Schismic–Mercator equivalence continuum - Revision history

FloraC: /* Countritonic */ + link

2026-05-20T11:23:13Z

Countritonic: + link

← Older revision		Revision as of 11:23, 20 May 2026
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	== Countritonic ==		== Countritonic ==
	: ''For extensions, see [[Ragismic microtemperaments #Ragitritonic]] and [[~~Hemifamity temperaments~~ #~~Countriton~~]].''		: ''For extensions, see [[Hemifamity temperaments #Countriton]], [[Ragismic microtemperaments #Ragitritonic]], and [[Garischismic clan #Garitritonic]].''

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

FloraC: Update

2026-05-20T10:42:11Z

Update

← Older revision		Revision as of 10:42, 20 May 2026
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	[[Badness]] (Sintel): 3.06		[[Badness]] (Sintel): 3.06

	== Countritonic ~~(5-limit)~~ ==		== Countritonic ==
	: ''For extensions, see [[Ragismic microtemperaments #~~Countritonic~~]] and [[Hemifamity temperaments #Countriton]].''		: ''For extensions, see [[Ragismic microtemperaments #Ragitritonic]] and [[Hemifamity temperaments #Countriton]].''

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

FloraC: +1 and + commas for fractional n and m temps

2026-05-09T15:08:37Z

+1 and + commas for fractional n and m temps

← Older revision		Revision as of 15:08, 9 May 2026
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	\|+ style="font-size: 105%;" \| Temperaments with fractional ''n'' and ''m''		\|+ style="font-size: 105%;" \| Temperaments with fractional ''n'' and ''m''
	\|-		\|-
	! Temperament !! ''n'' !! ''m''		! Temperament !! ''n'' !! ''m'' !! Comma
	\|-		\|-
	\| 53 & 3684 \|\| 11/6 = 1.8{{overline\|3}} \|\| 11/5 = 2.2		\| 53 & 3684 \|\| 11/6 = 1.8{{overline\|3}} \|\| 11/5 = 2.2 \|\| {{Monzo\| -339 230 -11 }}
	\|-		\|-
	\| 53 & ~~4190~~ \|\| 13/7 = 1.{{overline\|857142}} \|\| 13/6 = 2.1{{overline\|6}}		\| 53 & 4296 \|\| 13/7 = 1.{{overline\|857142}} \|\| 13/6 = 2.1{{overline\|6}} \|\| {{Monzo\| 393 -267 13 }}
	\|-		\|-
	\| [[Countritonic]] \|\| 9/2 = 4.5 \|\| 9/7 = 1.{{overline\|285714}}		\| [[Countritonic]] \|\| 9/2 = 4.5 \|\| 9/7 = 1.{{overline\|285714}} \|\| {{Monzo\| 33 -34 9 }}
	\|-		\|-
	\| [[Quartonic]] \|\| 11/2 = 5.5 \|\| 11/9 = 1.{{overline\|2}}		\| [[Quartonic]] \|\| 11/2 = 5.5 \|\| 11/9 = 1.{{overline\|2}} \|\| {{Monzo\| 3 -18 11 }}
	\|-		\|-
	\| [[Ditonic]] \|\| 13/2 = 6.5 \|\| 13/11 = 1.{{overline\|18}}		\| [[Maja]] \|\| 17/3 = 5.{{overline\|6}} \|\| 17/14 = 1.2{{overline\|142857}} \|\| {{Monzo\| -3 -23 17 }}
			\|-
			\| [[Ditonic]] \|\| 13/2 = 6.5 \|\| 13/11 = 1.{{overline\|18}} \|\| {{Monzo\| -27 -2 13 }}
	\|}		\|}

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

2026-05-09T14:57:23Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 14:57, 9 May 2026
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	\| [[Mercator]]		\| [[Mercator]]
	\| (52 digits)		\| (52 digits)
	\| {{~~monzo~~\| -84 53 }}		\| {{Monzo\| -84 53 }}
	\|-		\|-
	\| 1		\| 1
Line 62:		Line 62:
	\|-		\|-
	\| 9		\| 9
	\| [[~~High badness~~ temperaments #Untriton\|Untriton]]		\| [[Miscellaneous 5-limit temperaments #Untriton\|Untriton]]
	\| (32 digits)		\| (32 digits)
	\| {{Monzo\| -51 19 9 }}		\| {{Monzo\| -51 19 9 }}
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	{{See also\| Counterschisma }}		{{See also\| Counterschisma }}

	Counterschismic is ~~much~~ like [[schismic]], but the harmonic 5 is located at +45 fifths instead of schismic's -8. They unite in [[53edo]], of course.		Counterschismic is generated by a [[3/2\|perfect fifth]], like [[schismic]], but the [[5/1\|5th]] [[harmonic]] is located at +45 fifths instead of schismic's -8. They unite at [[53edo]], of course. [[730edo]] may be recommended as a tuning.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	[[Comma list]]: {{monzo\| -69 45 -1 }}		[[Comma list]]: {{monzo\| -69 45 -1 }}

	{{Mapping\|legend=1\| 1 ~~2 21~~ \| 0 -1 -45 }}		{{Mapping\|legend=1\| 1 0 -69 \| 0 1 45 }}
			: mapping generators: ~2, ~3

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000, ~3/2 = 701.~~9175~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0116{{c}}, ~3/2 = 701.9243{{c}}
			: [[error map]]: {{val\| +0.012 -0.019 +0.001 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9177{{c}}
			: error map: {{val\| 0.000 -0.037 -0.017 }}

	{{Optimal ET sequence\|legend=1\| 53, 412, 465, 518, 571, 624, 677, 730, 2973, 3703, 4433, 5163, 11056}}		{{Optimal ET sequence\|legend=1\| 53, 412, 465, 518, 571, 624, 677, 730, 2973, 3703, 4433, 5163, 11056, 16219b }}

	[[Badness]] (~~Smith~~): 0.~~09123~~		[[Badness]] (Sintel): 2.14

	== Demibuzzard ==		== Demibuzzard (5-limit) ==
	: ''For extensions, see [[Buzzardsmic clan #Demibuzzard]].''		: ''For extensions, see [[Buzzardsmic clan #Demibuzzard]].''

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	[[Comma list]]: 69198046875/68719476736		[[Comma list]]: 69198046875/68719476736

	{{Mapping\|legend=1\| 1 4 -1 \| 0 -8 11 }}		{{Mapping\|legend=1\| 1 -4 10 \| 0 8 -11 }}
			: mapping generators: ~2, ~16384/10125

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.0000, ~10125/~~8192~~ = ~~362~~.~~321~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0000{{c}}, ~16384/10125 = 837.8342{{c}}
			: [[error map]]: {{val\| +0.222 -0.171 -0.267 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~16384/10125 = 837.6794{{c}}
			: error map: {{val\| 0.000 -0.520 -0.787 }}

	{{Optimal ET sequence\|legend=1\| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}		{{Optimal ET sequence\|legend=1\| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}

	[[Badness]] (~~Smith~~): 0.~~130236~~		[[Badness]] (Sintel): 3.06

	== Countritonic ==		== Countritonic (5-limit) ==
	: ''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''		: ''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''

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	[[Comma list]]: {{monzo\| 33 -34 9 }}		[[Comma list]]: {{monzo\| 33 -34 9 }}

	{{Mapping\|legend=1\| 1 ~~6 19~~ \| 0 -9 -34 }}		{{Mapping\|legend=1\| 1 -3 -15 \| 0 9 34 }}
			: mapping generators: ~2, ~20480000/14348907

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000, ~14348907~~/10240000~~ = ~~588~~.~~636~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9228{{c}}, ~20480000/14348907 = 611.3248{{c}}
			: [[error map]]: {{val\| -0.077 +0.200 -0.113 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~20480000/14348907 = 611.3614{{c}}
			: error map: {{val\| 0.000 +0.297 -0.027 }}

	{{Optimal ET sequence\|legend=1\| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}		{{Optimal ET sequence\|legend=1\| 51c, 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}

	[[Badness]] (~~Smith~~): 0.~~256~~		[[Badness]] (Sintel): 6.00

	== 53 & 3684 ==		== 53 & 3684 ==
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	{{Mapping\|legend=1\| 1 2 11 \| 0 -11 -230 }}		{{Mapping\|legend=1\| 1 2 11 \| 0 -11 -230 }}
			: mapping generators: ~2, ~10737418240/10460353203

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000, ~10737418240/10460353203 = 45.~~2769~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.000272{{c}}, ~10737418240/10460353203 = 45.276910{{c}}
			: [[error map]]: {{val\| +0.0003 -0.0005 +0.0000 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~10737418240/10460353203 = 45.276898{{c}}
			: error map: {{val\| 0.0000 -0.0009 -0.0003 }}

	{{Optimal ET sequence\|legend=1\| 53, 3684, 11105 }}		{{Optimal ET sequence\|legend=1\| 53, …, 3313, 3366, 3419, 3472, 3525, 3578, 3631, 3684, 7421, 11105, 25894, 36999 }}

	[[Badness]] (~~Smith~~): 0.~~276036~~		[[Badness]] (Sintel): 6.48

	== 53 & ~~4190~~ ==		== 53 & 4296 ==
	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

	[[Comma list]]: {{monzo\| 393 -267 13 }}		[[Comma list]]: {{monzo\| 393 -267 13 }}

	{{Mapping\|legend=1\| 1 ~~6 93~~ \| 0 -13 -~~267~~ }}		{{Mapping\|legend=1\| 1 -7 -174 \| 0 13 267 }}
			: mapping generators: ~2, ~{{monzo\| 61 -41 2 }}

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.~~0000~~, ~{{monzo\| -60 41 -2 }} = ~~407~~.~~5419~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.999891{{c}}, ~{{monzo\| 61 -41 2 }} = 792.458032{{c}}
			: [[error map]]: {{val\| -0.0001 +0.0002 -0.0000 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 61 -41 2 }} = 792.458104{{c}}
			: error map: {{val\| 0.0000 +0.0004 +0.0002 }}

	{{Optimal ET sequence\|legend=1\| 53, 4190, 4243, 4296 }}		{{Optimal ET sequence\|legend=1\| 53, …, 3872, 3925, 3978, 4031, 4084, 4137, 4190, 4243, 4296, 34315, 38611, 42907, 47203, 51499, 55795, 60091, 64387, 68683 }}

	[[Badness]] (~~Smith~~): 0.~~173433~~		[[Badness]] (Sintel): 4.07

	[[Category:53edo]]		[[Category:53edo]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Overthink: + link

2026-03-12T03:41:07Z

+ link

← Older revision		Revision as of 03:41, 12 March 2026
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	\|-		\|-
	\| 1		\| 1
	\| Counterschismic		\| [[Counterschismic]]
	\| (44 digits)		\| (44 digits)
	\| [[Counterschisma\|{{Monzo\| -69 45 -1 }}]]		\| [[Counterschisma\|{{Monzo\| -69 45 -1 }}]]

Lériendil: submajor -> demibuzzard

2026-02-08T16:03:09Z

submajor -> demibuzzard

← Older revision		Revision as of 16:03, 8 February 2026
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	\|-		\|-
	\| 8		\| 8
	\| [[~~Submajor (temperament)~~\|~~Submajor~~]]		\| [[Buzzardsmic clan #Demibuzzard\|Demibuzzard]]
	\| (22 digits)		\| (22 digits)
	\| {{Monzo\| -36 11 8 }}		\| {{Monzo\| -36 11 8 }}
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	[[Badness]] (Smith): 0.09123		[[Badness]] (Smith): 0.09123

	== ~~Submajor~~ ==		== Demibuzzard ==
	: ''For extensions, see [[Buzzardsmic clan #~~Submajor~~]].''		: ''For extensions, see [[Buzzardsmic clan #Demibuzzard]].''

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

VectorGraphics at 04:42, 12 June 2025

2025-06-12T04:42:59Z

← Older revision		Revision as of 04:42, 12 June 2025
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	{{Mapping\|legend=1\| 1 2 21 \| 0 -1 -45 }}		{{Mapping\|legend=1\| 1 2 21 \| 0 -1 -45 }}

	~~{{Multival\|legend=1\| 1 45 69 }}~~

	[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9175		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9175
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	{{Mapping\|legend=1\| 1 2 11 \| 0 -11 -230 }}		{{Mapping\|legend=1\| 1 2 11 \| 0 -11 -230 }}

	~~{{Multival\|legend=1\| 11 230 339 }}~~

	[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~10737418240/10460353203 = 45.2769		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~10737418240/10460353203 = 45.2769
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	{{Mapping\|legend=1\| 1 6 93 \| 0 -13 -267 }}		{{Mapping\|legend=1\| 1 6 93 \| 0 -13 -267 }}

	~~{{Multival\|legend=1\| 13 267 393 }}~~

	[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~{{monzo\| -60 41 -2 }} = 407.5419		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~{{monzo\| -60 41 -2 }} = 407.5419

FloraC: Oops

2025-04-16T15:35:59Z

Oops

← Older revision		Revision as of 15:35, 16 April 2025
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	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

	[[Comma list[[: {{monzo\| 33 -34 9 }}		[[Comma list]]: {{monzo\| 33 -34 9 }}

	{{Mapping\|legend=1\| 1 6 19 \| 0 -9 -34 }}		{{Mapping\|legend=1\| 1 6 19 \| 0 -9 -34 }}

FloraC: Some cleanup

2025-04-16T15:35:01Z

Some cleanup

← Older revision		Revision as of 15:35, 16 April 2025
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	Counterschismic is much like [[schismic]], but the harmonic 5 is located at +45 fifths instead of schismic's -8. They unite in [[53edo]], of course.		Counterschismic is much like [[schismic]], but the harmonic 5 is located at +45 fifths instead of schismic's -8. They unite in [[53edo]], of course.

	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	Comma list: {{monzo\| -69 45 -1 }}		[[Comma list]]: {{monzo\| -69 45 -1 }}

	~~Mapping:~~ {{~~mapping~~\| 1 2 21 \| 0 -1 -45 }}		{{Mapping\|legend=1\| 1 2 21 \| 0 -1 -45 }}

	{{Multival\|legend=1\| 1 45 69 }}		{{Multival\|legend=1\| 1 45 69 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~3/2 = 701.9175		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9175

	{{Optimal ET sequence\|legend=1\| 53, 412, 465, 518, 571, 624, 677, 730, 2973, 3703, 4433, 5163, 11056}}		{{Optimal ET sequence\|legend=1\| 53, 412, 465, 518, 571, 624, 677, 730, 2973, 3703, 4433, 5163, 11056}}

	Badness: 0.09123		[[Badness]] (Smith): 0.09123

	== Submajor ==		== Submajor ==
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	{{Mapping\|legend=1\| 1 4 -1 \| 0 -8 11 }}		{{Mapping\|legend=1\| 1 4 -1 \| 0 -8 11 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~10125/8192 = 362.321		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~10125/8192 = 362.321

	{{Optimal ET sequence\|legend=1\| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}		{{Optimal ET sequence\|legend=1\| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}

	[[Badness]]: 0.130236		[[Badness]] (Smith): 0.130236

	== Countritonic ==		== Countritonic ==
	~~{{See also\| High badness temperaments #Countritonic }}~~
	: ''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''		: ''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''

	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	Comma list: {{monzo\| 33 -34 9 }}		[[Comma list[[: {{monzo\| 33 -34 9 }}

	~~Mapping:~~ {{~~mapping~~\| 1 6 19 \| 0 -9 -34 }}		{{Mapping\|legend=1\| 1 6 19 \| 0 -9 -34 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~14348907/10240000 = 588.636		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~14348907/10240000 = 588.636

	{{Optimal ET sequence\|legend=1\| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}		{{Optimal ET sequence\|legend=1\| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}

	Badness: 0.256		[[Badness]] (Smith): 0.256

	== 53 & 3684 ==		== 53 & 3684 ==
	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	Comma list: {{monzo\| -339 230 -11 }}		[[Comma list]]: {{monzo\| -339 230 -11 }}

	~~Mapping:~~ {{~~mapping~~\| 1 2 11 \| 0 -11 -230 }}		{{Mapping\|legend=1\| 1 2 11 \| 0 -11 -230 }}

	{{Multival\|legend=1\| 11 230 339 }}		{{Multival\|legend=1\| 11 230 339 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~10737418240/10460353203 = 45.2769		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~10737418240/10460353203 = 45.2769

	{{Optimal ET sequence\|legend=1\| 53, 3684, 11105 }}		{{Optimal ET sequence\|legend=1\| 53, 3684, 11105 }}

	Badness: 0.276036		[[Badness]] (Smith): 0.276036

	== 53 & 4190 ==		== 53 & 4190 ==
	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	Comma list: {{monzo\| 393 -267 13 }}		[[Comma list]]: {{monzo\| 393 -267 13 }}

	~~Mapping:~~ {{~~mapping~~\| 1 6 93 \| 0 -13 -267 }}		{{Mapping\|legend=1\| 1 6 93 \| 0 -13 -267 }}

	{{Multival\|legend=1\| 13 267 393 }}		{{Multival\|legend=1\| 13 267 393 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~{{monzo\| -60 41 -2 }} = 407.5419		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~{{monzo\| -60 41 -2 }} = 407.5419

	{{Optimal ET sequence\|legend=1\| 53, 4190, 4243, 4296 }}		{{Optimal ET sequence\|legend=1\| 53, 4190, 4243, 4296 }}

	Badness: 0.173433		[[Badness]] (Smith): 0.173433

	[[Category:53edo]]		[[Category:53edo]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

FloraC: Move submajor here. -mercator (addressed in mercator family)

2025-04-16T15:26:58Z

Move submajor here. -mercator (addressed in mercator family)

@@ Line 130: / Line 130: @@
 | [[Ditonic]] || 13/2 = 6.5 || 13/11 = 1.{{overline|18}}
 |}
 == Counterschismic ==
@@ Line 164: / Line 149: @@
 Badness: 0.09123
 == Countritonic ==