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

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

Below is a complete listing of all 193 11-limit rank-two temperaments with TE complexity less than 16 and TE badness less than 1/30, 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.

Solfege names

The solfege name is the pergen's name plus the mapping of primes 5, 7, 11, etc. expressed as a uniform solfege syllable. (Primes 2 and 3 are by definition Da and Sa.) See the list of uniform solfeges for pergens. If there are two possible solfege syllables, choose so that:

  • 5/4 is a 3rd, preferably a major 3rd
  • 7/4 is a 7th, preferably a minor 7th
  • 11/8 is a 4th, preferably a perfect 4th (perfect is a somewhat arbitrary choice)
  • 13/8 is a 6th, preferably a major 6th (major is also arbitrary)
  • 17/16 is a 2nd, preferably a minor 2nd
  • 19/16 is a 3rd, preferably a minor 3rd

In extremely inaccurate temperaments, two primes can map to the same note. Generally they will use different syllables, as in half-4th MuThoFo. The mapping is (1 2 3 3 4) (0 -2 -3 -1 -3). 5/4 = ^M3 and 11/8 = v4, but Mu = Fo because 11/10 vanishes.

If a prime is omitted, it's place is taken by "A". Thus 11-limit Porcupine is third-4th MoThaFu and 2.3.5.11 Porcupine is third-4th MoAFu. Thus the solfege name specifies the prime subgroup exactly.

Complex pergens have more than 5 fifthchains and require compound vowels, as shown below. The solfege becomes less singable but still functions well for naming. The sung solfege (as opposed to the naming solfege) might use additional vowels such as -ih or -uh instead of compound vowels.

unsplit (no-pair) solfege
-4 -3 -2 -1 0 1 2 3 4
d4 ddd dd dim plain aug AA AAA A4
-eye

"ay-yay"

-eyo -e -o -a -u -i -iyu -iyi

"ee-yee"

single-pair solfeges
-4 -3 -2 -1 0 1 2 3 4
quud trud dud down plain up dup trup quup
-eye -eyo -e -o -a -u -i -iyu -iyi
double-pair solfeges
down plain up
lift -owi -i -uwi
plain -o -a -u
drop -owe -e -uwe

Any compound vowel with a "w" is for double-pair only. Mnemonic: w = double-u = double-pair.

When devising a solfege for a double-pair pergen, the lift is generally larger than the up.

Solfege prefixes (consonants or consonant pairs) cover the range from dim5 to aug4. To go beyond that, the unsplit pergen (P8, P5) uses -u/-o to mean aug/dim and -i/-e to mean AA/dd. Thus Pa = A4, Pu = AA4, Pi = A34, Piyu = A44 and Piyi = A54. Thus Garibaldi is (P8, P5) FoDeRiyu where 11/8 = A32. And Kwai is (P8, P5) TiyiPiyuFle, where 5/4 = A47 and 7/4 = A44.

For any other pergen, if needed Aug and Dim are added before the solfege syllable, and AugPa = AA4. Thus Migration is "half-5th MaAugLuFu", where 7/4 = ^A6. And Sesquart is "quarter-5th DimFaThoFi", where 5/4 = d4 (hence Layo/Schismic).

Sometimes one can remove an Aug or Dim by adding or subtracting the enharmonic interval EI.

  • Migration: half-5th, EI = vvA1, MaAugLuFu --> MaLiyuFu, ^A6 --> ^3M6
  • Witchcraft: fifth-12th, EI = v\\m2, MoTheAugMi --> MoThePowe, /A3 --> v\A4
  • Hemififths: half-5th, EI = vvA1, AugRuLuFu --> RiyuLuFu, ^A2 --> ^^^M2
  • Marvo: (P8, ccP5/6), EI = v6A1, MoAugLeFi --> MoLiyi, vvA6 --> ^4M6
  • Guiron: (P8, P5/3), EI = v3m2, DimFaThoAugMu --> NiyuThoPe, d4 --> ^3m3, ^A3 --> vvA4
  • Sesquart: quarter-5th, EI = v4A1, DimFaThoFi --> FeyeThoFi, d4 --> v44
  • Bischismic = (P8/2, P5), EI = ^^d2, DimFaDimDimDoQuadDimTha --> MeTheyoSheye

Question: is this really better? obscures some things like Layo

  • Amity: (P8, P11/5), EI = v5A1, MoThoAugMu --> MoThoMiyiyi, NO GOOD
  • Quanharuk: (P8, P12/5), EI = ^^\d2, v\\m2, DimFaThoAugMi --> MowowiThoPowe, /A3 --> v\A4, NO GOOD
  • Pogo: (P8/2, P4/3), EI = ^^d2, \3A1, DimFaThuweSho --> MowoThuweSho, NO GOOD

Multi-edo pergens like (P8/5, ^1) map Sa to the perchain, not the genchain. Their name is the edo plus the solfege syllables. For example, Compton is pergen (P8/12, ^1) and is "12edo MoThePeyo", where 11/8 = v3A4.

"Tippy" pergens have two valid solfeges, called #1 and #2. Which one to use depends on the fifth's exact tuning. (#1 is always appropriate for a just 3/2.) Tippy pergens are marked with an asterisk in the list below. Solfege #1 is far more common than #2, so it's the default. The only #2 solfege is Injera, which is named (P8/2, P5) MaThoPa #2 or "halves MaThoPaBi".

The solfege for naming purposes is based on the optimal tuning. But that can vary within a temperament family depending on the exact comma set. For example, quarter-4th tips at 19edo. The optimal POTE 5th of 5-limit Negri (Laquadyo) is barely sharp of 19edo, so it's named using solfege #1 as quarter-4th Mo. (In practice single-comma temperaments would probably use the color name.) But 11-limit Negri's optimal 5th is slightly flat of 19edo. But solfege #1 is still used for the sake of consistency. Always use whichever solfege the simplest strong (same-pergen) restriction implies.

Question: 5-limit Diminished (Quadgu) is barely solfege #2, with POTE P5 = 699.507¢. Quadru is firmly solfege #1, with P5 = 768.284¢. Both are (P8/4, P5). Consider 7-limit Diminished, which is Quadgu & Quadru. Is it MoThu or MuThoBi?

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.

  • Mapping column: each mapping's implied generator matches the pergen, thus many have been modified from the original page.
  • Pergen column: all double-splits are false doubles unless otherwise noted. Solfege names with issues are bolded.
  • Commas column: ratios are grouped by prime limit with actual commas (","), and sorted within prime-limit by double odd limit.
  • Color name column: alternatives or objections are bolded
  • Co = 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
Name Mapping Pergen Name Commas Color Name Co Err Bad
1 1 1 1 1
0 1 2 3 4 		(P8, P5)

RaLaMa

10/9, 15/14, 22/21 Yo & Ruyo & Loru .655 54.775 22.549
3 5 7 8 10
0 0 0 1 0 		(P8/3, ^1)

FaSuFa

32/27, 10/9 (16/15), 11/10 Watri & Yo & Logu + za .680 74.627 32.666
1 1 3 3 5
0 1 -1 0 -2 		(P8, P5)

FaDaTha

16/15, 8/7 (15/14), 25/22 Gubi & Rubi & Luyoyobi .692 73.354 33.117
4 6 9 11 14
0 0 0 0 -1 		(P8/4, ^1)

NaLaPo?

9/8, 25/24, 15/14 Wabi & Yoyo & Ruyo + ila .712 47.618 22.540
2 3 5 6 8
0 0 -1 -1 -2 		(P8/2, ^1)

FoDoDe

9/8, 15/14 (21/20), 25/22 Wabi & Ruyo & Luyoyobi .718 57.400 27.551
1 1 2 2 3
0 2 1 3 2 		(P8, P5/2)

MoToSa

25/24, 15/14, 12/11 Yoyo & Ruyo & Lu .718 46.851 22.488
1 1 3 4 4
0 1 -1 -2 -1 		(P8, P5)

FaThaFa

16/15, 21/20, 11/10 Gubi & Zogu & Logu .727 44.826 21.957
3 5 7 9 11
0 0 0 -1 -1 		(P8/3, ^1)

FaDoFo

32/27, 10/9 (16/15), 22/21 Watri & Yo & Loru .771 47.381 25.592
1 1 3 4 3
0 1 -1 -2 1 		(P8, P5)

FaThaSa

16/15, 21/20, 12/11 Gubi & Zogu & Lu .776 45.662 24.928
1 2 3 3 4
0 -2 -3 -1 -3 		(P8, P4/2)

MuThoFo

27/25, 21/20, 11/10 (22/21) Gugu & Zogu & Logu .796 38.983 22.203
1 2 3 3 4
0 -2 -3 -1 -2 		(P8, P4/2)

MuThoSa

27/25, 21/20, 12/11 Gugu & Zogu & Lu .807 41.497 24.184
1 1 3 1 3
0 1 -1 3 1 		(P8, P5)

FaLaSa

16/15, 28/27, 12/11 Gubi & Zo & Lu .832 38.874 23.823
1 1 2 3 3
0 2 1 -1 1 		(P8, P5/2)

MoLoMo

25/24, 21/20, 11/10 (22/21) Yoyo & Zogu & Logu .833 47.271 29.071
Dicot 1 1 2 2 2
0 2 1 3 5 		(P8, P5/2)

MoToPo

25/24, 15/14, 22/21 Yoyo & Ruyo & Loru .854 30.986 19.854
1 1 3 1 4
0 1 -1 3 -1 		(P8, P5)

FaLaFa

16/15, 28/27, 11/10 Gubi & Zo & Logu .905 43.667 30.795
5 8 12 14 17
0 0 0 0 1 		(P8/5, ^1)

MaThaFu

256/243, 16/15, 21/20 (28/27) Sawa & Gubi & Zogu + ila .923 33.964 24.785
1 2 2 3 4
0 -2 1 -1 -3 		(P8, P4/2)

MoThoFo

75/64, 15/14 (35/32), 22/21 Yoyobi & Ruyo & Loru .931 43.645 32.259
1 1 3 4 6
0 1 -1 -2 -4 		(P8, P5)

FaThaFla

16/15, 21/20, 35/33 Gubi & Zogu & Luzoyo .979 40.847 32.831
1 1 3 1 1
0 1 -1 3 4 		(P8, P5)

FaLaMa

16/15, 28/27, 22/21 Gubi & Zo & Loru .986 25.28 20.589
1 1 2 3 4
0 2 1 -1 -2 		(P8, P5/2)

MoLoFa

25/24, 21/20, 33/32 Yoyo & Zogu & iLo 1.016 29.191 24.988
1 1 4 4 4
0 1 -3 -2 -1 		(P8, P5)

NaThaFa

135/128, 15/14, 22/21 (33/32) Layobi & Ruyo & Loru 1.023 30.999 26.828
1 1 0 1 0
0 1 4 3 6 		(P8, P5)

MaLaPa

81/80, 21/20 (28/27), 35/33 Gu & Zogu & Luzoyo 1.042 27.464 24.506
1 1 2 2 4
0 2 1 3 -2 		(P8, P5/2)

MoToFa

25/24, 15/14, 33/32 Yoyo & Ruyo & iLo 1.067 29.219 27.114
1 1 2 3 2
0 2 1 -1 5 		(P8, P5/2)

MoLoPo

25/24, 21/20, 45/44 Yoyo & Zogu & Luyo 1.087 26.805 25.660
Meanertone 1 1 0 1 4
0 1 4 3 -1 		(P8, P5)

MaLaFa

81/80, 21/20 (28/27), 33/32 Gu & Zogu & iLo 1.138 24.359 25.167
Pento 1 2 3 3 5
0 -2 -3 -1 -7 		(P8, P4/2)

MuThoPu

27/25, 21/20 [36/35], 45/44 Gugu & Zogu & Luyo 1.138 22.068 22.799
Pentoid 1 2 3 3 3
0 -2 -3 -1 2 		(P8, P4/2)

MuThoFa

27/25, 21/20, 33/32 Gugu & Zogu & iLo 1.142 21.771 22.649
Meansept 1 1 0 0 0
0 1 4 5 6 		(P8, P5)

MaTaPa

81/80, 15/14, 22/21 (45/44 55/49) Gu & Ruyo & Loru 1.148 30.989 32.521
Sharp 1 1 2 1 2
0 2 1 6 5 		(P8, P5/2)

MoLaPo

25/24, 28/27, 35/33 (45/44) Yoyo & Zo & Luzoyo 1.196 19.922 22.366
2 2 6 7 7
0 1 -1 -1 0 		(P8/2, P5) *

FaToPo

16/15, 50/49, 22/21 Gubi & Biruyo & Loru 1.208 25.57 29.193
1 1 4 5 4
0 1 -3 -4 -1 		(P8, P5)

NaFlaFa

135/128, 21/20, 33/32 (45/44) Layobi & Zogu & iLo 1.226 19.454 22.753
1 1 3 1 6
0 1 -1 3 -4 		(P8, P5)

FaLaFla

16/15, 28/27 [36/35], 80/77 (77/75) Gubi & Zo & Luruyo 1.258 23.058 28.153
Hystrix 1 2 3 3 4
0 -3 -5 -1 -4 		(P8, P4/3)

MoThuFu

250/243, 36/35, 22/21 [55/54] (80/77) Triyo & Rugu & Loru 1.335 19.86 26.790
Arnold 1 1 0 4 4
0 1 4 -2 -1 		(P8, P5)

MaThaFa

81/80, 36/35 (64/63), 22/21 (33/32) Gu & Rugu & Loru 1.340 19.265 26.141
5 8 12 14 17
0 0 -1 0 0 		(P8/5, ^1)

MoThaFa

256/243, 28/27, 22/21 (33/32) Sawa (& Zo & Loru) + ya 1.358 22.998 31.934
4 4 7 9 9
0 1 1 1 2 		(P8/4, P5) *

MoThuFu

648/625, 36/35 (50/49), 22/21 Quadgu & Rugu & Loru 1.415 18.282 27.164
1 1 2 4 4
0 2 1 -4 -2 		(P8, P5/2)

MoThaFa

25/24, 64/63, 22/21 (33/32) Yoyo & Ru & Loru 1.431 20.956 31.719
Ferrum 5 8 12 14 18
0 0 -1 0 -1 		(P8/5, ^1)

MoThaSo

256/243, 28/27 (49/48), 35/33 Sawa & Zo & Luzoyo 1.443 20.107 30.883
Decibel 2 4 5 6 7
0 -2 -1 -1 0 		(P8/2, P4/2)

MeThoFuwi

25/24, 49/48, 35/33 Yoyo & Zozo & Luzoyo 1.461 20.67 32.385
2 2 1 2 2
0 1 3 3 4 		(P8/2, P5)

NuLaMa

800/729, 28/27 (50/49), 22/21 (sayoyo is too obscure?) Sayoyo & Zo & Loru

(Zo & Biruyo & Loru?)

1.495 19.317 31.468
1 1 2 1 4
0 2 1 6 -2 		(P8, P5/2)

MoLaFa

25/24, 28/27, 33/32 Yoyo & Zo & iLo 1.500 19.693 32.239
August 3 3 7 5 7
0 1 0 2 2 		(P8/3, P5) *

MoThuPo

128/125, 36/35, 45/44 (56/55) Trigu & Rugu & Luyo 1.506 12.245 20.191
Domineering 1 1 0 4 0
0 1 4 -2 6 		(P8, P5)

MaThaPa

81/80, 36/35 (64/63), 45/44 Gu & Rugu & Luyo 1.523 13.075 21.978
Jamesbond 7 11 16 20 24
0 0 0 -1 0 		(P8/7,^1)

MaToFa

[-11 7], (25/24) 81/80, 33/32 (45/44) Lawa (& Gu & iLo) + za 1.564 13.396 23.524
Diminished 4 4 7 9 14
0 1 1 1 0 		(P8/4, P5) *

MoThuPe

648/625, 36/35 (50/49), 56/55 Quadgu & Rugu & Luzogu 1.582 12.367 22.132
Armodue 1 1 4 0 4
0 1 -3 5 -1 		(P8, P5)

NaTaFa

135/128, 36/35, 33/32 (45/44) Layobi & Rugu & iLo 1.603 14.879 27.211
Dichotic 1 1 2 4 2
0 2 1 -4 5 		(P8, P5/2)

MoThaPo

25/24, 64/63, 45/44 (55/54) Yoyo & Ru & Luyo 1.630 16.311 30.680
Opossum 1 2 3 4 4
0 -3 -5 -9 -4 		(P8, P4/3)

MoLaFu

250/243, 28/27, 56/55 ([55/54] 77/75) Triyo & Zo & Luzogu 1.692 11.146 22.325
Octokaidecal 2 2 1 2 7
0 1 3 3 0 		(P8/2, P5) *

NuLaPo

800/729, 28/27 (50/49), 56/55 (55/54) Sayoyo & Zo & Luzogu 1.698 15.008 30.235
Pajaric 2 2 7 8 7
0 1 -2 -2 0 		(P8/2, P5) *

MoThaPo

[11 -4 -2], (50/49) 64/63, 45/44 (56/55) (torsion) Sagugu & Ru & Luyo 1.722 11.548 23.798
Progression 1 1 2 2 3
0 5 3 7 4 		(P8, P5/5)

NiTeFu

[7 3 -5], 36/35, 56/55 (77/75) Quingubi & Rugu & Luzogu 1.749 12.314 26.050
Decimal 2 4 5 6 9
0 -2 -1 -1 -5 		(P8/2, P4/2)

MeThoFi

25/24, 49/48 (50/49), 45/44

true double

Yoyo & Zozo & Luyo 1.751 12.599 26.712
Blacksmith 5 8 12 14 17
0 0 -1 0 1 		(P8/5, ^1)

MoThaFu

256/243, 28/27 (49/48 64/63), 55/54 Sawa & Zo & Loyo 1.825 10.85 24.641
Demolished 4 4 7 9 7
0 1 1 1 3 		(P8/4, P5) *

MoThuPo

648/625, 36/35 (50/49), 45/44 Quadgu & Rugu & Luyo 1.831 11.635 26.574
Dominant 1 1 0 4 7
0 1 4 -2 -6 		(P8, P5)

MaThaSha

81/80, 36/35 (64/63), 56/55 Gu & Rugu & Luzogu 1.864 10.279 24.180
Decimated 2 4 5 6 6
0 -2 -1 -1 2 		(P8/2, P4/2)

MeThoFa

25/24, 49/48, 33/32

true double

Yoyo & Zozo & iLo 1.886 13.109 31.456
Meanenneadecal 1 1 0 -3 0
0 1 4 10 6 		(P8, P5)

MaLuPa

81/80, 126/125, 45/44 (56/55) Gu & Zotrigu & Luyo 1.918 8.680 21.423
Sidi 1 3 3 6 7
0 -4 -2 -9 -10 		(P8, P11/4) *

MeThoPe

25/24, 245/243, 45/44 (99/98) Yoyo & Zozoyo & Luyo 1.958 12.902 32.957
Ferrier 5 8 12 14 18
0 0 -1 0 -2 		(P8/5, ^1)

MoThaSe

256/243, 28/27 (49/48 64/63), 77/75 Sawa & Zo & Lozogugu 1.993 11.103 29.200
Superpelog 1 2 1 3 3
0 -2 6 -1 2 		(P8, P4/2)

NaThoFa

135/128, 49/48, 33/32 (45/44) Layobi & Zozo & iLo 2.016 10.640 28.535
Negri 1 2 2 3 4
0 -4 3 -2 -5 		(P8, P4/4) *

MoThePo

nearly 19edo

[-14 3 4], (49/48) 225/224, 45/44 (56/55) (torsion) Laquadyo & Ruyoyo & Luyo 2.038 9.594 26.190
Inflated 3 3 7 3 5
0 1 0 3 3 		(P8/3, P5) *

MoLaFu

128/125, 28/27, 56/55 [55/54] Trigu & Zo & Luzogu 2.102 10.843 31.171
Injera 2 2 0 1 0
0 1 4 4 6 		(P8/2, P5) *

MaThoPa #2

81/80, 50/49, 45/44 Gu & Biruyo & Luyo 2.153 7.728 23.124
Negric 1 2 2 3 3
0 -4 3 -2 4 		(P8, P4/4) *

MoTheFa

nearly 19edo

[-14 3 4], (49/48) 225/224, 33/32 (77/75) (torsion) Laquadyo & Ruyoyo & Lu 2.198 9.886 30.617
Triforce 3 6 7 9 11
0 -2 0 -1 -1 		(P8/3, P4/2)

MuweThoFi

128/125, 49/48, 56/55 Trigu & Zozo & Luzogu 2.201 8.427 26.152
Duodecim 12 19 28 34 41
0 0 0 0 1 		(P8/12, ^1)

MaThaFu

[-19 12], 81/80, 36/35 (50/49 64/63) Lalawa (& Gu & Rugu) + ila 2.201 9.839 30.536
Meanundeci 1 1 0 -3 4
0 1 4 10 -1 		(P8, P5)

MaLuFa

81/80, 126/125, 33/32 (55/54 77/75) Gu & Zotrigu & iLo 2.204 10.143 31.539
Semafour 1 2 4 3 3
0 -2 -8 -1 2 		(P8, P4/2)

MaThoFa

81/80, 49/48, 33/32 (55/54) Gu & Zozo & iLo 2.212 9.111 28.510
Augene 3 3 7 12 14
0 1 0 -2 -2 		(P8/3, P5)

MoThaShu

128/125, 64/63, 56/55 (100/99) Trigu & Ru & Luzogu 2.286 5.932 19.613
Godzilla 1 2 4 3 6
0 -2 -8 -1 -12 		(P8, P4/2)

MaThoPa

81/80, 49/48, 45/44 Gu & Zozo & Luyo 2.343 8.404 28.947
Darjeeling 1 0 1 2 0
0 6 5 3 13 		(P8, P12/6)

MuweThoFowi

[-6 -5 6], (49/48) 126/125, 55/54 (77/75) (torsion) Tribiyo & Zotrigu & Loyo 2.347 8.002 27.648
Progress 1 3 0 0 3
0 -3 5 6 1 		(P8, P11/3)

FoThaFu

[15 -5 -3], 64/63, 56/55 (77/75) Satrigu & Ru & Luzogu 2.399 8.662 31.036
Hedgehog 2 4 6 7 8
0 -3 -5 -5 -4 		(P8/2, P4/3) *

MoThuweFu

250/243, 50/49, 55/54 (99/98) Triyo & Biruyo & Loyo 2.439 6.273 23.095
Keemun 1 0 1 2 4
0 6 5 3 -2 		(P8, P12/6)

MuweThoFi

[-6 -5 6], (49/48) 126/125, 56/55 (100/99) (torsion) Tribiyo & Zozo & Luzogu 2.468 7.298 27.410
Porcupine 1 2 3 2 4
0 -3 -5 6 -4 		(P8, P4/3)

MoThaFu

250/243, 64/63, 55/54 (100/99) Triyo & Ru & Loyo 2.478 5.703 21.562
Pajara 2 2 7 8 14
0 1 -2 -2 -6 		(P8/2, P5) *

MoThaSha

[11 -4 -2], (50/49) 64/63, 100/99 (99/98) (torsion) Sagugu & Ru & Luyoyo 2.543 5.151 20.343
Nautilus 1 2 3 3 4
0 -6 -10 -3 -8 		(P8, P4/6)

MoTheFu

250/243, 49/48, 55/54 (100/99) Triyo & Zozo & Loyo 2.548 6.568 26.023
Pajarous 2 2 7 8 1
0 1 -2 -2 5 		(P8/2, P5) *

MoThaFu

[11 -4 -2], (50/49) 64/63, 55/54 Sagugu & Ru & Loyo 2.718 6.427 28.349
Telepathy 1 0 2 -1 -1
0 5 1 12 14 		(P8, P12/5) *

MoThePu

[-10 -1 5], 225/224, 55/54 (99/98 176/175) Laquinyo & Ruyoyo & Loyo 2.864 5.631 27.109
Sensis 1 -1 -1 -2 2
0 7 9 13 4 		(P8, ccP5/7)

no solfege

[2 9 -7], 126/125 (245/243), 56/55 [100/99] Sepgu & Zotrigu & Luzogu 2.98 5.578 28.680
Suprapyth 1 1 -3 4 7
0 1 9 -2 -6 		(P8, P5)

RuThaSha

[12 -9 1], 64/63, 55/54 (99/98) Sayo & Ru & Loyo 3.011 6.264 32.768
Porky 1 2 3 5 4
0 -3 -5 -16 -4 		(P8, P4/3)

MoLuFu

250/243, 225/224, 55/54 (100/99) Triyo & Ruyoyo & Loyo 3.020 5.186 27.268
Meantone 1 1 0 -3 -7
0 1 4 10 18 		(P8, P5)

MaLuMi

81/80, 126/125, 99/98 Gu & Zotrigu & Loruru 3.031 3.218 17.027
Ringo 1 1 5 4 2
0 2 -9 -4 5 		(P8, P5/2)

FoThaFu

[19 -9 -2], 64/63, 56/55 (243/242) Sasa-gugu & Ru & Luzogu 3.126 5.902 32.863
Orwell 1 0 3 1 3
0 7 -3 8 2 		(P8, P12/7)

NiTeyoFu

[-21 3 7], 225/224, 99/98 (121/120 176/175) Lasepyo & Ruyoyo & Loruru 3.242 2.574 15.231
Doublewide 2 1 3 4 8
0 4 3 3 -2 		(P8/2, cm7/8)

no solfege

[-9 -6 8], (50/49) 875/864, 100/99 (99/98 385/384) Quadbiyo & Zotriyo & Luyoyo 3.407 4.988 32.058
Superpyth 1 1 -3 4 -6
0 1 9 -2 16 		(P8, P5)

RuThaRi

[12 -9 1], 64/63 (245/243), 100/99 Sayo & Ru & Luyoyo 3.410 3.88 24.976
Squares 1 3 8 6 7
0 -4 -16 -9 -10 		(P8, P11/4) *

MaThoFi

81/80, [-3 9 0 -4], 99/98 (121/120) Gu & Laquadru & Loruru 3.486 3.240 21.636
Quasisupra 1 1 10 4 7
0 1 -13 -2 -6 		(P8, P5)

ShoThaSha

[23 -13 -1], 64/63, 99/98 (121/120) Sasagu & Ru & Loruru 3.49 4.812 32.203
Valentine 1 1 2 3 3
0 9 5 -3 7 		(P8, P5/9)

no solfege

[13 5 -9], 126/125, (121/120) 176/175 Satritrigu & Zotrigu & Lorugugu 3.651 2.313 16.687
Magic 1 0 2 -1 6
0 5 1 12 -8 		(P8, P12/5) *

MoTheShe

[-10 -1 5], 225/224 (245/243), 100/99 Laquinyo & Ruyoyo & Luyoyo 3.715 2.741 20.352
Meanpop 1 1 0 -3 11
0 1 4 10 -13 		(P8, P5)

MaLuSho

81/80, 126/125, 385/384 Gu & Zotrigu & Lozoyo 3.820 2.770 21.543
Mohajira 1 1 0 6 2
0 2 8 -11 5 		(P8, P5/2)

MaThoFu

81/80, 6144/6125, (121/120) 176/175 (243/242) Gu & Sarurutrigu & Lorugugu 3.863 3.288 26.064
Cassandra 1 1 7 11 14
0 1 -8 -14 -18 		(P8, P5)

FoDeFle

[-15 8 1], 225/224, 100/99 (245/242) Layo & Ruyoyo & Luyoyo 3.897 2.929 23.556
Nusecond 1 3 4 5 5
0 -11 -13 -17 -12 		(P8, P11/11)

no solfege

[5 13 -11], 126/125, 99/98 (121/120) Legu & Zotrigu & Loruru 3.927 3.146 25.621
Migration 1 1 0 -3 2
0 2 8 20 5 		(P8, P5/2)

MaLiyuFu

81/80, 126/125, 121/120 (243/242) Gu & Zotrigu & Lologu 3.935 3.123 25.516
Mothra 1 1 0 3 5
0 3 12 -1 -8 		(P8, P5/3)

MaThoFu

81/80, 1029/1024, 99/98 (385/384) Gu & Latrizo & Loruru 3.99 3.066 25.642
Octacot 1 1 1 2 2
0 8 18 11 20 		(P8, P5/8)

no solfege

[5 -9 4], 245/243, 100/99 (243/242 245/242) Saquadyo & Zozoyo & Luyoyo 4.070 2.785 24.078
Myna 1 -1 0 1 -3
0 10 9 7 25 		(P8, ccP5/10)

no solfege

[9 9 -10], 126/125, 176/175 (243/242) Quinbigu & Zotrigu & Lorugugu 4.127 1.903 16.842
Superkleismic 1 4 5 2 4
0 -9 -10 3 -2 		(P8, ccP4/9)

no solfege

[-5 -10 9], 875/864, 100/99 (245/242 385/384) Tritriyo & Zotriyo & Luyoyo 4.137 2.888 25.659
Würschmidt 1 -1 2 -3 -3
0 8 1 18 20 		(P8, ccP5/8)

no solfege

[17 1 -8], 225/224, 99/98 (176/175 243/242) Saquadbigu & Ruyoyo & Loruru 4.344 2.533 24.413
Miracle 1 1 3 3 2
0 6 -7 -2 15 		(P8, P5/6)

MuweThoFi

[-25 7 6], 225/224, 385/384 (441/440) Lala-tribiyo & Ruyoyo & Lozoyo 4.405 1.083 10.684
Mosura 1 1 0 3 -1
0 3 12 -1 23 		(P8, P5/3)

MaThoPo

81/80, 1029/1024, 176/175 Gu & Latrizo & Lorugugu 4.411 3.170 31.334
Sensus 1 -1 -1 -2 -8
0 7 9 13 31 		(P8, ccP5/7)

no solfege

[2 9 -7], 126/125, 176/175 Sepgu & Zotrigu & Lorugugu 4.503 2.882 29.486
Shrutar 2 3 5 5 7
0 2 -4 7 -1 		(P8/2, M2/4)

NiLuFu

[11 -4 -2], 245/243, (121/120) 176/175 Sagugu & Zozoyo & Lorugugu 4.530 2.563 26.489
Revelation 1 1 3 3 5
0 6 -7 -2 -16 		(P8, P5/6)

MuweThoFu

[-25 7 6], 225/224 (1029/1024), 99/98 [176/175] Lala-tribiyo & Ruyoyo & Loruru 4.531 3.187 32.946
Tritonic 1 4 -3 -3 2
0 -5 11 12 3 		(P8, ccP4/5)

NiThoFu

[-29 11 5], 225/224, (121/120) 441/440 Lala-quinyo & Ruyoyo & Luzozogu 4.596 2.234 23.659
Bunya 1 1 1 -1 2
0 4 9 26 10 		(P8, P5/4)

MoLiFi

[5 -9 4], 225/224, 100/99 (243/242) Saquadyo & Ruyoyo & Luyoyo 4.833 2.722 31.332
Diaschismic 2 2 7 15 21
0 1 -2 -8 -12 		(P8/2, P5) *

MoThoSho

2048/2025, 126/125, 176/175 Sagugu & Zotrigu & Lorugugu 5.048 2.023 25.034
Septimin 1 4 1 5 5
0 -11 6 -10 -7 		(P8, ccP4/11)

no solfege

[-35 6 11], 225/224, (245/242) 385/384 Lala-leyo & Ruyoyo & Lozoyo 5.089 2.496 31.309
Witchcraft 1 0 2 -1 -7
0 5 1 12 33 		(P8, P12/5) *

MoTheAugMi

[-10 -1 5], 225/224 (245/243), 441/440 Laquinyo & Ruyoyo & Luzozogu 5.419 2.204 30.706
Thuja 1 -4 0 7 3
0 12 5 -9 1 		(P8, c5P5/12)

no solfege

[20 5 -12], 126/125, 176/175 (1344/1331) Saquadtrigu & Zotrigu & Lorugugu 5.622 2.233 33.078
Hemiwur 1 -1 2 2 2
0 16 2 5 9 		(P8, ccP5/16)

no solfege

[17 1 -8], (2401/2400) 3136/3125, (121/120) 176/175 (1375/1372) Saquadbigu & Zozoquingu & Lorugugu 5.723 1.918 29.270
Rodan 1 1 -1 3 6
0 3 17 -1 -13 		(P8, P5/3)

MoThoSho

[20 -17 3], (245/243) 5120/5103, 385/384 (441/440) Sasa-triyo & Saruyo & Lozoyo 5.754 1.50 23.093
Echidna 2 4 3 7 5
0 -3 6 -5 7 		(P8/2, P4/3)

NuwiThuweFi

2048/2025, 1728/1715, 176/175 (540/539 896/891) Sagugu & Triru-agu & Lorugugu 5.898 1.62 25.987
Semisept 1 -5 0 -3 -7
0 17 6 15 27 		(P8,c6P5/17)

no solfege

1331/1323 176/175 540/539 5.969 1.373 22.476
Newspeak 1 0 3 1 -4
0 7 -3 8 33 		(P8, P12/7)

NiTeyoPo

1728/1715 225/224 441/440 6.006 1.901 31.438
Hemififths 1 1 -5 -1 2
0 2 25 13 5 		(P8, P5/2)

AugRuLuFu

896/891 243/242 441/440 6.148 1.367 23.498
Garibaldi 1 1 7 11 -10
0 1 -8 -14 23 		(P8, P5)

FoDeRiyu

2200/2187 225/224 385/384 6.365 1.504 27.396
Wizard 2 1 5 2 8
0 6 -1 10 -3 		(P8/2,cM9/12)

no solfege

225/224 385/384 4000/3993 6.421 1.003 18.539
Slender 1 2 2 3 4
0 -13 10 -6 -17 		(P8, P4/13)

no solfege

1331/1323 225/224 385/384 6.727 1.269 25.342
Compton 12 19 28 34 42
0 0 -1 -2 -3 		(P8/12, ^1)

MoThePeyo

225/224 4375/4356 441/440 6.767 1.102 22.235
Hemithirds 1 4 2 2 7
0 -15 2 5 -22 		(P8, ccP4/15)

no solfege

3136/3125 385/384 441/440 7.040 .882 19.003
Catakleismic 1 0 1 -3 9
0 6 5 22 -21 		(P8, P12/6)

MuweLiFu

225/224 385/384 4375/4374 7.254 .965 21.849
Harry 2 4 7 7 9
0 -6 -17 -10 -15 		(P8/2, P4/6)

no solfege

243/242 441/440 4000/3993 7.373 .682 15.867
Pluto 1 5 15 15 2
0 -7 -26 -25 3 		(P8, c3P4/7)

MoLiFi

896/891 1375/1372 540/539 7.524 1.24 29.844
Unidec 2 5 8 5 6
0 -6 -11 2 3 		(P8/2, cm7/12)

no solfege

385/384 441/440 12005/11979 7.532 .642 15.479
Ennealimmic 9 9 13 20 18

0 2 3 2 5

(P8/9, P5/2)

no solfege

4375/4356 243/242 441/440 7.578 .835 20.347
Tritikleismic 3 6 8 8 11
0 -6 -5 2 -3 		(P8/3, P4/6)

no solfege

385/384 441/440 4000/3993 7.587 .792 19.333
Hemiwürschmidt 1 -1 2 2 -3
0 16 2 5 40 		(P8, ccP5/16)

no solfege

243/242 3136/3125 441/440 7.793 .825 21.069
Marvolo 1 2 1 1 2
0 -6 19 26 21 		(P8, P4/6)

NuwiThoFi

225/224 441/440 4000/3993 7.935 1.101 28.965
Bikleismic 2 6 7 16 14
0 -6 -5 -22 -15 		(P8/2, P11/6)

no solfege

225/224 4375/4356 243/242 8.191 1.057 29.319
Catalytic 1 0 1 -3 -10
0 6 5 22 51 		(P8, P12/6)

MuweLiMo

225/224 441/440 4375/4374 8.212 1.092 30.422
Enneaportent 9 18 19 29 33
0 -2 1 -2 -1 		(P8/9, P4/2)

no solfege

225/224 385/384 12005/11979 8.286 1.076 30.426
Marvo 1 -1 -5 -17 -3
0 6 17 46 15 		(P8, ccP5/6)

MoAugLeFi

225/224 243/242 4000/3993 8.731 1.027 31.685
Octoid 8 16 23 28 31
0 -3 -4 -5 -3 		(P8/8, P4/3)

no solfege

1375/1372 540/539 4000/3993 9.170 .421 14.097
Tertia 1 3 2 3 5
0 -22 5 -3 -24 		(P8, P11/22)

no solfege

1331/1323 385/384 1375/1372 9.182 .899 30.171
Guiron 1 1 7 3 -2
0 3 -24 -1 28 		(P8, P5/3)

DimFaThoAugMu

10976/10935 385/384 441/440 9.377 .767 26.648
Neominor 1 3 12 8 7
0 -6 -41 -22 -15 		(P8, P11/6)

MuweLiFu

243/242 35937/35840 441/440 9.493 .788 27.959
Grendel 1 9 2 7 17
0 -23 1 -13 -42 		(P8, c7P4/23)

no solfege

1375/1372 540/539 5632/5625 9.729 .537 19.845
Hemiseven 1 4 14 2 -5
0 -6 -29 2 21 		(P8, ccP4/6)

MoThePiyu

19683/19600 385/384 441/440 9.733 .770 28.467
Sqrtphi 1 12 11 16 17
0 -30 -25 -38 -39 		(P8, c10P4/30)

no solfege

4375/4356 1375/1372 540/539 9.756 .687 25.515
Commatic 2 8 23 23 33
0 -5 -19 -18 -27 		(P8/2, ccP4/5)

no solfege

3388/3375 8019/8000 441/440 9.831 .810 30.461
Sesquart 1 1 7 5 2
0 4 -32 -15 10 		(P8, P5/4)

DimFaThoFi

243/242 16384/16335 441/440 9.891 .772 29.306
Quadritikleismic 4 12 14 15 11
0 -6 -5 -4 3 		(P8/4, P11/6)

no solfege

385/384 1375/1372 9801/9800 10.315 .575 23.406
Mirkat 3 2 1 2 9
0 6 13 14 3 		(P8/3, ccM6/18)

no solfege

8019/8000 1375/1372 540/539 10.575 .521 22.126
Bisupermajor 2 1 6 1 8
0 8 -5 17 -4 		(P8/2, cM9/16)

no solfege

3388/3375 385/384 9801/9800 10.578 .755 32.080
Cotritone 1 -13 -4 -4 2
0 30 13 14 3 		(P8, c14P5/30)

no solfege

385/384 1375/1372 4000/3993 10.735 .740 32.225
Kwai 1 1 -17 -13 14
0 1 33 27 -18 		(P8, P5)

TiyiPiyuFle

16384/16335 1375/1372 540/539 11.134 .567 26.219
Triwell 1 7 0 1 13
0 -21 9 7 -37 		(P8, c5P4/21)

no solfege

385/384 441/440 456533/455625 11.163 .642 29.807
Supers 2 4 11 7 13
0 -3 -23 -5 -22 		(P8/2, P4/3)

MuweThuwePe

5120/5103 540/539 4000/3993 11.476 .580 28.240
Ennealiminal 9 9 13 20 39
0 2 3 2 -3 		(P8/9, P5/2)

no solfege

385/384 1375/1372 4375/4374 11.678 .621 31.123
Bischismic 2 2 14 29 42
0 1 -8 -20 -30 		(P8/2, P5) *

DimFaDimDimDo

QuadDimTha

3136/3125 8019/8000 441/440 11.743 .557 28.160
Septisuperfourth 2 4 4 7 6
0 -9 7 -15 10 		(P8/2, P4/9)

no solfege

540/539 4000/3993 5632/5625 12.086 .464 24.619
Amity 1 3 6 -2 21
0 -5 -13 17 -62 		(P8, P11/5)

MoThoAugMu

5120/5103 540/539 5632/5625 12.537 .559 31.506
Quincy 1 2 3 3 4
0 -30 -49 -14 -39 		(P8, P4/30)

no solfege

441/440 4000/3993 41503/41472 12.684 .537 30.875
Octowerck 8 24 45 30 39
0 -3 -7 -2 -3 		(P8/8, P11/3)

no solfege

441/440 8019/8000 41503/41472 13.282 .486 30.159
Hemiamity 2 6 12 -4 -1
0 -5 -13 17 14 		(P8/2, P11/5)

no solfege

5120/5103 3025/3024 4375/4374 13.714 .478 31.307
Eris 1 10 0 6 20
0 -29 8 -11 -57 		(P8, c8P4/29)

no solfege

1375/1372 540/539 65625/65536 13.875 .414 27.621
Unthirds 1 -13 -14 -9 -8
0 42 47 34 33 		(P8, c14P5/42)

no solfege

2401/2400, 3025/3024, 4000/3993 14.390 .323 22.926
Alphaquarter 1 2 2 0 3
0 -9 7 61 10 		(P8, P4/9)

no solfege

5120/5103 4000/3993 3025/3024 14.588 .408 29.638
Hemiennealimmal 18 36 53 58 75
0 -2 -3 -2 -1 		(P8/18, P4/2)

no solfege

2401/2400 3025/3024 4375/4374 14.648 .0860 6.283
Vishnu 2 4 5 10 10
0 -7 -3 -37 -26 		(P8/2, P4/7)

no solfege

3025/3024 4375/4374 5632/5625 14.963 .187 14.180
Quanharuk 1 0 15 12 -7
0 5 -40 -29 33 		(P8, P12/5) *

DimFaThoAugMi

1375/1372 540/539 32805/32768 15.170 .407 31.549
Sternscape 6 9 13 16 20
0 6 11 10 9 		(P8/6, M2/12)

no solfege

540/539 4000/3993 137781/137500 15.352 .406 32.096
Pogo 2 4 -2 7 0
0 -3 24 -5 25 		(P8/2, P4/3)

DimFaThuweSho

540/539 4000/3993 32805/32768 15.953 .378 31.857

Junk temperaments

Some of these contain the trivial commas 1-edo, Yobi, Rubi and Loquad, 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.

A fourth 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.

Mapping Generator Pergen Commas Color Name Comp Error Badness
1 2 2 3 0
0 0 0 0 1 		11/8 (P8, P4) 4/3, 5/4, 8/7 (7/6) Waquad & Yobi & Rubi + ila

or ila nowa (2.11 JI)

.193 327.406 17.646
1 2 2 0 3
0 0 0 1 0 		8/7 (P8, M2) 4/3, 5/4, 11/8 (11/10) Waquad & Yobi & Loquad + za

or za nowa (2.7 JI)

.228 385.465 27.274
1 2 2 0 1
0 0 0 1 1 		7/4 = 11/8 (P8, P4) 4/3, 5/4, 14/11 Waquad & Yobi & Luzotri

or Luzotri nowa

.267 336.13 30.988
1 2 0 3 1
0 0 1 0 1 		5/4 = 11/8 (P8, P4) 4/3, 8/7 (7/6), 11/10 Waquad & Rubi & Logu

or Logu nowa

.319 218.143 27.130
1 2 0 0 1
0 0 1 1 1 		5/4 = 7/4 = 11/8 (P8, P4) 4/3, 7/5, 11/10 (14/11) Waquad & Zoguquad & Logu .324 253.143 32.311
1 1 2 2 3
0 1 1 1 1 		3/2 = 5/4 = 7/4 (P8, P5)

SaSaSa

6/5, 7/6, 12/11 (11/10) Gubi & Zobi & Lu .328 164.655 21.432
1 1 2 2 3
0 1 0 1 1 		3/2 = 7/4 = 11/8 (P8, P5)

DaSaSa

5/4, 7/6, 12/11 Yobi & Zobi & Lu .354 167.706 24.774
1 1 2 2 3
0 1 0 1 0 		3/2 = 7/4 (P8, P5)

DaSaDa

5/4, 7/6, 11/8 (11/10) Yobi & Zobi & Loquad .369 153.296 24.223
2 3 5 6 7
0 0 0 0 -1 		11/8 (P8/2, ^1)

FaDaFu

9/8, 6/5, 8/7 Wabi & Gutri & Rubi + ila

or Wabi & Gutri + ila

.375 124.872 20.250
1 1 2 3 3
0 1 0 0 1 		3/2 = 11/8 (P8, P5)

DaDaSa

5/4, 8/7, 12/11 Yobi & Rubi & Lu .390 188.818 32.775
1 1 2 3 3
0 1 1 0 1 		3/2 = 5/4 = 11/8 (P8, P5)

SaDaSa

6/5, 8/7, 12/11 (11/10) Gutri & Rubi & Lu .406 110.926 20.608
1 1 2 2 3
0 1 1 2 1 		3/2 = 5/4 = 11/8 (P8, P5)

SaRaSa

6/5, 9/7, 12/11 (11/10) Gutri & Rutri & Lu .408 125.430 23.415
1 1 1 2 2
0 1 2 1 2 		3/2 = 7/4 (P8, P5)

RaSaRa

10/9, 7/6, 11/10 Yo & Zobi & Logu .452 94.454 20.943
2 3 5 6 7
0 0 0 -1 0 		8/7 (P8/2, ^1)

FaDoFa

9/8, 6/5, 12/11 (11/10) Wabi & Gutri & Lu + za .455 110.141 24.702
1 1 1 2 3
0 1 2 1 1 		3/2 = 7/4 = 11/8 (P8, P5)

RaSaFa

10/9, 7/6, 12/11 Yo & Zobi & Lu .471 104.885 24.915
1 1 2 0 2
0 1 1 2 3 		3/2 = 5/4 (P8, P5)

SaRaLa

6/5, 9/7 (15/14), 22/21 Gutri & Rutri & Loru .483 125.665 31.158
2 3 5 6 7
0 0 0 -1 -1 		8/7 (P8/2, ^1)

FaDoFo

9/8, 6/5 (16/15), 22/21 Wabi & Gutri & Loru .508 117.970 31.811
2 3 5 6 7
0 0 -1 0 0 		5/4 (P8/2, ^1)

FoDaFa

9/8, 8/7, 12/11 Wabi & Rubi & Lu + ya .549 103.420 31.715
3 5 7 8 10
0 0 0 0 1 		11/8 (P8/3, ^1)

FaSaFu

32/27, 10/9 (16/15), 7/6 Watri & Yo & Zobi + ila .550 86.198 26.496
2 3 5 6 7
0 0 -1 -1 -1 		5/4 = 11/8 (P8/2, ^1)

FoDoFo

9/8, 15/14, 11/10 Wabi & Ruyo & Logu .557 60.511 18.993
1 1 1 3 3
0 1 2 0 1 		3/2 = 11/8 (P8, P5)

RaDaSa

10/9, 8/7, 12/11 Yo & Rubi & Lu .567 71.691 23.207
1 1 1 3 2
0 1 2 0 2 		3/2 (P8, P5)

RaDaRa

10/9, 8/7, 11/10 Yo & Rubi & Logu .574 93.134 30.760
1 1 3 3 3
0 1 -1 0 1 		3/2 = 11/8 (P8, P5)

FaDaSa

16/15, 8/7 (15/14), 12/11 Gubi & Rubi & Lu .575 60.585 20.049
1 1 3 3 4
0 1 -1 0 -1 		3/2 (P8, P5)

FaDaFa

16/15, 8/7 (15/14), 11/10 Gubi & Rubi & Logu .588 78.370 26.952
2 3 5 6 7
0 0 -1 -1 0 		5/4 (P8/2, ^1)

FoDoSa

9/8, 15/14, 12/11 Wabi & Ruyo & Lu .606 60.327 21.810
1 1 1 1 3
0 1 2 3 1 		3/2 = 11/8 (P8, P5)

RaLaSa

10/9, 15/14, 12/11 Yo & Ruyo & Lu .622 69.361 26.170
1 1 1 2 4
0 1 2 1 -1 		3/2 = 7/4 (P8, P5)

RaSaFa

10/9, 7/6 (21/20), 33/32 Yo & Rubi & iLo .645 82.949 33.250
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