Wizardharry clan: Difference between revisions

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=== 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:

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* ''[[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 ==

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 225/224, 4000/3993

: 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 ==

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{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224, 629, 781, 853c }}

[[Badness]] (Sintel): 1.28

[[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.

@@ Line 19: / Line 19: @@
 === 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:
@@ Line 27: / Line 27: @@
 * ''[[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 ==
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 {{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224, 629, 781, 853c }}
-[[Badness]] (Sintel): 1.28
+[[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.