Wizardharry clan: Difference between revisions

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=== Overview to extensions ===
=== 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.
The second comma in the comma list determines how we extend the no-7 subgroup temperament to include the harmonic 7. Marvelpine adds [[225/224]], 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:  
Discussed elsewhere are:  
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* ''[[History (temperament)|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]]
* ''[[Tritiwiz]]'' (+385/384) → [[Keenanismic temperaments #Tritiwiz|Keenanismic temperaments]]


Considered below are moctpine and naiad, besides the no-7 subgroup temperament.  
Considered below are marvelpine, moctpine, and naiad, besides the no-7 subgroup temperament.  
 
== Marvelpine ==
{{see also| Marvel family }}
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 225/224, 4000/3993
 
{{Mapping|legend=1| 1 2 0 -1 1 | 0 -3 0 -6 1 | 0 0 1 2 1 }}
: Mapping generators: ~2, ~11/10, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.519{{c}}, ~11/10 = 166.548{{c}}, ~5/4 = 383.747{{c}}
: [[error map]]: {{val| +0.519 -0.562 -1.528 +0.936 +0.536 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~11/10 = 166.444{{c}}, ~5/4 = 383.826{{c}}
: error map: {{val| 0.000 -1.288 -2.488 +0.160 -1.048 }}
 
{{Optimal ET sequence|legend=1| 7d, 15d, 21, 22, 43, 50, 72, 166 }}
 
[[Badness]] (Sintel): 1.265


== Moctpine ==
== Moctpine ==
{{see also| Moctdelismic clan }}
{{see also| Moctdelismic clan }}


Named by [[Xenllium]] in 2026, moctpine tempers out [[4000/3993]].  
Named by [[Xenllium]] in 2026, moctpine tempers out [[1375/1372]] and [[4000/3993]].  


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
Line 48: Line 69:
{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224, 629, 781, 853c }}
{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224, 629, 781, 853c }}


[[Badness]] (Sintel): 1.28
[[Badness]] (Sintel): 1.275


== 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]].''
: ''For the no-three version of this temperament, see [[No-threes subgroup temperaments #No-threes 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.
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
Line 60: Line 82:


{{Mapping|legend=1| 1 5 0 2 0 | 0 -9 0 -4 3 | 0 0 1 1 1 }}
{{Mapping|legend=1| 1 5 0 2 0 | 0 -9 0 -4 3 | 0 0 1 1 1 }}
: Mapping generators: ~2, ~100/77, ~5
: Mapping generators: ~2, ~98/75, ~5


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.723{{c}}, ~100/77 = 455.134{{c}}, ~5/4 = 387.934{{c}}
* [[WE]]: ~2 = 1199.723{{c}}, ~98/75 = 455.134{{c}}, ~5/4 = 387.934{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~100/77 = 455.259{{c}}, ~5/4 = 387.694{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~98/75 = 455.259{{c}}, ~5/4 = 387.694{{c}}


{{Optimal ET sequence|legend=1| 8d, 21, 29, 37, 50, 58, 87, 145 }}
{{Optimal ET sequence|legend=1| 8d, 21, 29, 37, 50, 58, 87, 145 }}

Latest revision as of 23:16, 6 February 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

Optimal tunings:

  • 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. Marvelpine adds 225/224, 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:

Considered below are marvelpine, moctpine, and naiad, besides the no-7 subgroup temperament.

Marvelpine

See also: Marvel family

Subgroup: 2.3.5.7.11

Comma list: 225/224, 4000/3993

Mapping: [⟨1 2 0 -1 1], ⟨0 -3 0 -6 1], ⟨0 0 1 2 1]]

Mapping generators: ~2, ~11/10, ~5

Optimal tunings:

  • WE: ~2 = 1200.519 ¢, ~11/10 = 166.548 ¢, ~5/4 = 383.747 ¢
error map: ⟨+0.519 -0.562 -1.528 +0.936 +0.536]
  • CWE: ~2 = 1200.000 ¢, ~11/10 = 166.444 ¢, ~5/4 = 383.826 ¢
error map: ⟨0.000 -1.288 -2.488 +0.160 -1.048]

Optimal ET sequence: 7d, 15d, 21, 22, 43, 50, 72, 166

Badness (Sintel): 1.265

Moctpine

See also: Moctdelismic clan

Named by Xenllium in 2026, moctpine tempers out 1375/1372 and 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

Optimal tunings:

  • 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): 1.275

Naiad

For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Naiad.
For the no-three version of this temperament, see No-threes subgroup temperaments #No-threes 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, ~98/75, ~5

Optimal tunings:

  • WE: ~2 = 1199.723 ¢, ~98/75 = 455.134 ¢, ~5/4 = 387.934 ¢
  • CWE: ~2 = 1200.000 ¢, ~98/75 = 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

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