Wizardharry clan: Difference between revisions
Created page with "{{Technical data page}} The '''wizardharry clan''' of rank-3 temperaments tempers out the wizardharry comma, 4000/3993, the amount by which a stack of three 11/10's falls short of the fourth, 4/3. == Homalic == Subgroup: 2.3.5.11 Comma list: 4000/3993 {{Mapping|legend=2| 1 2 0 1 | 0 -3 0 1 | 0 0 1 1 }} : Mapping generators: ~2, ~11/10, ~5 Optimal tunings: * WE: ~2 = 1199.917..." Tags: Mobile edit Mobile web edit |
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Discussed elsewhere are: | Discussed elsewhere are: | ||
* ''[[Hanuman]]'' (+3025/3024) → [[Lehmerismic temperaments #Hanuman|Lehmerismic temperaments]] | * ''[[Hanuman]]'' (+3025/3024) → [[Lehmerismic temperaments #Hanuman|Lehmerismic temperaments]] | ||
* ''[[History]]'' (+441/440) → [[Werckismic temperaments #History|Werckismic temperaments | * ''[[History (temperament)|History]]'' (+441/440) → [[Werckismic temperaments #History|Werckismic temperaments]] | ||
* ''[[Hades]]'' (+540/539 or 9801/9800) → [[Swetismic temperaments #Hades|Swetismic temperaments]] | * ''[[Hades]]'' (+540/539 or 9801/9800) → [[Swetismic temperaments #Hades|Swetismic temperaments]] | ||
Considered below are naiad besides the no-7 subgroup temperament. | Considered below are moctpine and naiad, besides the no-7 subgroup temperament. | ||
== Moctpine == | |||
{{see also| Moctdelismic clan }} | |||
Named by [[Xenllium]] in 2026, moctpine tempers out [[4000/3993]]. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 1375/1372, 4000/3993 | |||
{{Mapping|legend=1| 1 2 1 1 2 | 0 -3 -1 -1 0 | 0 0 3 4 3 }} | |||
: Mapping generators: ~2, ~11/10, ~7/5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9745{{c}}, ~11/10 = 165.9846{{c}}, ~7/5 = 583.8721{{c}} | |||
: [[error map]]: {{val| -0.025 +0.040 -0.707 +0.652 +0.247 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 165.9939{{c}}, ~7/5 = 583.8766{{c}} | |||
: error map: {{val| 0.000 +0.063 -0.678 +0.686 +0.312 }} | |||
{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224, 629, 781, 853c }} | |||
[[Badness]] (Sintel): 1.28 | |||
== Naiad == | == Naiad == | ||
: ''For the 7-limit version of this temperament, see [[Miscellaneous 7-limit temperaments #Naiad]].'' | : ''For the 7-limit version of this temperament, see [[Miscellaneous 7-limit temperaments #Naiad]].'' | ||
Named by [[Xenllium]] in 2026, naiad tempers out [[3773/3750]] and [[5488/5445]] in the 11-limit. | Named by [[Xenllium]] in 2026, naiad tempers out [[3773/3750]] and [[5488/5445]] in the 11-limit. It can be extended to the 13-limit by adding 196/195, 364/363, or 1001/1000 to the comma basis. | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
Revision as of 15:38, 31 January 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The wizardharry clan of rank-3 temperaments tempers out the wizardharry comma, 4000/3993, the amount by which a stack of three 11/10's falls short of the fourth, 4/3.
Homalic
Subgroup: 2.3.5.11
Comma list: 4000/3993
Subgroup-val mapping: [⟨1 2 0 1], ⟨0 -3 0 1], ⟨0 0 1 1]]
- Mapping generators: ~2, ~11/10, ~5
- WE: ~2 = 1199.917 ¢, ~11/10 = 165.946 ¢, ~5/4 = 386.212 ¢
- CWE: ~2 = 1200.000 ¢, ~11/10 = 165.977 ¢, ~5/4 = 386.130 ¢
Optimal ET sequence: 7, 8, 15, 22, 50, 58, 65, 72
Badness (Sintel): 0.247
Overview to extensions
The second comma in the comma list determines how we extend the no-7 subgroup temperament to include the harmonic 7. Hanuman adds 3025/3024, history adds 441/440, and moctpine adds 1375/1372. Hades adds 540/539 as well as 9801/9800, splitting the octave in two.
Discussed elsewhere are:
- Hanuman (+3025/3024) → Lehmerismic temperaments
- History (+441/440) → Werckismic temperaments
- Hades (+540/539 or 9801/9800) → Swetismic temperaments
Considered below are moctpine and naiad, besides the no-7 subgroup temperament.
Moctpine
Named by Xenllium in 2026, moctpine tempers out 4000/3993.
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4000/3993
Mapping: [⟨1 2 1 1 2], ⟨0 -3 -1 -1 0], ⟨0 0 3 4 3]]
- Mapping generators: ~2, ~11/10, ~7/5
- WE: ~2 = 1199.9745 ¢, ~11/10 = 165.9846 ¢, ~7/5 = 583.8721 ¢
- error map: ⟨-0.025 +0.040 -0.707 +0.652 +0.247]
- CWE: ~2 = 1200.0000 ¢, ~11/10 = 165.9939 ¢, ~7/5 = 583.8766 ¢
- error map: ⟨0.000 +0.063 -0.678 +0.686 +0.312]
Optimal ET sequence: 29, 37, 43, 72, 152, 224, 629, 781, 853c
Badness (Sintel): 1.28
Naiad
- For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Naiad.
Named by Xenllium in 2026, naiad tempers out 3773/3750 and 5488/5445 in the 11-limit. It can be extended to the 13-limit by adding 196/195, 364/363, or 1001/1000 to the comma basis.
Subgroup: 2.3.5.7.11
Comma list: 3773/3750, 4000/3993
Mapping: [⟨1 5 0 2 0], ⟨0 -9 0 -4 3], ⟨0 0 1 1 1]]
- Mapping generators: ~2, ~100/77, ~5
- WE: ~2 = 1199.723 ¢, ~100/77 = 455.134 ¢, ~5/4 = 387.934 ¢
- CWE: ~2 = 1200.000 ¢, ~100/77 = 455.259 ¢, ~5/4 = 387.694 ¢
Optimal ET sequence: 8d, 21, 29, 37, 50, 58, 87, 145
Badness (Sintel): 3.098
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 364/363, 1001/1000
Mapping: [⟨1 5 0 2 0 1], ⟨0 -9 0 -4 3 1], ⟨0 0 1 1 1 1]]
Optimal tunings:
- WE: ~2 = 1199.622 ¢, ~13/10 = 455.074 ¢, ~5/4 = 387.918 ¢
- CWE: ~2 = 1200.000 ¢, ~13/10 = 455.243 ¢, ~5/4 = 387.576 ¢
Optimal ET sequence: 8d, 21, 29, 37, 50, 58, 87, 145
Badness (Sintel): 1.182
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 196/195, 221/220, 364/363
Mapping: [⟨1 5 0 2 0 1 1], ⟨0 -9 0 -4 3 1 2], ⟨0 0 1 1 1 1 1]]
Optimal tunings:
- WE: ~2 = 1200.088 ¢, ~13/10 = 455.350 ¢, ~5/4 = 387.578 ¢
- CWE: ~2 = 1200.000 ¢, ~13/10 = 455.311 ¢, ~5/4 = 387.658 ¢
Optimal ET sequence: 8d, 21, 29g, 50, 58, 87g
Badness (Sintel): 1.337