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Rastmic clan: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''rastmic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[rastma]], {{nowrap|243/242 {{=}} {{monzo| -1 5 0 0 -2 }}}}.
The '''rastmic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[rastma]], 243/242 ({{monzo| -1 5 0 0 -2 }}).


== Neutral ==
== Neutral ==
Neutral is the 2.3.11-[[subgroup]] temperament with a [[generator]] of a neutral third which can be taken to represent {{nowrap|[[11/9]] [[~]] [[27/22]]}}, two of which make up a perfect fifth of [[3/2]]. It can be thought of as the 2.3.11 version of either [[mohajira]] or [[neutrominant]], as well as [[suhajira]] and [[archytas clan #Ringo|ringo]]. Among other things, it is the temperament optimizing the [[neutral tetrad]].
Neutral is the 2.3.11-[[subgroup]] temperament with a [[generator]] of a neutral third which can be taken to represent [[11/9]][[~]][[27/22]], two of which make up a perfect fifth of [[3/2]]. It can be thought of as the 2.3.11 version of either [[mohajira]] or [[neutrominant]], as well as [[suhajira]] and [[ringo]]. Among other things, it is the temperament optimizing the [[neutral tetrad]].


[[Subgroup]]: 2.3.11
[[Subgroup]]: 2.3.11
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{{Mapping|legend=2| 1 1 2 | 0 2 5 }}
{{Mapping|legend=2| 1 1 2 | 0 2 5 }}
: mapping generators: ~2, ~11/9


{{Mapping|legend=3| 1 1 0 0 2 | 0 2 0 0 5 }}
{{Mapping|legend=3| 1 1 0 0 2 | 0 2 0 0 5 }}


: [[gencom]]: [2 11/9; 243/242]
: mapping generators: ~2, ~11/9


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~11/9 = 350.572
* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.572{{c}}
* [[POTE]]: ~2 = 1\1, ~11/9 = 350.525
* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.525{{c}}


{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 }}
{{Optimal ET sequence|legend=1| 7, 17, 24, 65, 89, 202, 291, 380 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents
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{{Mapping|legend=3| 1 1 0 0 2 4 | 0 2 0 0 5 -1 }}
{{Mapping|legend=3| 1 1 0 0 2 4 | 0 2 0 0 5 -1 }}
: gencom: [2 11/9; 144/143 243/242]


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: 2 = 1\1, ~11/9 = 350.746
* [[CTE]]: 2 = 1200.000{{c}}, ~11/9 = 350.746{{c}}
* [[CWE]]: 2 = 1\1, ~11/9 = 351.270
* [[CWE]]: 2 = 1200.000{{c}}, ~11/9 = 351.270{{c}}
* [[POTE]]: 2 = 1\1, ~11/9 = 351.488
* [[POTE]]: 2 = 1200.000{{c}}, ~11/9 = 351.488{{c}}


{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 58, 99ef, 239eefff, 338eeeffff }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 58, 99ef, 239eefff, 338eeeffff }}
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{{Mapping|legend=2| 1 1 4 2 | 0 2 -4 5 }}
{{Mapping|legend=2| 1 1 4 2 | 0 2 -4 5 }}
: sval mapping generators: ~2, ~11/9


{{Mapping|legend=3| 1 1 0 4 2 | 0 2 0 -4 5 }}
{{Mapping|legend=3| 1 1 0 4 2 | 0 2 0 -4 5 }}
: [[gencom]]: [2 11/9; 64/63 243/242]


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~11/9 = 353.139
* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 353.139{{c}}
* [[POTE]]: ~2 = 1\1, ~11/9 = 353.958
* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 353.958{{c}}


{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de }}
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Comma list: 64/63, 78/77, 144/143
Comma list: 64/63, 78/77, 144/143


Sval mapping: {{mapping| 1 1 4 2 4 | 0 2 -4 5 -1 }}
Subgroup-val mapping: {{mapping| 1 1 4 2 4 | 0 2 -4 5 -1 }}


Gencom mapping: {{mapping| 1 1 0 4 2 4 | 0 2 0 -4 5 -1 }}
Gencom mapping: {{mapping| 1 1 0 4 2 4 | 0 2 0 -4 5 -1 }}
: gencom: [2 11/9; 64/63 78/77 144/143]


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 353.219
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 353.219{{c}}
* POTE: ~2 = 1\1, ~11/9 = 353.775
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 353.775{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7, 10, 17, 44e, 61de }}
{{Optimal ET sequence|legend=0| 7, 10, 17, 44e, 61de }}


Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
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{{Mapping|legend=2| 1 1 0 2 | 0 2 8 5 }}
{{Mapping|legend=2| 1 1 0 2 | 0 2 8 5 }}
: sval mapping generators: ~2, ~11/9


{{Mapping|legend=3| 1 1 0 0 2 | 0 2 8 0 5 }}
{{Mapping|legend=3| 1 1 0 0 2 | 0 2 8 0 5 }}
: [[gencom]]: [2 11/9; 81/80 121/120]


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~11/9 = 348.8296
* [[CTE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.8296{{c}}
* [[POTE]]: ~2 = 1\1, ~11/9 = 348.0938
* [[POTE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.0938{{c}}


{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}
{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}
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Comma list: 66/65, 81/80, 121/120
Comma list: 66/65, 81/80, 121/120


Sval mapping: {{mapping| 1 1 0 2 4| 0 2 8 5 -1 }}
Subgroup-val mapping: {{mapping| 1 1 0 2 4| 0 2 8 5 -1 }}
 
: sval mapping generators: ~2, ~11/9


Gencom mapping: {{mapping| 1 1 0 0 2 4 | 0 2 8 0 5 -1 }}
Gencom mapping: {{mapping| 1 1 0 0 2 4 | 0 2 8 0 5 -1 }}
: gencom: [2 11/9; 66/65 81/80 121/120]


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 348.8794
* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.8794{{c}}
* POTE: ~2 = 1\1, ~11/9 = 348.9155
* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.9155{{c}}


{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 55 }}
{{Optimal ET sequence|legend=0| 7, 17c, 24, 31, 55 }}


Scales: [[mohaha7]], [[mohaha10]]
Scales: [[mohaha7]], [[mohaha10]]
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 348.5324
* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5324{{c}}
* POTE: ~2 = 1\1, ~11/9 = 348.182
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.182{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
{{Optimal ET sequence|legend=0| 7d, 24d, 31, 100de, 131bdee, 162bdee }}


Badness: 0.025516
Badness: 0.025516
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 348.5444
* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5444{{c}}
* POTE: ~2 = 1\1, ~11/9 = 348.490
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.490{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7d, 24d, 31 }}
{{Optimal ET sequence|legend=0| 7d, 24d, 31 }}


Badness: 0.028071
Badness: 0.028071
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 346.905
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 346.905{{c}}
* POTE: ~2 = 1\1, ~11/9 = 346.922
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 346.922{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7, 31dd, 38d, 45e, 83bcddee }}
{{Optimal ET sequence|legend=0| 7, 31dd, 38d, 45e, 83bcddee }}


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 346.754
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 346.754{{c}}
* POTE: ~2 = 1\1, ~11/9 = 346.910
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 346.910{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
{{Optimal ET sequence|legend=0| 7, 31ddf, 38df, 45ef, 83bcddeeff }}


Badness: 0.034316
Badness: 0.034316
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 349.865
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 349.865{{c}}
* POTE: ~2 = 1\1, ~11/9 = 350.934
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.934{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7, 17c, 24d, 41cd }}
{{Optimal ET sequence|legend=0| 7, 17c, 24d, 41cd }}


Badness: 0.040240
Badness: 0.040240
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/9 = 349.904
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 349.904{{c}}
* POTE: ~2 = 1\1, ~11/9 = 350.816
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.816{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7, 17c, 24d, 41cd }}
{{Optimal ET sequence|legend=0| 7, 17c, 24d, 41cd }}


Badness: 0.027214
Badness: 0.027214


== Semisema ==
== Semisema ==
In addition to dividing the perfect fifth into two equal parts of {{nowrap|11/9 ~ 27/22}}, semisema, being an extension of [[semaphore]], also divides the perfect fourth into two equal parts of {{nowrap|7/6 ~ 8/7}}.
In addition to dividing the perfect fifth into two equal parts of 11/9~27/22, semisema, being an extension of [[semaphore]], also divides the perfect fourth into two equal parts of {{nowrap|7/6 ~ 8/7}}.


Subgroup: 2.3.7.11
Subgroup: 2.3.7.11
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Comma list: 49/48, 243/242
Comma list: 49/48, 243/242


{{Mapping|2 2 5 4|0 2 1 5|legend=2}}
{{Mapping|legend=2| 2 2 5 4 | 0 2 1 5 }}
 
: sval mapping generators: ~77/54, ~11/9


{{Mapping|2 2 0 5 4|0 2 0 1 5|legend=3}}
{{Mapping|legend=3| 2 2 0 5 4 | 0 2 0 1 5 }}


: [[gencom]]: [77/54 11/9; 49/48 243/242]
: mapping generators: ~77/54, ~11/9


Optimal tunings:
Optimal tunings:
* CTE: ~77/54 = 1\2, ~11/9 = 351.181
* CTE: ~77/54 = 600.000{{c}}, ~11/9 = 351.181{{c}}
* POTE: ~77/54 = 1\2, ~11/9 = 348.728
* POTE: ~77/54 = 600.000{{c}}, ~11/9 = 348.728{{c}}


Optimal ET Sequence: {{Optimal ET sequence|10, 14, 24, 62dd}}
{{Optimal ET sequence|legend=0| 10, 14, 24, 62dd }}


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Rastmic_clan"