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Schismic–countercommatic equivalence continuum: Difference between revisions

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! Monzo
! Monzo
|-
|-
| −7
| −7
| [[Merman]]
| [[Merman]]
| 1121008359375 / 1099511627776
| 1121008359375 / 1099511627776
| {{monzo| -40 15 7 }}
| {{monzo| -40 15 7 }}
|-
|-
| −6
| −6
| [[Syntonic–31 equivalence continuum|Ampersand]]
| [[Syntonic–31 equivalence continuum|Ampersand]]
| 34171875 / 33554432
| 34171875 / 33554432
| {{monzo| -25 7 6 }}
| {{monzo| -25 7 6 }}
|-
|-
| −5
| −5
| [[Magic]]
| [[Magic]]
| 3125 / 3072
| 3125 / 3072
| {{monzo| -10 -1 5 }}
| {{monzo| -10 -1 5 }}
|-
|-
| −4
| −4
| [[Tetracot]]
| [[Tetracot]]
| 20000 / 19683
| 20000 / 19683
| {{monzo| 5 -9 4 }}
| {{monzo| 5 -9 4 }}
|-
|-
| −3
| −3
| [[Rodan]]
| [[Rodan]]
| 131072000 / 129140163
| 131072000 / 129140163
| {{monzo| 20 -17 3 }}
| {{monzo| 20 -17 3 }}
|-
|-
| −2
| −2
| [[Hemififths]]
| [[Hemififths]]
| 858993459200 / 847288609443
| 858993459200 / 847288609443
| {{monzo| 35 -25 2 }}
| {{monzo| 35 -25 2 }}
|-
|-
| −1
| −1
| [[Kwai]]
| [[Kwai]]
| (32 digits)
| (32 digits)
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|-
|-
| 3
| 3
| 41 & 282
| 41 & 282
| (68 digits)
| (68 digits)
| {{monzo| 110 -65 -3 }}
| {{monzo| 110 -65 -3 }}
|-
|-
| 4
| 4
| 41 & 335
| 41 & 335
| (76 digits)
| (76 digits)
| {{monzo| 125 -73 -4 }}
| {{monzo| 125 -73 -4 }}
|-
|-
| 5
| 5
| 41 & 388
| 41 & 388
| (86 digits)
| (86 digits)
| {{monzo| 140 -81 -5 }}
| {{monzo| 140 -81 -5 }}
|-
|-
| 6
| 6
| 41 & 441
| 41 & 441
| (94 digits)
| (94 digits)
| {{monzo| 155 -89 -6 }}
| {{monzo| 155 -89 -6 }}
|-
|-
| 7
| 7
| 41 & 453
| 41 & 453
| (104 digits)
| (104 digits)
| {{monzo| 170 -97 -7 }}
| {{monzo| 170 -97 -7 }}
|-
|-
| 8
| 8
| 41 & 506
| 41 & 506
| (112 digits)
| (112 digits)
| {{monzo| 185 -105 -8 }}
| {{monzo| 185 -105 -8 }}
|-
|-
| 9
| 9
| 41 & 559
| 41 & 559
| (122 digits)
| (122 digits)
| {{monzo| 200 -113 -9 }}
| {{monzo| 200 -113 -9 }}
|-
|-
| 10
| 10
| 41 & 571
| 41 & 571
| (130 digits)
| (130 digits)
| {{monzo| 215 -121 -10 }}
| {{monzo| 215 -121 -10 }}
|-
|-
| 11
| 11
| 41 & 624
| 41 & 624
| (140 digits)
| (140 digits)
| {{monzo| -230 129 11 }}
| {{monzo| -230 129 11 }}
|-
|-
| 12
| 12
| 41 & 677
| 41 & 677
| (148 digits)
| (148 digits)
| {{monzo| -245 137 12 }}
| {{monzo| -245 137 12 }}
|-
|-
| 13
| 13
| 41 & 730
| 41 & 730
| (158 digits)
| (158 digits)
| {{monzo| -260 145 13 }}
| {{monzo| -260 145 13 }}
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Examples of temperaments with fractional values of ''n'':  
Examples of temperaments with fractional values of ''n'':  
* [[Marvel temperaments #Septimin|Septimin]] ({{nowrap|''n'' {{=}} −11/2}})
* [[Marvel temperaments #Septimin|Septimin]] ({{nowrap|''n'' {{=}} −11/2}})
* [[Shibboleth family|Shibboleth]] ({{nowrap|''n'' {{=}} −9/2}})
* [[Shibboleth family|Shibboleth]] ({{nowrap|''n'' {{=}} −9/2}})
* [[Mirkwai clan #Pluto|Pluto]] ({{nowrap|''n'' {{=}} −7/2}})
* [[Mirkwai clan #Pluto|Pluto]] ({{nowrap|''n'' {{=}} −7/2}})
* 3737 & 5585 ({{nowrap|''n'' {{=}} 31/3 {{=}} 10.{{overline|3}}}})
* 3737 & 5585 ({{nowrap|''n'' {{=}} 31/3 {{=}} 10.{{overline|3}}}})
* 1277 & 2513 ({{nowrap|''n'' {{=}} 21/2}})
* 1277 & 2513 ({{nowrap|''n'' {{=}} 21/2}})


== Rodan (5-limit) ==
== Rodan (5-limit) ==
{{See also| Gamelismic clan #Rodan }}
: ''For extensions, see [[Gamelismic clan #Rodan]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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== Hemififths (5-limit) ==
== Hemififths (5-limit) ==
{{See also| Breedsmic temperaments #Hemififths }}
: ''For extensions, see [[Breedsmic temperaments #Hemififths]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 174: Line 174:


== Kwai (5-limit) ==
== Kwai (5-limit) ==
{{See also| Mirkwai clan #Kwai }}
: ''For extensions, see [[Mirkwai clan #Kwai]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 187: Line 187:


[[Badness]]: 0.636715
[[Badness]]: 0.636715
== Countercomp ==
:''See also: [[Countercomp family]] and [[41-comma]]''
[[Subgroup]]: 2.3.5
[[Comma list]]: {{monzo| 65 -41 }}
{{Mapping|legend=1| 41 65 0 | 0 0 1 }}
[[Optimal tuning]] ([[POTE]]): ~5/4 = 386.668
{{Optimal ET sequence|legend=1| 41, 123, 164, 205, 369, 574, 779, 2132bc }}
[[Badness]]: 0.934310


== Cotoneum (5-limit) ==
== Cotoneum (5-limit) ==
{{See also| Garischismic clan #Cotoneum }}
: ''For extensions, see [[Garischismic clan #Cotoneum]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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== Newt (5-limit) ==
== Newt (5-limit) ==
{{See also| Breedsmic temperaments #Newt }}
: ''For extensions, see [[Breedsmic temperaments #Newt]].''


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