Wizardharry clan - Revision history

Xenllium at 23:16, 6 February 2026

2026-02-06T23:16:04Z

← Older revision		Revision as of 23:16, 6 February 2026
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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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	* ''[[Tritiwiz]]'' (+385/384) → [[Keenanismic temperaments #Tritiwiz\|Keenanismic 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 ==
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	{{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.

Xenllium at 21:59, 6 February 2026

2026-02-06T21:59:14Z

← Older revision		Revision as of 21:59, 6 February 2026
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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 moctpine and naiad, besides the no-7 subgroup temperament.

Xenllium at 15:55, 31 January 2026

2026-01-31T15:55:48Z

← Older revision		Revision as of 15:55, 31 January 2026
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	{{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
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	: ''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. 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
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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 }}

Xenllium at 15:38, 31 January 2026

2026-01-31T15:38:02Z

← Older revision		Revision as of 15:38, 31 January 2026
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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]]
	* ''[[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]]

	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

Xenllium: 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..."

2026-01-31T15:30:50Z

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..."

New 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]].

== 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 tuning]]s:
* [[WE]]: ~2 = 1199.917{{c}}, ~11/10 = 165.946{{c}}, ~5/4 = 386.212{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~11/10 = 165.977{{c}}, ~5/4 = 386.130{{c}}

{{Optimal ET sequence|legend=1| 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 #Hanuman|Lehmerismic temperaments]]
* ''[[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]]

Considered below are naiad besides the no-7 subgroup temperament.

== 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.

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 3773/3750, 4000/3993

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

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

{{Optimal ET sequence|legend=1| 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: {{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{{c}}, ~13/10 = 455.074{{c}}, ~5/4 = 387.918{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.243{{c}}, ~5/4 = 387.576{{c}}

{{Optimal ET sequence|legend=0| 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: {{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{{c}}, ~13/10 = 455.350{{c}}, ~5/4 = 387.578{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.311{{c}}, ~5/4 = 387.658{{c}}

{{Optimal ET sequence|legend=0| 8d, 21, 29g, 50, 58, 87g }}

Badness (Sintel): 1.337

[[Category:Temperament clans]]
[[Category:Wizardharry clan| ]] 
[[Category:Rank 3]]