Dimcomp family - Revision history

FloraC: + intro to octopod

2026-02-12T08:41:23Z

+ intro to octopod

← Older revision		Revision as of 08:41, 12 February 2026
Line 53:		Line 53:

	== Octopod ==		== Octopod ==
			Octopod is [[octoid]] with an independent generator for [[prime interval\|prime]] [[13/1\|13]].

	[[Subgroup]]: 2.3.5.7.11.13		[[Subgroup]]: 2.3.5.7.11.13

FloraC: + optimal tunings

2026-02-12T08:36:13Z

+ optimal tunings

← Older revision		Revision as of 08:36, 12 February 2026
Line 10:		Line 10:
	: mapping generators: ~25/21, ~3, ~5		: mapping generators: ~25/21, ~3, ~5

	{{Optimal ET sequence\|legend=1\| ~~8d,~~ 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}		[[Optimal tuning]]s:
			* [[WE]]: ~25/21 = 300.0036{{c}}, ~3/2 = 702.0854{{c}}, ~5/4 = 385.6631{{c}}
			: [[error map]]: {{val\| +0.014 +0.145 -0.622 +0.454 }}
			* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0885{{c}}, ~5/4 = 385.6745{{c}}
			: error map: {{val\| 0.000 +0.133 -0.639 +0.435 }}

			{{Optimal ET sequence\|legend=1\| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}

	[[Badness]] (Sintel): 3.45		[[Badness]] (Sintel): 3.45
Line 21:		Line 27:
	{{Mapping\|legend=1\| 4 0 0 -1 5 \| 0 1 0 -1 -3 \| 0 0 1 2 3 }}		{{Mapping\|legend=1\| 4 0 0 -1 5 \| 0 1 0 -1 -3 \| 0 0 1 2 3 }}

	{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}		[[Optimal tuning]]s:
			* [[WE]]: ~25/21 = 300.0093{{c}}, ~3/2 = 701.9976{{c}}, ~5/4 = 385.6591{{c}}
			: [[error map]]: {{val\| +0.037 +0.080 -0.580 +0.597 -0.176 }}
			* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0009{{c}}, ~5/4 = 385.6895{{c}}
			: error map: {{val\| 0.000 +0.046 -0.624 +0.552 -0.252 }}

			{{Optimal ET sequence\|legend=1\| 12, …, 68, 72, 140, 152, 224, 364, 436, 588 }}

	[[Badness]] (Sintel): 0.751		[[Badness]] (Sintel): 0.751
Line 31:		Line 43:

	Mapping: {{mapping\| 4 0 0 -1 5 -16 \| 0 1 0 -1 -3 -1 \| 0 0 1 2 3 4 }}		Mapping: {{mapping\| 4 0 0 -1 5 -16 \| 0 1 0 -1 -3 -1 \| 0 0 1 2 3 4 }}

			Optimal tunings:
			* WE: ~25/21 = 300.0140{{c}}, ~3/2 = 701.9679{{c}}, ~5/4 = 385.5977{{c}}
			* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.9549{{c}}, ~5/4 = 385.6140{{c}}

	{{Optimal ET sequence\|legend=0\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}		{{Optimal ET sequence\|legend=0\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
Line 42:		Line 58:

	{{Mapping\|legend=1\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}		{{Mapping\|legend=1\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}
			: mapping generators: ~12/11, ~7/5, ~13

			[[Optimal tuning]]s:
			* [[WE]]: ~12/11 = 150.0093{{c}}, ~7/5 = 583.9356{{c}}, ~13/8 = 840.6906{{c}}
			: [[error map]]: {{val\| -0.055 -0.155 -0.592 +0.832 +0.380 -0.001 }}
			* [[CWE]]: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9477{{c}}, ~13/8 = 840.6394{{c}}
			: error map: {{val\| 0.000 -0.112 -0.523 +0.913 +0.525 +0.112 }}

	{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}		{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}

FloraC: - redundant category

2026-02-12T08:24:06Z

- redundant category

← Older revision		Revision as of 08:24, 12 February 2026
Line 49:		Line 49:
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Dimcomp family\| ]] <!-- main article -->		[[Category:Dimcomp family\| ]] <!-- main article -->
	~~[[Category:Dimcomp\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Switch to Sintel's badness

2026-02-12T08:23:55Z

Switch to Sintel's badness

← Older revision		Revision as of 08:23, 12 February 2026
Line 12:		Line 12:
	{{Optimal ET sequence\|legend=1\| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}		{{Optimal ET sequence\|legend=1\| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}

	[[Badness]] (~~Smith~~): 0.~~783 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 3.45

	== Undecimal dimcomp ==		== Undecimal dimcomp ==
Line 23:		Line 23:
	{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}		{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}

	[[Badness]] (~~Smith~~): 0.~~624 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.751

	=== 13-limit ===		=== 13-limit ===
Line 34:		Line 34:
	{{Optimal ET sequence\|legend=0\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}		{{Optimal ET sequence\|legend=0\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}

	Badness (~~Smith~~): 0.~~820 × 10<sup>-3</sup>~~		Badness (Sintel): 0.767

	== Octopod ==		== Octopod ==
Line 41:		Line 41:
	[[Comma list]]: 540/539, 1375/1372, 4000/3993		[[Comma list]]: 540/539, 1375/1372, 4000/3993

	~~Mapping:~~ {{~~mapping~~\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}		{{Mapping\|legend=1\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}

	{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}		{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}

	[[Badness]] (~~Smith~~): 1.~~244 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 1.16

	[[Category:Temperament families]]		[[Category:Temperament families]]

FloraC: Units & misc. cleanup

2026-02-12T08:21:38Z

Units & misc. cleanup

← Older revision		Revision as of 08:21, 12 February 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962.		The '''dimcomp family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[dimcomp comma]] ({{monzo\|legend=1\| -1 -4 8 -4 }}, [[ratio]]: 390625/388962).

	== Dimcomp ==		== Dimcomp ==
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: [[390625/388962]]		[[Comma list]]: 390625/388962

	{{Mapping\|legend=1\| 4 0 0 -1 \| 0 1 0 -1 \| 0 0 1 2 }}		{{Mapping\|legend=1\| 4 0 0 -1 \| 0 1 0 -1 \| 0 0 1 2 }}

	: mapping generators: ~25/21, ~3, ~5		: mapping generators: ~25/21, ~3, ~5

	{{Optimal ET sequence\|legend=1\| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}		{{Optimal ET sequence\|legend=1\| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}

	[[Badness]]: 0.783 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.783 × 10<sup>-3</sup>

	== Undecimal dimcomp ==		== Undecimal dimcomp ==
Line 24:		Line 23:
	{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}		{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}

	[[Badness]]: 0.624 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.624 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
Line 33:		Line 32:
	Mapping: {{mapping\| 4 0 0 -1 5 -16 \| 0 1 0 -1 -3 -1 \| 0 0 1 2 3 4 }}		Mapping: {{mapping\| 4 0 0 -1 5 -16 \| 0 1 0 -1 -3 -1 \| 0 0 1 2 3 4 }}

	{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}		{{Optimal ET sequence\|legend=0\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}

	Badness: 0.820 × 10<sup>-3</sup>		Badness (Smith): 0.820 × 10<sup>-3</sup>

	== Octopod ==		== Octopod ==
	Subgroup: 2.3.5.7.11.13		[[Subgroup]]: 2.3.5.7.11.13

	Comma list: 540/539, 1375/1372, 4000/3993		[[Comma list]]: 540/539, 1375/1372, 4000/3993

	Mapping: {{mapping\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}		Mapping: {{mapping\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}
Line 46:		Line 45:
	{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}		{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}

	Badness: 1.244 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.244 × 10<sup>-3</sup>

	[[Category:Temperament families]]		[[Category:Temperament families]]

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:18:44Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:18, 27 November 2025
Line 49:		Line 49:

	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Dimcomp family\| ]] <!-- main article -->		[[Category:Dimcomp family\| ]] <!-- main article -->
	[[Category:Dimcomp\| ]] <!-- key article -->		[[Category:Dimcomp\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:31:29Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:31, 24 June 2025
Line 49:		Line 49:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Dimcomp family\| ]] <!-- main article -->		[[Category:Dimcomp family\| ]] <!-- main article -->
	[[Category:Dimcomp\| ]] <!-- key article -->		[[Category:Dimcomp\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:46:22Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:46, 13 April 2025
Line 1:		Line 1:
	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962.		The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962.

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:36:54Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 11:36, 13 April 2025
Line 1:		Line 1:
	The '''dimcomp family''' of rank-3 ~~temperaments~~ tempers out the [[dimcomp comma]], 390625/388962.		{{Technical data page}}<br><br>
			The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962.

	== Dimcomp ==		== Dimcomp ==

FloraC: Update keys

2023-09-12T08:58:05Z

Update keys

← Older revision		Revision as of 08:58, 12 September 2023
Line 1:		Line 1:
	The '''dimcomp family''' of rank-3 temperaments tempers out the [[dimcomp comma]], 390625/388962.		The '''dimcomp family''' of rank-3 temperaments tempers out the [[dimcomp comma]], 390625/388962.

	== Dimcomp ==		== Dimcomp ==
	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: [[390625/388962]]		[[Comma list]]: [[390625/388962]]

	~~[[Mapping]]: [~~{{~~val~~\| 4 0 0 -1 ~~}}, {{val~~\| 0 1 0 -1 ~~}}, {{val~~\| 0 0 1 2 }}]		{{Mapping\|legend=1\| 4 0 0 -1 \| 0 1 0 -1 \| 0 0 1 2 }}

			: mapping generators: ~25/21, ~3, ~5

	{{Optimal ET sequence\|legend=1\| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}		{{Optimal ET sequence\|legend=1\| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
Line 12:		Line 14:
	[[Badness]]: 0.783 × 10<sup>-3</sup>		[[Badness]]: 0.783 × 10<sup>-3</sup>

	== Undecimal dimcomp ==		== Undecimal dimcomp ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 1375/1372, 6250/6237		[[Comma list]]: 1375/1372, 6250/6237

	~~[[Mapping]]: [~~{{~~val~~\| 4 0 0 -1 5 ~~}}, {{val~~\| 0 1 0 -1 -3 ~~}}, {{val~~\| 0 0 1 2 3 }}]		{{Mapping\|legend=1\| 4 0 0 -1 5 \| 0 1 0 -1 -3 \| 0 0 1 2 3 }}

	{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}		{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152, 224, 364, 436, 588 }}
Line 23:		Line 25:
	[[Badness]]: 0.624 × 10<sup>-3</sup>		[[Badness]]: 0.624 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 625/624, 1375/1372, 2080/2079		Comma list: 625/624, 1375/1372, 2080/2079

	Mapping: [{{~~val~~\| 4 0 0 -1 5 -16 ~~}}, {{val~~\| 0 1 0 -1 -3 -1 ~~}}, {{val~~\| 0 0 1 2 3 4 }}]		Mapping: {{mapping\| 4 0 0 -1 5 -16 \| 0 1 0 -1 -3 -1 \| 0 0 1 2 3 4 }}

	{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}		{{Optimal ET sequence\|legend=1\| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
Line 34:		Line 36:
	Badness: 0.820 × 10<sup>-3</sup>		Badness: 0.820 × 10<sup>-3</sup>

	== Octopod ==		== Octopod ==
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 540/539, 1375/1372, 4000/3993		Comma list: 540/539, 1375/1372, 4000/3993

	Mapping: [{{~~val~~\| 8 1 3 3 16 0 ~~}}, {{val~~\| 0 3 4 5 3 0 ~~}}, {{val~~\| 0 0 0 0 0 1 }}]		Mapping: {{mapping\| 8 1 3 3 16 0 \| 0 3 4 5 3 0 \| 0 0 0 0 0 1 }}

	{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}		{{Optimal ET sequence\|legend=1\| 72, 144, 152f, 224, 824d }}
Line 46:		Line 48:

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Dimcomp]]		[[Category:Dimcomp family\| ]] <!-- main article -->
			[[Category:Dimcomp\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]