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 | cedgie |
|---|---|---|---|---|---|---|---|---|
| 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 | (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 | Sawa & 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 | Sawa (& 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 | Lawa (& 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) *
MoTha |
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)
NiTe |
[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) *
MeTho |
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)
MaTho |
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)
MaLu |
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) *
MaThoBi |
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) *
MoLa |
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) *
MoThe/MuThi |
[-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)
MuweTho |
[-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)
NaTho |
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) *
MoTha |
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)
MoThu |
[-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)
MuweTho |
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)
FoTha |
[-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) *
MeThu/MiTho |
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)
MoThuwe (MoLi) |
250/243, 50/49 (245/243)
not best ya ext. of Latribiru |
2 4 6 7 0 -3 -5 -5 |
2.784 | 6.810 | 43.983 | <<6 10 10 2 -1 -5]] |
| Porcupine | Triyo (& Ru) | (P8, P4/3)
MoTha |
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)
RuTha |
[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, cm7/8) | [-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 | Lalawa (& 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, ccP5/7) | [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, ccP5/10) | [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, ccP5/8) | [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, ccP4/9) | [-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, ccP4/5) | [-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, c4P4/12) | [-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, ccP4/11) | [-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 | Lalawa & 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, cM9/12) | [-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, c6P5/17) | [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, ccP5/16) | [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, ccP5/7) | 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, c3P4/7) | [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, c3P4/7) | [-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, c3P4/13) | [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, ccP4/15) | [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, cm7/12) | [-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, ccP4/6) | [-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, c4P4/14) | [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-twethegu & Sazoquinbigu | (P8, c7P4/23) | [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, ccM6/18) | [-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-twenegu & 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, c8P5/34) | [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-twetheyo & Zoquadyo | (P8, c4P4/23) | [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 | Lathiwegu & Zoquadyo | (P8, c11P5/31) | [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, ccP5/17) | [-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-twetheyo & Lazoquinyo | (P8, c9P4/23) | [-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, c4P5/14) | [-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, c19P4/40) | [-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, ccP4/7) | [-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, c8P5/38) | [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-thiseyo & Zoquadyo | (P8, c13P4/37) | [-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-foweyo & Lala-ruquadquadyo | (P8, c15P5/41) | [-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, ccP5/26) | [-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, c8P4/32) | [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, ccP5/13) | [-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, c22P5/52) | [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, ccP5/13) | [-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 | cedgie |
|---|---|---|---|---|---|---|---|---|
| 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 they combine to make Saquadyo & Bizozogu (octocot), which 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)