No-sevens subgroup temperaments: Difference between revisions
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=== Superpine === | === Superpine === | ||
{{see also|Meantone family #Superpine}} | {{see also|Meantone family #Superpine}} | ||
{{see also|Meantone family #Trimean}} | |||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
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Comma list: 81/80, 1350/1331 | Comma list: 81/80, 1350/1331 | ||
{{Mapping|legend=0| 1 2 4 5 | 0 -3 -12 -11 }} | |||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/10 = 167.712 | * CTE: ~2 = 1200.000, ~11/10 = 167.712 | ||
* CWE: ~2 = 1200.000, ~11/10 = 167.882 | * CWE: ~2 = 1200.000, ~11/10 = 167.882 | ||
{{Optimal ET sequence|legend=0| 7, 29ce, 36, 43, 50 }} | |||
==== 2.3.5.11.13 ==== | |||
Subgroup: 2.3.5.11.13 | |||
Comma list: 81/80, 144/143, 975/968 | |||
{{Mapping|legend=0| 1 2 4 5 | 0 -3 -12 -11 5 }} | |||
Optimal tunings: | |||
* CTE: ~2 = 1200.000, ~11/10 = 167.729 | |||
* CWE: ~2 = 1200.000, ~11/10 = 167.846 | |||
{{Optimal ET sequence|legend=0| 7, 29ce, 36, 43, 50 }} | {{Optimal ET sequence|legend=0| 7, 29ce, 36, 43, 50 }} | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.1171 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1171 cents | ||
==== 2.3.5.13.17 | ==== 2.3.5.13.17 ==== | ||
The comma list shown here is interestingly a possible minimal [[S-expression]]-based comma list for majvam: {[[676/675|S13/S15 = S26]], [[24576/24565|S16/S17]], [[2601/2600|S51]]} (though the order of the last two commas is swapped to make the commas appear in ascending prime limit). | The comma list shown here is interestingly a possible minimal [[S-expression]]-based comma list for majvam: {[[676/675|S13/S15 = S26]], [[24576/24565|S16/S17]], [[2601/2600|S51]]} (though the order of the last two commas is swapped to make the commas appear in ascending prime limit). | ||
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[[Comma list]]: 676/675, 256000/255879 | [[Comma list]]: 676/675, 256000/255879 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -6 -7 | 0 4 21 27 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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[[Badness]] (Sintel): 0.301 | [[Badness]] (Sintel): 0.301 | ||
==== 2.3.5.13.19 | ==== 2.3.5.13.19 ==== | ||
Subgroup: 2.3.5.13.19 | Subgroup: 2.3.5.13.19 | ||
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: ''For full 17- and 19-limit extensions, see [[Schismatic family #Quintilipyth]] or [[Schismatic family #Quintaschis]].'' | : ''For full 17- and 19-limit extensions, see [[Schismatic family #Quintilipyth]] or [[Schismatic family #Quintaschis]].'' | ||
{{Main| Schismatic family #Quintilischis (2.3.5.17) }} | {{Main| Schismatic family #Quintilischis (2.3.5.17) }} | ||
=== Srutal Archagall === | |||
{{Main|Srutal archagall}} | |||
== 2.3.5.19 temperaments == | == 2.3.5.19 temperaments == | ||
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[[Comma list]]: 1035/1024, 16875/16606, 192375/188416 | [[Comma list]]: 1035/1024, 16875/16606, 192375/188416 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 11 -10 -3 -2 | 0 -13 17 10 9 }} | ||
: Sval mapping generators: ~2 = 1200.000, ~368/225 = 869.420 | : Sval mapping generators: ~2 = 1200.000, ~368/225 = 869.420 | ||
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[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Subgroup temperaments]] | [[Category:Subgroup temperaments]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||