Syntonic–chromatic equivalence continuum - Revision history

FloraC: + error map. Review optimal ET sequence. Unify precision

2026-02-25T14:49:42Z

+ error map. Review optimal ET sequence. Unify precision

← Older revision		Revision as of 14:49, 25 February 2026
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	{{Mapping\|legend=1\| 1 0 -15 \| 0 1 11 }}		{{Mapping\|legend=1\| 1 0 -15 \| 0 1 11 }}

	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

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	{{Mapping\|legend=1\| 1 0 18 \| 0 1 -10 }}		{{Mapping\|legend=1\| 1 0 18 \| 0 1 -10 }}

	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

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	{{Mapping\|legend=1\| 1 1 -1 \| 0 2 15 }}		{{Mapping\|legend=1\| 1 1 -1 \| 0 2 15 }}

	: mapping generators: ~2, ~2560/2187		: mapping generators: ~2, ~2560/2187

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

	: mapping generators: ~2, ~16/15		: mapping generators: ~2, ~16/15

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	{{Mapping\|legend=1\| 1 2 5 \| 0 -3 -19 }}		{{Mapping\|legend=1\| 1 2 5 \| 0 -3 -19 }}

	: mapping generators: ~2, ~729/640		: mapping generators: ~2, ~729/640

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	{{Mapping\|legend=1\| 1 3 4 \| 0 -5 -6 }}		{{Mapping\|legend=1\| 1 3 4 \| 0 -5 -6 }}

	: mapping generators: ~2, ~6/5		: mapping generators: ~2, ~6/5

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	{{Mapping\|legend=1\| 7 0 -17 \| 0 1 3 }}		{{Mapping\|legend=1\| 7 0 -17 \| 0 1 3 }}

	: mapping generators: ~800/729, ~3		: mapping generators: ~800/729, ~3

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	{{Mapping\|legend=1\| 7 0 -6 \| 0 1 2 }}		{{Mapping\|legend=1\| 7 0 -6 \| 0 1 2 }}

	: mapping generators: ~10/9, ~3		: mapping generators: ~10/9, ~3

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	{{Mapping\|legend=1\| 7 0 5 \| 0 1 1 }}		{{Mapping\|legend=1\| 7 0 5 \| 0 1 1 }}

	: mapping generators: ~125/108, ~3		: mapping generators: ~125/108, ~3

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	{{Mapping\|legend=1\| 1 -1 -4 \| 0 9 22 }}		{{Mapping\|legend=1\| 1 -1 -4 \| 0 9 22 }}

	: mapping generators: ~2, ~243/200		: mapping generators: ~2, ~243/200

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	{{Mapping\|legend=1\| 1 -3 -10 \| 0 16 43 }}		{{Mapping\|legend=1\| 1 -3 -10 \| 0 16 43 }}

	: mapping generators: ~2, ~8000/6561		: mapping generators: ~2, ~8000/6561

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	{{Mapping\|legend=1\| 1 0 -2 \| 0 11 30 }}		{{Mapping\|legend=1\| 1 0 -2 \| 0 11 30 }}

	: mapping generators: ~2, ~177147/160000		: mapping generators: ~2, ~177147/160000

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.~~060~~{{c}}, ~177147/160000 = 172.~~886~~{{c}}		* [[WE]]: ~2 = 1200.0596{{c}}, ~177147/160000 = 172.8864{{c}}
	* [[CWE]]: ~2 = 1200.000{{c}}, ~177147/160000 = 172.~~880~~{{c}}		: [[error map]]: {{val\| +0.060 -0.204 +0.161 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~177147/160000 = 172.8804{{c}}
			: error map: {{val\| 0.000 -0.271 +0.098 }}

	{{Optimal ET sequence\|legend=1\| 7, …, 111, 118, 1541, 1659, 1777, 1895b }}		{{Optimal ET sequence\|legend=1\| 7, …, 111, 118, 1541, 1659, 1777, 1895b, …, 2839b, 2957b }}

	[[Badness]] (Sintel): 4.~~086~~		[[Badness]] (Sintel): 4.09

	[[Category:7edo]]		[[Category:7edo]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Xenllium at 12:15, 6 February 2026

2026-02-06T12:15:44Z

@@ Line 94: / Line 94: @@
 | {{Monzo| -17 21 -7 }}
 |-
 | …
 | …
@@ Line 412: / Line 413: @@
 [[Badness]] (Sintel): 2.78
 [[Category:7edo]]
 [[Category:Equivalence continua]]

FloraC: /* Enipucrop */ correction

2025-11-25T16:45:20Z

Enipucrop: correction

← Older revision		Revision as of 16:45, 25 November 2025
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1210.1294{{c}}, ~16/15 = 174.5613{{c}}		* [[WE]]: ~2 = 1210.1294{{c}}, ~16/15 = 174.5613{{c}}
	: [[error map]]: {{val\| +3.~~120~~ -6.~~264 +1~~.~~733~~ }}		: [[error map]]: {{val\| +10.129 -5.380 -16.932 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}}
	: error map: {{val\| 0.000 -10.~~757~~ -2.~~326~~ }}		: error map: {{val\| 0.000 -19.341 -41.390 }}

	{{Optimal ET sequence\|legend=1\| 6b, 7 }}		{{Optimal ET sequence\|legend=1\| 6b, 7 }}

FloraC: - CTE & POTE tunings

2025-09-06T11:48:42Z

- CTE & POTE tunings

← Older revision		Revision as of 11:48, 6 September 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 689.3122{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 689.3122{{c}}
	: error map: {{val\| 0.000 -12.643 -3.879 }}		: error map: {{val\| 0.000 -12.643 -3.879 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 689.879{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 33, 40, 47, 54b }}		{{Optimal ET sequence\|legend=1\| 7, 33, 40, 47, 54b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 682.6617{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 682.6617{{c}}
	: error map: {{val\| 0.000 -19.293 -12.931 }}		: error map: {{val\| 0.000 -19.293 -12.931 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.801{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }}		{{Optimal ET sequence\|legend=1\| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~2560/2187 = 345.5992{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~2560/2187 = 345.5992{{c}}
	: error map: {{val\| 0.000 -10.757 -2.326 }}		: error map: {{val\| 0.000 -10.757 -2.326 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~2560/2187 = 345.946{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 38c, 45c, 52, 59b, 66b }}		{{Optimal ET sequence\|legend=1\| 7, 38c, 45c, 52, 59b, 66b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}}
	: error map: {{val\| 0.000 -10.757 -2.326 }}		: error map: {{val\| 0.000 -10.757 -2.326 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 170.671{{c}}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 173.101{{c}} -->

	{{Optimal ET sequence\|legend=1\| 6b, 7 }}		{{Optimal ET sequence\|legend=1\| 6b, 7 }}
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	* [[CWE]]: ~2 = 1200.000{{c}}, ~729/640 = 169.2234{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~729/640 = 169.2234{{c}}
	: error map: {{val\| 0.000 -9.625 -1.559 }}		: error map: {{val\| 0.000 -9.625 -1.559 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~729/640 = 168.983{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 57c, 64, 71b, 78b, 85b }}		{{Optimal ET sequence\|legend=1\| 7, 57c, 64, 71b, 78b, 85b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 338.1959{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 338.1959{{c}}
	: error map: {{val\| 0.000 +7.065 -15.489 }}		: error map: {{val\| 0.000 +7.065 -15.489 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.005{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +8.020 -14.344 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.365{{c}}
	~~: error map: {{val\| 0.000 +6.217 -16.507 }} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 25, 32, 39c }}		{{Optimal ET sequence\|legend=1\| 7, 25, 32, 39c }}
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	* [[CWE]]: ~800/729 = 171.4286{{c}}, ~3/2 = 700.3453{{c}} (~81/80 = 14.6310{{c}})		* [[CWE]]: ~800/729 = 171.4286{{c}}, ~3/2 = 700.3453{{c}} (~81/80 = 14.6310{{c}})
	: error map: {{val\| 0.000 +7.065 -15.489 }}		: error map: {{val\| 0.000 +7.065 -15.489 }}
	~~<!-- * [[CTE]]: ~800/729 = 171.429{{c}}, ~3/2 = 700.538{{c}} (~81/80 = 14.824{{c}})~~
	* [[POTE]]: ~800/729 = 171.429{{c}}, ~3/2 = 700.187{{c}} (~81/80 = 14.473{{c}}) -->

	{{Optimal ET sequence\|legend=1\| 7, …, 70, 77, 84, 329, 413b, 497b }}		{{Optimal ET sequence\|legend=1\| 7, …, 70, 77, 84, 329, 413b, 497b }}
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	* [[CWE]]: ~10/9 = 171.4286{{c}}, ~3/2 = 705.9119{{c}} (~250/243 = 20.1977{{c}})		* [[CWE]]: ~10/9 = 171.4286{{c}}, ~3/2 = 705.9119{{c}} (~250/243 = 20.1977{{c}})
	: error map: {{val\| 0.000 +3.957 -3.061 }}		: error map: {{val\| 0.000 +3.957 -3.061 }}
	~~<!-- * [[CTE]]: ~10/9 = 171.429{{c}}, ~3/2 = 705.526{{c}} (~250/243 = 19.812{{c}})~~
	* [[POTE]]: ~10/9 = 171.429{{c}}, ~3/2 = 706.288{{c}} (~250/243 = 20.574{{c}}) -->

	{{Optimal ET sequence\|legend=1\| 7, …, 42, 49, 56, 119 }}		{{Optimal ET sequence\|legend=1\| 7, …, 42, 49, 56, 119 }}
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	* [[CWE]]: ~125/108 = 171.4286{{c}}, ~3/2 = 708.3739{{c}} (~25/24 = 22.6596{{c}})		* [[CWE]]: ~125/108 = 171.4286{{c}}, ~3/2 = 708.3739{{c}} (~25/24 = 22.6596{{c}})
	: error map: {{val\| 0.000 +6.419 -20.797 }}		: error map: {{val\| 0.000 +6.419 -20.797 }}
	~~<!-- * [[CTE]]: ~125/108 = 171.429{{c}}, ~3/2 = 710.606{{c}} (~25/24 = 24.891{{c}})~~
	* [[POTE]]: ~125/108 = 171.429{{c}}, ~3/2 = 706.410{{c}} (~25/24 = 20.696{{c}}) -->

	{{Optimal ET sequence\|legend=1\| 7, 35b, 42c }}		{{Optimal ET sequence\|legend=1\| 7, 35b, 42c }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/200 = 344.8041{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/200 = 344.8041{{c}}
	: error map: {{val\| 0.000 +1.282 -0.624 }}		: error map: {{val\| 0.000 +1.282 -0.624 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~400/243 = 855.213{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, … 73, 80, 87 }}		{{Optimal ET sequence\|legend=1\| 7, … 73, 80, 87 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~8000/6561 = 343.8683{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~8000/6561 = 343.8683{{c}}
	: error map: {{val\| 0.000 -0.062 +0.024 }}		: error map: {{val\| 0.000 -0.062 +0.024 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~8000/6561 = 343.868{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, …, 157, 164, 171, 506, 677, 848 }}		{{Optimal ET sequence\|legend=1\| 7, …, 157, 164, 171, 506, 677, 848 }}

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

2025-09-06T11:47:52Z

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

Show changes

FloraC: Move 5-limit geb here

2025-09-06T11:08:37Z

Move 5-limit geb here

@@ Line 369: / Line 369: @@
 [[Badness]] (Smith): 0.348
 [[Category:7edo]]
 [[Category:Equivalence continua]]

FloraC at 10:55, 6 September 2025

2025-09-06T10:55:09Z

← Older revision		Revision as of 10:55, 6 September 2025
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	\|}		\|}

	We may invert the continuum by setting ''m'' such that {{nowrap\| 1/''m'' + 1/''n'' }} {{=}} 1}}. This may be called the ''mavila–chromatic equivalence continuum'', which is essentially the same thing. The just value of ''m'' is 1.2333… The [[135/128\|mavila comma]] is both larger and more complex than the syntonic comma. As such, this continuum does not contain as many useful temperaments, but still interesting nonetheless.		We may invert the continuum by setting ''m'' such that {{nowrap\| 1/''m'' + 1/''n'' {{=}} 1}}. This may be called the ''mavila–chromatic equivalence continuum'', which is essentially the same thing. The just value of ''m'' is 1.2333… The [[135/128\|mavila comma]] is both larger and more complex than the syntonic comma. As such, this continuum does not contain as many useful temperaments, but still interesting nonetheless.

	{\| class="wikitable center-1"		{\| class="wikitable center-1"

FloraC: Units. Cleanup. Style

2025-09-06T10:50:03Z

Units. Cleanup. Style

Show changes

VectorGraphics at 08:59, 25 August 2025

2025-08-25T08:59:48Z

← Older revision		Revision as of 08:59, 25 August 2025
Line 295:		Line 295:
	: ''For extensions, see [[Porwell temperaments #Absurdity]].''		: ''For extensions, see [[Porwell temperaments #Absurdity]].''

	Absurdity corresponds to {{nowrap\|''n'' {{=}} 7}}, and can be described as the 77 & 84 temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9)/(81/80).		Absurdity corresponds to {{nowrap\|''n'' {{=}} 7}}, and can be described as the 77 & 84 temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9)/(81/80). It tempers out the ''absurditon'', 10460353203/10240000000.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

FloraC at 14:04, 2 June 2025

2025-06-02T14:04:37Z

← Older revision		Revision as of 14:04, 2 June 2025
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	\| −4		\| −4
	\| −2		\| −2
	\| [[~~Syntonic–chromatic equivalence continuum#Nethertone\|~~Nethertone]]		\| [[Nethertone]]
	\| [[14348907/13107200]]		\| [[14348907/13107200]]
	\| {{monzo\| -19 15 -2 }}		\| {{monzo\| -19 15 -2 }}
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	\| −3		\| −3
	\| −1		\| −1
	\| [[~~Syntonic–chromatic equivalence continuum#Deeptone a.k.a. tragicomical\|~~Deeptone a.k.a. tragicomical]]		\| [[Deeptone]] a.k.a. tragicomical
	\| [[177147/163840]]		\| [[177147/163840]]
	\| {{monzo\| -15 11 -1 }}		\| {{monzo\| -15 11 -1 }}