Xenharmonic Wiki:Deleted temperament entries: Difference between revisions

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Created page with "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) == Proposed by Eufalesio in 2026, maqamschismic is equivalent to the no-7 cassandra. The 2.3.5.11.13 subgroup adds 352/351 to the comma list and tempers 1..."
 
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Badness (Sintel): 0.862
Badness (Sintel): 0.862
== Quintapole ==
The ''quintapole'' temperament (12&amp;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 [[Marvel family #Apollo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintapole" as /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[#Quintupole|quint<u>'''u'''</u>pole]] temperament (12&amp;121).''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 7812500/7411887
[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.959¢, ~21/20 = 98.908¢
* [[CWE]]: ~2 = 1200.000¢, ~21/20 = 98.968¢
{{Optimal ET sequence|legend=1| 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: [{{val| 1 2 1 1 0 }}, {{val| 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: {{Optimal ET sequence| 12, 73ce, 85, 97d }}
Badness (Sintel): 3.450
==== Galileic ====
The name ''galileic'' comes from "{{w|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: [{{val| 1 2 1 1 0 -1 }}, {{val| 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: {{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: [{{val| 1 2 1 1 0 -1 5 }}, {{val| 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: {{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: [{{val| 1 2 1 1 0 -1 5 4 }}, {{val| 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: {{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: [{{val| 1 2 1 1 0 0 }}, {{val| 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: {{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: [{{val| 1 2 1 1 0 0 5 }}, {{val| 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: {{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: [{{val| 1 2 1 1 0 0 5 4 }}, {{val| 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: {{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: [{{val| 1 2 1 1 1 }}, {{val| 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: {{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: [{{val| 1 2 1 1 1 0 }}, {{val| 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: {{Optimal ET sequence| 12f, 61cf, 73c, 85e }}
Badness (Sintel): 3.302

Revision as of 02:26, 16 June 2026

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)

Proposed by Eufalesio in 2026, 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

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