Xenharmonic Wiki:Deleted temperament entries

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These temperament names are no longer in use, although older material may still reference them. If one must refer to these temperaments, it is recommended to do so with an ET join (e. g. "11-limit 12 & 85") or as a restriction of a different temperament (e. g. "no-7s cassandra")

Maqamschismic (2.3.5.11)

Maqamschismic is equivalent to the no-7 cassandra. The 2.3.5.11.13 subgroup adds 352/351 to the comma list and tempers 11/9~39/32 together (and 16/13~27/22), providing a very simple framework for tuning maqamat (especially the Turkish version), as outlined by Ozan Yarman. 41edo and 53edo are simplest, but 94edo is more optimized. It is only slightly worse than the no-7 helenus.

Subgroup: 2.3.5.11

Comma list: 2200/2187, 4125/4096

Subgroup-val mapping: [⟨1 0 15 -33], ⟨0 1 -8 23]]

Optimal tunings:

  • WE: ~2 = 1200.5458 ¢ ~3/2 = 702.4021 ¢
  • CWE: 2 = 1200.0000 ¢, ~3/2 = 702.0906 ¢

Optimal ET sequence: 12e, …, 41, 53, 94, 147e, 241ce, 335ce

Badness (Sintel): 1.34

2.3.5.11.13 subgroup

Subgroup: 2.3.5.11.13

Comma list: 325/324, 352/351, 4125/4096

Subgroup-val mapping: [⟨1 0 15 -33 -28], ⟨0 1 -8 23 20]]

Optimal tunings:

  • WE: ~2 = 1200.4565 ¢ ~3/2 = 702.3057 ¢
  • CWE: 2 = 1200.0000 ¢, ~3/2 = 702.0485 ¢

Optimal ET sequence: 12e, …, 41, 53, 94, 147e

Badness (Sintel): 0.862

Quintapole

The quintapole temperament (12&85) tempers out the marvel comma (225/224) and 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the apollo temperament, and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). Xenllium proposes the pronunciation of the word "quintapole" as /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". Not to be confused with quintupole temperament (12&121).

Subgroup: 2.3.5.7

Comma list: 225/224, 7812500/7411887

Mapping: [⟨1 2 1 1], ⟨0 -5 16 22]]

Optimal tunings:

  • WE: ~2 = 1198.959¢, ~21/20 = 98.908¢
  • CWE: ~2 = 1200.000¢, ~21/20 = 98.968¢

Optimal ET sequence: 12, 73c, 85, 97d

Badness (Sintel): 4.872

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 225/224, 85184/84035

Mapping: [⟨1 2 1 1 0], ⟨0 -5 16 22 42]]

Optimal tunings:

  • WE: ~2 = 1198.982¢, ~21/20 = 98.870¢
  • CWE: ~2 = 1200.000¢, ~21/20 = 98.931¢

Optimal ET sequence: 12, 73ce, 85, 97d

Badness (Sintel): 3.450

Galileic

The name galileic comes from "Vincenzo Galilei", because this temperament is strongly related to Galilei's tuning.

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 225/224, 275/273, 12168/12005

Mapping: [⟨1 2 1 1 0 -1], ⟨0 -5 16 22 42 57]]

Optimal tunings:

  • WE: ~2 = 1198.912¢, ~21/20 = 98.902¢
  • CWE: ~2 = 1200.000¢, ~21/20 = 98.970¢

Optimal ET sequence: 12f, 73ceff, 85f, 97d

Badness (Sintel): 3.231

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 100/99, 120/119, 225/224, 275/273, 2431/2401

Mapping: [⟨1 2 1 1 0 -1 5], ⟨0 -5 16 22 42 57 -11]]

Optimal tunings:

  • WE: ~2 = 1198.798¢, ~18/17 = 98.903¢
  • CWE: ~2 = 1200.000¢, ~18/17 = 98.986¢

Optimal ET sequence: 12f, 73ceffg, 85fg, 97dg

Badness (Sintel): 2.997

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 100/99, 120/119, 225/224, 247/245, 275/273, 361/357

Mapping: [⟨1 2 1 1 0 -1 5 4], ⟨0 -5 16 22 42 57 -11 3]]

Optimal tunings:

  • WE: ~2 = 1199.031¢, ~18/17 = 98.907¢
  • CWE: ~2 = 1200.000¢, ~18/17 = 98.976¢

Optimal ET sequence: 12f, 73ceffg, 85fg, 97dg

Badness (Sintel): 2.765

Catagali

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 225/224, 847/845, 1040/1029

Mapping: [⟨1 2 1 1 0 0], ⟨0 -5 16 22 42 45]]

Optimal tunings:

  • WE: ~2 = 1199.021¢, ~21/20 = 98.801¢
  • CWE: ~2 = 1200.000¢, ~21/20 = 98.860¢

Optimal ET sequence: 12f, 73ce, 85

Badness (Sintel): 3.065

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 100/99, 120/119, 225/224, 442/441, 847/845

Mapping: [⟨1 2 1 1 0 0 5], ⟨0 -5 16 22 42 45 -11]]

Optimal tunings:

  • WE: ~2 = 1198.792¢, ~18/17 = 98.805¢
  • CWE: ~2 = 1200.000¢, ~18/17 = 98.887¢

Optimal ET sequence: 12f, 73ceg, 85g

Badness (Sintel): 2.951

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 100/99, 120/119, 209/208, 225/224, 361/357, 442/441

Mapping: [⟨1 2 1 1 0 0 5 4], ⟨0 -5 16 22 42 45 -11 3]]

Optimal tunings:

  • WE: ~2 = 1199.037¢, ~18/17 = 98.808¢
  • CWE: ~2 = 1200.000¢, ~18/17 = 98.875¢

Optimal ET sequence: 12f, 73ceg, 85g

Badness (Sintel): 2.720

Quintain

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 5000/4851

Mapping: [⟨1 2 1 1 1], ⟨0 -5 16 22 30]]

Optimal tunings:

  • WE: ~2 = 1198.804¢, ~21/20 = 98.718¢
  • CWE: ~2 = 1200.000¢, ~21/20 = 98.784¢

Optimal ET sequence: 12, 61c, 73c, 85e

Badness (Sintel): 3.730

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 245/242, 275/273, 1040/1029

Mapping: [⟨1 2 1 1 1 0], ⟨0 -5 16 22 30 45]]

Optimal tunings:

  • WE: ~2 = 1198.830¢, ~21/20 = 98.700¢
  • CWE: ~2 = 1200.000¢, ~21/20 = 98.768¢

Optimal ET sequence: 12f, 61cf, 73c, 85e

Badness (Sintel): 3.302

Bixby

Main article: Bixby

Subgroup: 2.3.5

Comma list: 4/3

Mapping: [⟨1 2 0], ⟨0 0 1]]

Optimal tunings:

  • WE: ~2 = 1020.058 ¢, ~5/4 = 674.394 ¢
error map: ⟨-179.942 +138.161 -71.803]
  • CWE: ~2 = 1200.000 ¢, ~5/4 = 629.521 ¢
error map: ⟨0.000 +498.045 +243.208]

Optimal ET sequence: 1c, 2b, 3bbcc

Badness (Sintel): 0.424

Archon

Main article: Archon

Subgroup: 2.3.5

Comma list: 5/4

Mapping: [⟨1 0 2], ⟨0 1 0]]

Optimal tunings:

  • WE: ~2 = 1268.274 ¢, ~3/2 = 612.921 ¢
error map: ⟨+68.274 -20.760 -249.765]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 614.055 ¢
error map: ⟨0.000 -87.900 -386.314]

Optimal ET sequence: 2c

Badness (Sintel): 0.474

Seesaw

Main article: Seesaw

Seesaw tempers out the classic minor third (6/5), equating the fifth and sixth harmonics. It was named by Xenllium in 2026.

Subgroup: 2.3.5

Comma list: 6/5

Mapping: [⟨1 0 1], ⟨0 1 1]]

Optimal tunings:

  • WE: ~2 = 1155.569 ¢, ~3/2 = 643.349 ¢
error map: ⟨-44.431 -103.037 +168.173]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 627.511 ¢
error map: ⟨0.000 -74.444 +241.197]

Optimal ET sequence: 2

Badness (Sintel): 0.367

2.3.5.11 subgroup

This temperament is extended to the 2.3.5.11 subgroup naturally, tempering out both 11/10 and 12/11, undecimal neutral seconds.

Subgroup: 2.3.5.11

Comma list: 6/5, 11/10

Mapping: [⟨1 0 1 2], ⟨0 1 1 1]]

Optimal tunings:

  • WE: ~2 = 1156.418 ¢, ~3/2 = 643.202 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 627.023 ¢

Optimal ET sequence: 2

Badness (Sintel): 0.499

Heavy windmill

Heavy windmill tempers out 9/7 and 15/14 in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 6/5, 9/7

Mapping: [⟨1 0 1 0], ⟨0 1 1 2]]

Optimal tunings:

  • WE: ~2 = 1161.600 ¢, ~3/2 = 571.169 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 559.563 ¢

Optimal ET sequence: 2

Badness (Sintel): 0.676

11-limit

Subgroup: 2.3.5.7.11

Comma list: 6/5, 9/7, 11/10

Mapping: [⟨1 0 1 0 2], ⟨0 1 1 2 1]]

Optimal tunings:

  • WE: ~2 = 1166.584 ¢, ~3/2 = 568.073 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 558.941 ¢

Optimal ET sequence: 2

Badness (Sintel): 0.774

Light windmill

Light windmill tempers out 8/7 and 21/20 in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 6/5, 8/7

Mapping: [⟨1 0 1 3], ⟨0 1 1 0]]

Optimal tunings:

  • WE: ~2 = 1134.018 ¢, ~3/2 = 670.285 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 667.893 ¢

Optimal ET sequence: 2

Badness (Sintel): 0.629

11-limit

Subgroup: 2.3.5.7.11

Comma list: 6/5, 8/7, 11/10

Mapping: [⟨1 0 1 3 2], ⟨0 1 1 0 1]]

Optimal tunings:

  • WE: ~2 = 1136.109 ¢, ~3/2 = 672.403 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 668.374 ¢

Optimal ET sequence: 2

Badness (Sintel): 0.681

Sixseven

Sixseven tempers out the septimal minor third (7/6), equating the sixth and seventh harmonics. It was named by Xenllium in 2026.

Subgroup: 2.3.7

Comma list: 7/6

Mapping: [⟨1 0 1], ⟨0 1 1]]

Optimal tunings:

  • WE: ~2 = 1218.135 ¢, ~3/2 = 734.187 ¢
error map: ⟨+18.135 +50.367 -198.368]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 738.927 ¢
error map: ⟨0.000 +36.972 -229.899]

Optimal ET sequence: 1, 2d, 3, 5dd

Badness (Sintel): 0.329

2.3.7.13 subgroup

This temperament is extended to the 2.3.7.13 subgroup naturally, tempering out both 13/12 and 14/13, tridecimal neutral seconds.

Subgroup: 2.3.7.13

Comma list: 7/6, 13/12

Mapping: [⟨1 0 1 2], ⟨0 1 1 1]]

Optimal tunings:

  • WE: ~2 = 1220.937 ¢, ~3/2 = 734.003 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 739.780 ¢

Optimal ET sequence: 1, 2d, 3, 5ddf

Badness (Sintel): 0.422

Heaven

Heaven tempers out 11/9 and 22/21 in the 2.3.7.11 subgroup.

Subgroup: 2.3.7.11

Comma list: 7/6, 11/9

Mapping: [⟨1 0 1 0], ⟨0 1 1 2]]

Optimal tunings:

  • WE: ~2 = 1210.810 ¢, ~3/2 = 783.079 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 785.173 ¢

Optimal ET sequence: 1e, 2de, 3

Badness (Sintel): 0.577

2.3.7.11.13 subgroup

Subgroup: 2.3.7.11.13

Comma list: 7/6, 11/9, 13/12

Mapping: [⟨1 0 1 0 2], ⟨0 1 1 2 1]]

Optimal tunings:

  • WE: ~2 = 1210.595 ¢, ~3/2 = 783.176 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 784.989 ¢

Optimal ET sequence: 1e, 2de, 3

Badness (Sintel): 0.627

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