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Wizardharry clan: Difference between revisions

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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..."
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{{Technical data page}}
{{Technical data page}}
The '''wizardharry clan''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s [[tempering out|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]].  
The '''wizardharry clan''' of [[rank-3 temperament]]s [[tempering out|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 ==
== Homalic ==
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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:  
* ''[[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]]
* ''[[Moctpine]]'' (+1375/1372) → [[Moctdelismic clan #Moctpine|Moctdelismic clan]]
* ''[[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 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 ==
{{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|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): 1.275


== 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.  
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
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{{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 }}
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