Ripple family - Revision history

Overthink: impractically complex given low accuracy

2026-06-28T01:54:19Z

impractically complex given low accuracy

← Older revision		Revision as of 01:54, 28 June 2026
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	Badness (Sintel): 1.93		Badness (Sintel): 1.93

	~~== Cohemiripple ==~~
	~~{{See also\| Sensamagic clan }}~~

	~~Cohemiripple tempers out 245/243 and splits the octave complement of the semitone generator of ripple in two, each of which is used for ~7/5. Its ploidacot is delta-decacot.~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 245/243, 1323/1250~~

	~~{{Mapping\|legend=1\| 1 -3 -5 -5 \| 0 10 16 17 }}~~

	~~: mapping generators: ~2, ~7/5~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1200.6977{{c}}, ~7/5 = 550.2638{{c}}
	~~: error map: {{val\| +0.698 -1.410 +14.418 -17.830 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/5 = 549.9979{{c}}
	~~: error map: {{val\| 0.000 -1.976 +13.653 -18.861 }}~~

	~~{{Optimal ET sequence\|legend=1\| 11cd, 13cd, 24 }}~~

	~~[[Badness]] (Sintel): 4.81~~

	~~=== 11-limit ===~~
	~~Subgroup: 2.3.5.7.11~~

	~~Comma list: 77/75, 243/242, 245/242~~

	~~Mapping: {{mapping\| 1 -3 -5 -5 -8 \| 0 10 16 17 25 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1200.6959{{c}}, ~7/5 = 550.2641{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 549.9969{{c}}

	~~{{Optimal ET sequence\|legend=0\| 11cdee, 13cdee, 24 }}~~

	~~Badness (Sintel): 2.73~~

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

	~~Comma list: 66/65, 77/75, 147/143, 243/242~~

	~~Mapping: {{mapping\| 1 -3 -5 -5 -8 -5 \| 0 10 16 17 25 19 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1200.1161{{c}}, ~7/5 = 550.0107{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 549.9663{{c}}

	~~{{Optimal ET sequence\|legend=0\| 11cdeef, 13cdeef, 24 }}~~

	~~Badness (Sintel): 2.06~~

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

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

2025-11-27T12:17:17Z

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

← Older revision		Revision as of 12:17, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Ripple family\| ]] <!-- main article -->		[[Category:Ripple family\| ]] <!-- main article -->
	[[Category:Ripple\| ]] <!-- key article -->		[[Category:Ripple\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: + overview to extensions

2025-08-22T14:46:20Z

+ overview to extensions

← Older revision		Revision as of 14:46, 22 August 2025
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	[[Badness]] (Sintel): 3.26		[[Badness]] (Sintel): 3.26

			=== Overview to extensions ===
			The second comma of the comma list defines which 7-limit family member we are looking at:
			* Septimal ripple adds [[126/125]];
			* Rip adds [[36/35]];

			Both use the same nominal generator as ripple.

			For weak extensions, we have hemiripple and cohemiripple. Hemiripple adds [[49/48]], spliting the semitone generator in two. Cohemiripple adds [[245/243]], spliting the [[octave complement]] of the semitone generator in two.

	== Septimal ripple ==		== Septimal ripple ==
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	{{See also\| Sensamagic clan }}		{{See also\| Sensamagic clan }}

	Cohemiripple tempers out 245/243 and splits the [[octave complement]] of the semitone generator of ripple in two, each of which is used for ~7/5. Its ploidacot is delta-decacot.		Cohemiripple tempers out 245/243 and splits the octave complement of the semitone generator of ripple in two, each of which is used for ~7/5. Its ploidacot is delta-decacot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: + intro to each temp. + mapping generators

2025-08-22T14:41:04Z

+ intro to each temp. + mapping generators

← Older revision		Revision as of 14:41, 22 August 2025
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	== Ripple ==		== Ripple ==
	The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. The ploidacot of ripple is omega-pentacot. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered fourth reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice sometimes even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often very flat, so that ripple can in practice be thought of as a [[dual-fifth temperament]] unless you use tunings close to [[12edo]].		The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. The [[ploidacot]] of ripple is omega-pentacot. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered fourth reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice sometimes even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often very flat, so that ripple can in practice be thought of as a [[dual-fifth temperament]] unless you use tunings close to [[12edo]].

	Reasonable [[patent val]] tunings not appearing in the optimal ET sequence are [[35edo]] and [[47edo]].		Reasonable [[patent val]] tunings not appearing in the optimal ET sequence are [[35edo]] and [[47edo]].
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	== Hemiripple ==		== Hemiripple ==
			Hemiripple tempers out 49/48 and splits the semitone generator in two for ~36/35. Its ploidacot is omega-decacot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	{{Mapping\|legend=1\| 1 2 3 3 \| 0 -10 -16 -5 }}		{{Mapping\|legend=1\| 1 2 3 3 \| 0 -10 -16 -5 }}

			: mapping generators: ~2, ~36/35

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	== Cohemiripple ==		== Cohemiripple ==
	{{See also\| Sensamagic clan }}		{{See also\| Sensamagic clan }}

			Cohemiripple tempers out 245/243 and splits the [[octave complement]] of the semitone generator of ripple in two, each of which is used for ~7/5. Its ploidacot is delta-decacot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	[[Comma list]]: 245/243, 1323/1250		[[Comma list]]: 245/243, 1323/1250

	{{Mapping\|legend=1\| 1 ~~7 11 12~~ \| 0 -10 -16 -17 }}		{{Mapping\|legend=1\| 1 -3 -5 -5 \| 0 10 16 17 }}

			: mapping generators: ~2, ~7/5

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	Comma list: 77/75, 243/242, 245/242		Comma list: 77/75, 243/242, 245/242

	Mapping: {{mapping\| 1 ~~7 11 12 17~~ \| 0 -10 -16 -17 -25 }}		Mapping: {{mapping\| 1 -3 -5 -5 -8 \| 0 10 16 17 25 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 66/65, 77/75, 147/143, 243/242		Comma list: 66/65, 77/75, 147/143, 243/242

	Mapping: {{mapping\| 1 ~~7 11 12 17 14~~ \| 0 -10 -16 -17 -25 -19 }}		Mapping: {{mapping\| 1 -3 -5 -5 -8 -5 \| 0 10 16 17 25 19 }}

	Optimal tunings:		Optimal tunings:

FloraC: - CTE & POTE tunings

2025-08-22T14:37:08Z

- CTE & POTE tunings

← Older revision		Revision as of 14:37, 22 August 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/25 = 100.7982{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/25 = 100.7982{{c}}
	: [[error map]]: {{val\| 0.000 -5.946 +7.300 }}		: [[error map]]: {{val\| 0.000 -5.946 +7.300 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 100.752{{c}}~~
	~~: error map: {{val\| 0.000 -5.717 +7.668 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 100.838{{c}}
	~~: error map: {{val\| 0.000 -6.145 +6.982 }} -->~~

	[[Tuning ranges]]:		[[Tuning ranges]]:
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 101.7772{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 101.7772{{c}}
	: error map: {{val\| 0.000 -10.841 -0.531 +6.294 }}		: error map: {{val\| 0.000 -10.841 -0.531 +6.294 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 101.538{{c}}~~
	~~: error map: {{val\| 0.000 -9.643 +1.385 +9.647 }}~~
	* [[CEE]]: ~2 = 1200.000{{c}}, ~15/14 = 101.881{{c}}
	~~: error map: {{val\| 0.000 -11.361 -1.364 +4.837 }} -->~~

	{{Optimal ET sequence\|legend=1\| 11cd, 12, 35, 47 }}		{{Optimal ET sequence\|legend=1\| 11cd, 12, 35, 47 }}
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	* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 102.2972{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 102.2972{{c}}
	: error map: {{val\| 0.000 -13.441 -4.691 -0.986 +7.333 }}		: error map: {{val\| 0.000 -13.441 -4.691 -0.986 +7.333 }}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~15/14 = 101.538{{c}}~~
	~~: error map: {{val\| 0.000 -11.785 -2.041 +3.651 +13.296 }}~~
	* CEE: ~2 = 1200.000{{c}}, ~15/14 = 102.319{{c}}
	~~: error map: {{val\| 0.000 -13.551 -4.868 -1.296 +6.935 }} -->~~

	{{Optimal ET sequence\|legend=0\| 11cdee, 12, 23de, 35 }}		{{Optimal ET sequence\|legend=0\| 11cdee, 12, 23de, 35 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 100.1093{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 100.1093{{c}}
	: error map: {{val\| 0.000 -2.501 +12.812 +30.956 }}		: error map: {{val\| 0.000 -2.501 +12.812 +30.956 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 101.089{{c}}~~
	~~: error map: {{val\| 0.000 -7.402 +4.970 +28.995 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 99.483{{c}}
	~~: error map: {{val\| 0.000 +0.632 +17.825 +32.209 }} -->~~

	{{Optimal ET sequence\|legend=1\| 11c, 12 }}		{{Optimal ET sequence\|legend=1\| 11c, 12 }}
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	* WE: ~2 = 1192.7877{{c}}, ~21/20 = 98.7876{{c}}		* WE: ~2 = 1192.7877{{c}}, ~21/20 = 98.7876{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 100.3202{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 100.3202{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 101.923{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~21/20 = 99.385{{c}} -->

	{{Optimal ET sequence\|legend=0\| 11c, 12 }}		{{Optimal ET sequence\|legend=0\| 11c, 12 }}
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	* WE: ~2 = 1189.8521{{c}}, ~21/20 = 97.7384{{c}}		* WE: ~2 = 1189.8521{{c}}, ~21/20 = 97.7384{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 99.7618{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 99.7618{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 102.376{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~21/20 = 98.572{{c}} -->

	{{Optimal ET sequence\|legend=0\| 11c, 12f, 37ccddeeeeffff }}		{{Optimal ET sequence\|legend=0\| 11c, 12f, 37ccddeeeeffff }}
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	* [[WE]]: ~2 = 1203.5561{{c}}, ~36/35 = 50.9765{{c}}		* [[WE]]: ~2 = 1203.5561{{c}}, ~36/35 = 50.9765{{c}}
	: error map: {{val\| +3.556 -4.608 +8.730 -13.040 }}		: error map: {{val\| +3.556 -4.608 +8.730 -13.040 }}
	* [[CWE]]: ~2 = 1200.~~000~~{{c}}, ~36/35 = 50.5928{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 50.5928{{c}}
	: error map: {{val\| 0.000 -7.883 +4.201 -21.790 }}		: error map: {{val\| 0.000 -7.883 +4.201 -21.790 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~36/35 = 50.231{{c}}~~
	~~: [[error map]]: {{val\| 0.000 -4.264 +9.991 -19.981 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~36/35 = 50.826{{c}}
	~~: error map: {{val\| 0.000 -10.214 +0.472 -22.956 }} -->~~

	{{Optimal ET sequence\|legend=1\| 23d, 24, 47d }}		{{Optimal ET sequence\|legend=1\| 23d, 24, 47d }}
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	* WE: ~2 = 1203.5344{{c}}, ~36/35 = 50.9757{{c}}		* WE: ~2 = 1203.5344{{c}}, ~36/35 = 50.9757{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 50.5870{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 50.5870{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~36/35 = 50.186{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~36/35 = 50.826{{c}} -->

	{{Optimal ET sequence\|legend=0\| 23de, 24, 47de }}		{{Optimal ET sequence\|legend=0\| 23de, 24, 47de }}
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	* WE: ~2 = 1202.0936{{c}}, ~36/35 = 50.7232{{c}}		* WE: ~2 = 1202.0936{{c}}, ~36/35 = 50.7232{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 50.5048{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 50.5048{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~36/35 = 50.225{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~36/35 = 50.635{{c}} -->

	{{Optimal ET sequence\|legend=0\| 23de, 24 }}		{{Optimal ET sequence\|legend=0\| 23de, 24 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/5 = 549.9979{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/5 = 549.9979{{c}}
	: error map: {{val\| 0.000 -1.976 +13.653 -18.861 }}		: error map: {{val\| 0.000 -1.976 +13.653 -18.861 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/5 = 550.063{{c}}~~
	~~: error map: {{val\| 0.000 -1.328 +14.690 -17.760 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = 549.944{{c}}
	~~: error map: {{val\| 0.000 -2.515 +12.791 -19.777 }} -->~~

	{{Optimal ET sequence\|legend=1\| 11cd, 13cd, 24 }}		{{Optimal ET sequence\|legend=1\| 11cd, 13cd, 24 }}
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	* WE: ~2 = 1200.6959{{c}}, ~7/5 = 550.2641{{c}}		* WE: ~2 = 1200.6959{{c}}, ~7/5 = 550.2641{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 549.9969{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 549.9969{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~7/5 = 550.060{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~7/5 = 549.945{{c}} -->

	{{Optimal ET sequence\|legend=0\| 11cdee, 13cdee, 24 }}		{{Optimal ET sequence\|legend=0\| 11cdee, 13cdee, 24 }}
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.1161{{c}}, ~7/5 = 550.0107{{c}}		* WE: ~2 = 1200.1161{{c}}, ~7/5 = 550.0107{{c}}
	* CWE: ~2 = 1200.~~000~~{{c}}, ~7/5 = 549.9663{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 549.9663{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~7/5 = 549.987{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~7/5 = 549.958{{c}} -->

	{{Optimal ET sequence\|legend=0\| 11cdeef, 13cdeef, 24 }}		{{Optimal ET sequence\|legend=0\| 11cdeef, 13cdeef, 24 }}

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus. Review

2025-08-22T14:36:03Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus. Review

Show changes

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

2025-06-24T00:26:34Z

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

← Older revision		Revision as of 00:26, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Ripple family\| ]] <!-- main article -->		[[Category:Ripple family\| ]] <!-- main article -->
	[[Category:Ripple\| ]] <!-- key article -->		[[Category:Ripple\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 04:53, 12 June 2025

2025-06-12T04:53:36Z

← Older revision		Revision as of 04:53, 12 June 2025
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	{{Mapping\|legend=1\| 1 2 3 3 \| 0 -5 -8 -2 }}		{{Mapping\|legend=1\| 1 2 3 3 \| 0 -5 -8 -2 }}

	~~{{Multival\|legend=1\| 5 8 2 1 -11 -18 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=1\| 1 2 3 3 \| 0 -10 -16 -5 }}		{{Mapping\|legend=1\| 1 2 3 3 \| 0 -10 -16 -5 }}

	~~{{Multival\|legend=1\| 10 16 5 2 -20 -33 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=1\| 1 7 11 12 \| 0 -10 -16 -17 }}		{{Mapping\|legend=1\| 1 7 11 12 \| 0 -10 -16 -17 }}

	~~{{Multival\|legend=1\| 10 16 17 2 -1 -5 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: + CTE and CWE tunings; + error maps

2025-04-29T10:33:38Z

+ CTE and CWE tunings; + error maps

Show changes

FloraC: Cleanup

2025-04-28T13:31:31Z

Cleanup

← Older revision		Revision as of 13:31, 28 April 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''ripple family''' of temperaments [[tempering out\|tempers out]] the [[ripple comma]], 6561/6250 = {{monzo\| -1 8 -5 }}, which equates a stack of five [[27/25]]'s with [[4/3]].		The '''ripple family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ripple comma]] ([[ratio]]: 6561/6250, {{monzo\|legend=1\| -1 8 -5 }}), which equates a stack of five [[27/25]]'s with [[4/3]].

	== Ripple ==		== Ripple ==
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	== Septimal ripple ==		== Septimal ripple ==
	{{ See also \| Dual-fifth temperaments }}		{{ See also \| Dual-fifth temperaments }}
	Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~21/16 * ~4/3 = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy.		Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~(21/16)⋅(4/3) = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy.

	''If you are looking for the former canonical ~~extension~~ extension, see: [[#Rip]].''		''If you are looking for the former canonical extension, see: [[#Rip]].''

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	* [[CTE]]: ~15/14 = 101.538		* [[CTE]]: ~15/14 = 101.538
	: [[error map]]: {{val\| 0 -11.785, -2.041, 3.651, 13.296 }}		: [[error map]]: {{val\| 0 -11.785, -2.041, 3.651, 13.296 }}
	* [[CE]]: ~15/14 = 102.319 ~~(preferred for dual-fifths 11-limit)~~		* [[CE]]: ~15/14 = 102.319
	: [[error map]]: {{val\| 0 -13.551 -4.868 -1.296 6.935 }}		: [[error map]]: {{val\| 0 -13.551 -4.868 -1.296 6.935 }}

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	== Rip ==		== Rip ==
	Formerly known as ~~[[#Ripple]]~~, but de-canonized in favour of canonizing a significantly more accurate extension of similar efficiency so that [[#Ripple]] admits nontrivial edo tunings of interest. The reason for de-canonization is not coming close to preserving the damage level of 5-limit ripple to the 7-limit or even of this 7-limit damage level to the 11-limit.		Formerly known as ''septimal ripple'', but de-canonized in favour of canonizing a significantly more accurate extension of similar efficiency so that [[#Ripple]] admits nontrivial edo tunings of interest. The reason for de-canonization is not coming close to preserving the damage level of 5-limit ripple to the 7-limit or even of this 7-limit damage level to the 11-limit.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7