No-sevens subgroup temperaments: Difference between revisions
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[[Tp tuning #T2 tuning|RMS error]]: 0.2830 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2830 cents | ||
=== Superpine === | |||
{{see also|Meantone family #Superpine}} | |||
{{see also|Meantone family #Trimean}} | |||
Subgroup: 2.3.5.11 | |||
Comma list: 81/80, 1350/1331 | |||
Mapping: {{mapping| 1 2 4 5 | 0 -3 -12 -11 }} | |||
Optimal tunings: | |||
* CTE: ~2 = 1200.000, ~11/10 = 167.712 | |||
* 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: {{mapping| 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 }} | |||
=== Dicot === | === Dicot === | ||
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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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=== Tricot === | === Tricot === | ||
{{Main|Tricot family #2.3.5.13 subgroup }} | {{Main| Tricot family #2.3.5.13 subgroup }} | ||
=== Taylor === | === Taylor === | ||
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{{Optimal ET sequence|legend=1| 53, 164, 217, 270 }} | {{Optimal ET sequence|legend=1| 53, 164, 217, 270 }} | ||
[[Badness]] ( | [[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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=== Stützel === | === Stützel === | ||
{{Main| Meantone family #Stützel (2.3.5.19) }} | {{Main| Meantone family #Stützel (2.3.5.19) }} | ||
== Higher-limit subgroup temperaments == | |||
=== Reversed marvel === | |||
As the [[Marvel|marvel temperament]] is based on the marvel comma, [[225/224]], identifying the [[7/4|harmonic seventh (7/4)]] as a stack of two [[15/8|classical major sevenths (15/8)]] [[Octave reduction|octave-reduced]] and tempering 3rd and 5th harmonics slightly flat, tempering [[226/225]] instead results in sharper 3rd and 5th harmonics, and a stack of two classical major sevenths equivalent to the 113th harmonic instead of the 7th, so it might as well be called reversed marvel. | |||
Subgroup: 2.3.5.113 | |||
[[Comma list]]: 226/225 | |||
{{Mapping|legend=2|1 0 0 -1|0 1 0 2|0 0 1 2}} | |||
: Sval mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]]s: | |||
* CTE: ~3/2 = 702.449, ~5/4 = 387.373 | |||
* CWE: ~3/2 = 702.522, ~5/4 = 387.479 | |||
{{Optimal ET sequence|legend=1| 12, 22, 31, 34, 46, 53 }} | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Subgroup temperaments]] | [[Category:Subgroup temperaments]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||