & Zoquadyo (P8/2, Wm7/12) [-7 22 -12], (1029/1024= Lz3) 4375/4374 (torsion) 2 5 8 5
0 -6 -11 2
7.662 0.785 38.393 <<12 22 -4 7 -40 -71]]
Ennealimmal Satritribiyo & Zoquadyo (P8/9, P5/2) [1 -27 18], (2401/2400 = z4gg) 4375/4374 (torsion) 9 1 1 12
0 2 3 2
7.714 0.073 3.610 <<18 27 18 1 -22 -34]]
Guiron Layo & Latrizo

(best Slendric ext is undefined)

(P8, P5/3) [-11 8 1], 1029/1024

(10976/10935)

1 1 7 3
0 3 -24 -1
7.795 0.939 47.544 <<3 -24 -1 -45 -10 65]]
Misty Sasa-trigu & Saruyo (P8/3, P5) [26 -12 -3], (3136/3125 = zzg5)

5120/5103 (torsion)

3 0 26 56
0 1 -4 -10
7.993 0.691 36.802 <<3 -12 -30 -26 -56 -36]]
Hendecatonic Trisa-legu & Sazoquadgu (P8/11, P5) [43 -11 -11], (6144/6125 = srrg3

[5 -7 -1 3]) [16 -6 -4 1]

11 0 43 -4
0 1 -1 2
8.442 0.692 41.081 <<11 -11 22 -43 4 82]]
Harry Lala-tribigu & Labirugu (P8/2, P4/6)

true double

[-13 17 -6], (2401/2400 = z4gg)

19683/19600 (torsion)

2 4 7 7
0 -6 -17 -10
8.457 0.572 34.077 <<12 34 20 26 -2 -49]]
Hemiseven Trila-tribigu & Lazogugu (P8, WWP4/6) [-32 29 -6], (1029/1024 19683/19600) [-14 10 -2 -1] 1 4 14 2
0 -6 -29 2
8.570 0.924 56.557 <<6 29 -2 32 -20 -86]]
Tritikleismic Tribiyo & Latrizo (P8/3, P4/6)

true double

15625/15552, 1029/1024 3 0 3 10
0 6 5 -2
8.707 0.892 56.337 <<18 15 -6 -18 -60 -56]]
Quadritikleismic Tribiyo & Bizozogu (P8/4, P11/6)

true double

15625/15552, 2401/2400 4 0 4 7
0 6 5 4
8.908 0.593 39.231 <<24 20 16 -24 -42 -19]]
Hemischis Layo & Sarurutrigu (P8, P4/2) [-15 8 1], 6144/6125

(19683/19600 = Lrrgg)

1 0 15 -17
0 2 -16 25
9.155 0.656 45.817 <<2 -16 25 -30 34 103]]
Subpental Sepgu & Zozoquingu (P8, W4P4/14) [2 9 -7], 3136/3125

(19683/19600 = Lrrgg)

1 6 8 17
0 -14 -18 -45
9.279 0.757 54.303 <<14 18 45 -4 32 54]]
Countercata Tribiyo & Saruyo (P8, P12/6) 15625/15552, 5103/5120 1 0 1 11
0 6 5 -31
9.466 0.698 52.128 <<6 5 -31 -6 -66 -86]]
Grendel Trisa-twenty-thegu & Sazoquinbigu (P8, W7P4/23) [55 -1 -23], (6144/6125 = srrg3

16875/16807 = r5y4) [22 -1 -10 1]

1 9 2 7
0 -23 1 -13
9.823 0.645 51.834 <<23 -1 13 -55 -44 33]]
Kwai Quinsayo & Saruyo (P8, P5) [50 -33 1], 5120/5103

(16875/16807)

1 0 -50 -40
0 1 33 27
9.844 0.675 54.476 <<1 33 27 50 40 -30]]
Hemischismic Layo & Zozoquingu (P8/2, P5) [-15 8 1], 3136/3125

([-9 8 -4 2])

2 0 30 69
0 1 -8 -20
10.11 0.643 54.744 <<2 -16 -40 -30 -69 -48]]
Sesquiquartififths Layo & Bizozogu (P8, P5/4) [-15 8 1], 2400/2401

([-35 15 0 4])

1 1 7 5
0 4 -32 -15
10.196 0.130 11.244 <<4 -32 -15 -60 -35 55 ]]
Octoid Saquadtribiyo & Zoquadyo (P8/8, P4/3) [-5 -32 24], 4375/4374 (16875/16807) 8 1 3 3
0 3 4 5
10.207 0.491 42.670 <<24 32 40 -5 -4 3]]
Tertiaseptal Quadla-lebiyo & Lazoquinyo (P8, P11/22) [-59 5 22], (2401/2400 = z4gg)

65625/65536

1 3 2 3
0 -22 5 -3
10.247 0.149 12.995 <<22 -5 3 -59 -57 21]]
Mirkat Trila-tritribigu & Lazoquadbiru (P8/3, WWM6/18) [-20 39 -18], (16875/16807 = r5y4 19683/19600) [-8 15 -8 1] 3 2 1 2
0 6 13 14
10.652 0.628 59.376 <<18 39 42 20 16 -12]]
Pontiac Layo & Zoquadyo (P8, P5) [-15 8 1], 4375/4374

(65625/65536)

1 0 15 -59
0 1 -8 39
10.787 0.146 14.133 <<1 -8 39 -15 59 113]]
Nessafof Saseptrigu & Zotritrigu (P8/3, P11/7) [25 15 -21], (6144/6125 = srrg3

(250047/250000 = z3g6) [7 7 -9 1]

3 2 5 10
0 7 5 -4
10.834 0.461 45.048 <<21 15 -12 -25 -78 -70]]
Chromat Saquinyo & Satrizo-agu (P8/3, P11/5) [9 -13 5], 10976/10935

(235298/234375 = z6g7)

3 4 5 6
0 5 13 16
11.375 0.533 57.499 <<15 39 48 27 34 2]]
Septiquarter Quadsa-sepyo & Saruyo (P8, P11/7) [44 -38 7], 5103/5120

(420175/419904 = z5yy)

1 3 10 2
0 -7 -38 4
11.425 0.494 53.760 <<7 38 -4 44 -26 -116]]
Sengagen Sasa-twenty-negu & Saruquadtrigu (P8, P5/29) [42 16 -29], (3136/3125 = zzg5

420175/419904) [18 8 -12 -1]

1 1 2 2
0 29 16 40
11.446 0.531 57.978 <<29 16 40 -42 -18 48]]
Enneadecal Neyo & Zoquadyo (P8/19, P5) [-14 -19 19] 4375/4374

(703125/702464)

19 0 14 -37
0 1 1 3
11.926 0.092 10.954 <<19 19 57 -14 37 79]]
Septisuperfourth Sasa-tritrigu & Sarurutrigu (P8/2, P4/9) [32 -7 -9], 6144/6125

(118098/117649 = Lr6)

2 4 4 7
0 -9 7 -15
11.986 0.495 59.241 <<18 -14 30 -64 -3 109]]
Quinmite Sasebigu & Zotritrigu (P8, W8P5/34) [33 29 -34], (2401/2400)

1959552/1953125 = zg9

1 27 24 20
0 -34 -29 -23
12.636 0.281 37.322 <<34 29 23 -33 -59 -28]]
Gamera Sasa-twenty-theyo & Zoquadyo (P8, W4P4/23) [10 -40 23], 4375/4374

(589824/588245 = sr6g)

1 6 10 3
0 -23 -40 -1
12.911 0.271 37.648 <<23 40 1 10 -63 -110]]
Amicable Saquinyo & Bizozogu (P8, P11/20) 1600000/1594323, 2401/2400 1 3 6 5
0 -20 -52 -31
12.973 0.324 45.473 <<20 52 31 36 -7 -74]]
Semidimfourth Lathirty-wegu & Zoquadyo (P8, W11P5/31) [7 41 -31], 4375/4374 (235298/234375) 1 21 28 36
0 -31 -41 -53
13.269 0.377 55.249 <<31 41 53 -7 -3 8]]
Term Layo & Trizogugu (P8/3, P5) 32805/32768, 250047/250000 3 0 45 94
0 1 -8 -18
13.877 0.124 19.950 <<3 -24 -54 -45 -94 -58]]
Mitonic Trila-segu & Zoquadyo (P8, WWP5/17) [-16 35 -17], 4375/4374

(2100875/2097152)

1 16 32 -15
0 -17 -35 21
14.474 0.144 25.184 <<17 35 -21 16 -81 -147]]
Fifthplus Quinla-twenty-theyo & Lazoquinyo (P8, W9P4/23) [-74 13 23], 65625/65536 (420175/419904) 1 11 -3 20
0 -23 13 -42
14.679 0.144 25.840 <<23 -13 42 -74 2 134]]
Emmthird Tribila-sepbigu & Lala-rutrigu (P8, W4P5/14) [-61, 59, -14], (2401/2400)

14348907/14336000

1 11 42 25
0 -14 -59 -33
14.897 0.090 16.736 <<14 59 33 61 13 -89]]
Decoid Quadsa-quinbigu & Sasa-birugugu (P8/10, P4/2) true double [47 -15 -10], (2400/2401 = z4gg) 67108864/66976875 10 0 47 36
0 2 -3 -1
14.948 0.182 33.902 <<20 -30 -10 -94 -72 61]]
Neptune Laquinquadyo & Laruruleyo (P8, W19P4/40) [-29 -11 20], (2401/2400) 48828125/48771072 1 21 13 13
0 -40 -22 -21
15.001 0.125 23.427 <<40 22 21 -58 -79 -13]]
Mutt Trila-septriyo & Lazoquinyo (P8/3, WWP4/7) [-44 -3 21], 65625/65536 (250047/250000 = z3g6) 3 5 7 8
0 -7 -1 12
15.075 0.150 28.406 <<21 3 -36 -44 -116 -92]]
Tsaharuk Layo & Quinzo-ayoyo (P8, P5/5) 32805/32768, 420175/419904 1 1 7 0
0 5 -40 24
15.750 0.148 30.697 <<5 -40 24 -75 24 168]]
Septichrome Quinla-quintrigu & Lala-rutrigu (P8/3, P5/5) [-46 51 -15], (250047/250000 = z3g6 2460375/2458624 = Lr4y3) [-14 15 -3 -1] 3 3 1 0
0 5 17 24
16.640 0.073 16.814 <<15 51 72 46 72 24]]
Quasiorwell TrIbisa-nebigu & Sazoquinbigu (P8, W8P5/38) [93 -3 -38], (2401/2400 = z4gg)

[22 -1 -10 1]

1 31 0 9
0 -38 3 -8
16.766 0.153 35.832 <<38 -3 8 -93 -94 27]]
Vishnu Sasepbigu & Zoquadyo (P8/2, P4/7) [23 6 -14], 4375/4374 (29360128/29296875 = Lr4y3) 2 4 5 10
0 -7 -3 -37
16.789 0.178 41.912 <<14 6 74 -23 78 155]]
Newt Quadbisa-gugu & Sasaru (P8, P5/2) [95 -57 -2], (2401/2400)

33554432/33480783 = ssr

1 1 19 11
0 2 -57 -28
16.876 0.176 41.878 <<2 -57 -28 -95 -50 95]]
Supermajor Sa-thirty-seyo & Zoquadyo (P8, W13P4/37) [-13 -46 37], 4375/4374

(52734375/52706752 = Lr7y9)

1 15 19 30
0 -37 -46 -75
16.944 0.045 10.836 <<37 46 75 -13 15 45]]
Qak Quadla-forty-weyo & Lala-ruquadquadyo (P8, W15P5/41) [-73 -14 41], ([-6 -8 2 5]

(703125/702464 = Lr3y7) [-28 -4 16 -1]

1 27 11 40
0 -41 -14 -60
17.375 0.116 29.267 <<41 14 60 -73 -20 100]]
Vulture Sasa-quadyo & Zoquadyo (P8, P12/4) [24 -21 4], 4375/4374

(33554432/33480783 = ssr)

1 0 -6 25
0 4 21 -56
17.675 0.142 36.985 <<4 21 -56 24 -100 -189]]
Septidiasemi Tritrila-thebiyo & Lalazo-atribiyo (P8, WWP5/26) [-119 37 26], (2401/2400 = z4gg)

2152828125/2147483648

1 25 -31 -8
0 -26 37 12
18.931 0.148 44.115 <<26 -37 -12 -119 -92 76]]
Acrokleismic Quadquadbigu & Zoquadyo (P8, W8P4/32) [22 33 -32], 4375/4374

(2202927104/2197265625 = sz5g12)

1 10 11 27
0 -32 -33 -92
19.245 0.182 56.184 <<32 33 92 -22 56 121]]
Pnict Lathetriyo & Ruquintriyo (P8/3, WWP5/13) [-43 -30 39], (250047/250000 = z3g6 [-21 0 3 5]) [-13 -12 15 -1] 3 10 11 6
0 -13 -10 6
19.517 0.144 45.660 <<39 30 -18 -43 -138 -126]]
Maviloid Thegu & Bizozogu (P8, W22P5/52) [8 14 -13], 2401/2400 1 31 34 26
0 -52 -56 -41
19.870 0.175 57.632 <<52 56 41 -32 -81 -62]]
Tokko Quadbila-thegu & Lala-rutrigu (P8, WWP5/13) [-76 67 -13], ([-6 -8 2 5]

[-20 7 -1 4]) [-14 15 -3 -1]

1 12 56 -2
0 -13 -67 6
19.992 0.133 44.417 <<13 67 -6 76 -46 -202]]

Junk temperaments

Some of these contain the trivial commas Yobi and Rubi, which set some prime to some number of octaves, and in effect remove the prime from the subgroup. These trivial commas can be omitted from the temperament name if desired. 1-edo can be replaced with nowa.

A third comma is included in the comma list if it has the same or smaller odd limit, and roughly the same or smaller size in cents. This comma isn't used in the temperament name, and is in parentheses.

TO DO: correct the mappings

Name Commas Pergen Generator Mapping Comp Error Badness Wedgie
1-edo (& Yobi) + za 4/3, 5/4 (P8, M2) 8/7 1 2 2 0
0 0 0 1
0.266 400.986 23.561 <<0 0 1 0 2 2]]
1-edo (& Rubi) + ya 4/3, 8/7 (7/6) (P8, M3) 5/4 1 2 0 3
0 0 1 0
0.340 252.955 24.334 <<0 1 0 2 0 -3]]
1-edo & Zoguquad 4/3, 7/5 (P8, M3) 5/4 = 7/4 1 2 0 0
0 0 1 1
0.367 309.005 34.752 <<0 1 1 2 2 0]]
Gutri & Zobi 6/5, 7/6 (P8, P5) 3/2 1 0 1 1
0 1 1 1
0.373 199.358 23.114 <<1 1 1 -1 -1 0]]
Yobi & Zobi 5/4, 7/6 (P8, P5) 3/2 1 0 2 1
0 1 0 1
0.401 168.811 22.624 <<1 0 1 -2 -1 2]]
Yobi & Rubi 5/4, 8/7 (P8, P5) 3/2 1 0 2 3
0 1 0 0
0.437 223.834 35.689 <<1 0 0 -2 -3 0]]
Gutri & Rutri 6/5, 9/7 (P8, P5) 3/2 1 0 1 0
0 1 1 2
0.458 152.797 26.720 <<1 1 2 -1 0 2]]
Gutri & Rubi 6/5, 8/7 (P8, P5) 3/2 1 0 1 3
0 1 1 0
0.470 135.120 24.843 <<1 1 0 -1 -3 -3]]
2-edo & Gutri + za 9/8, 6/5 (P8/2, ^1) 8/7 2 3 5 0
0 0 0 1
0.508 134.886 29.047 <<0 0 2 0 3 5]]
Yo & Zobi 10/9, 7/6 (P8, P5) 3/2 1 0 -1 1
0 1 2 1
0.517 100.760 22.434 <<1 2 1 1 -1 -3]]
Yobi & Zotri 5/4, 21/16 (21/20) (P8, P5) 3/2 1 0 2 4
0 1 0 -1
0.536 159.295 38.111 <<1 0 -1 -2 -4 -2]]
Gutri & Zotri 6/5, 21/16 (P8, P5) 3/2 1 0 1 4
0 1 1 -1
0.603 180.305 54.612 <<1 1 -1 -1 -4 -5]]
2-edo (& Rubi) + ya 9/8, 8/7 (P8/2, ^1) 5/4 2 3 0 6
0 0 1 0
0.613 126.550 39.612 <<0 2 0 3 0 -6]]
2-edo & Ruyo 9/8,15/14 (P8/2, ^1) 5/4 = 7/6 2 3 0 1
0 0 1 1
0.631 58.311 19.373 <<0 2 2 3 3 -1]]
Gubi (& Rubi) 16/15, 8/7 (15/14) (P8, P5) 3/2 1 0 4 3
0 1 -1 0
0.637 70.842 23.922 <<1 -1 0 -4 -3 3]]
Yo (& Rubi) 10/9, 8/7 (P8, P5) 3/2 1 0 -1 3
0 1 2 0
0.648 81.437 28.454 <<1 2 0 1 -3 -6]]
Gubi & Zobi 16/15, 7/6 (P8, P5) 3/2 1 0 4 1
0 1 -1 1
0.649 103.614 36.419 <<1 -1 1 -4 -1 5]]
Yo & Ruyo 10/9, 15/14 (P8, P5) 3/2 1 0 -1 -2
0 1 2 3
0.656 66.836 23.962 <<1 2 3 1 2 1]]
Yoyoquad & Zobi 25/18, 7/6 (25/21) (P8/2, P5) 3/2 2 0 1 2
0 1 1 1
0.724 136.735 59.654 <<2 2 2 -1 -2 -1]]
Yoyo & Zobi 25/24, 7/6 (28/25) (P8, P5/2) 5/4 1 1 2 2
0 2 1 2
0.736 97.698 44.046 <<2 1 2 -3 -2 2]]
Guquad & Rutri 27/20, 9/7 (21/20) (P8, P5) 3/2 1 0 -2 0
0 1 3 2
0.736 132.937 59.948 <<1 3 2 2 0 -4]]

Notes to self:

Overall, the best Rule #3 seems to be minimal odd limit, with one elaboration to help minimize name length: You can subtract commas. Gu & Rugu becomes Gu & Ru, because the Rugu comma is the sum of the Ru and the Gu commas.

Yazalatha Orwell is Lasepyo & Ruyoyo & Loruru & Thuloruyoyo. Subtract Ruyoyo from the last comma to make Thulo. Or, we can justify Thulo using rungspan as a metric, which is the triangularized weighted taxicab distance. Thulo = 352/351 = (x, -3, 0, 0, 1, -1), rungspan = 13 x 27 = 351. Thuloruyoyo = 275/273 = (x, -1, 2, -1, 1, -1), rungspan = 13 x 7 x 5 = 455.

Alternative for minimal odd limit rule is minimal rungspan. Odd limit (25/21) = 25, rungspan (25/21) = 35, so sometimes rungspan is greater.

Saquadyo is quarter-5th, and Bizozogu is rank-3 half-5th, and Saquadyo & Bizozogu (octocot) is eighth-5th. Yet Lulu is half-5th and Quadluyo is rank-3 quarter-5th (G = 11/10), and Lulu & Quadluyo is only quarter-5th. So sometimes P5/4 + P5/2 = P5/4, and sometimes it's P5/8!

ya (P8, P5/4) + yaza (P8, P5/2, ^1) = (P8, P5/8)

ila (P8, P5/2) + yala (P8, P5/4, ^1) = (P8, P5/4)