No-sevens subgroup temperaments: Difference between revisions
→2.3.5.13 temperaments: +2.3.5.13.19-subgroup vulture |
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{{Technical data page}} | |||
This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 7. Many of these have been removed from this page and placed on their appropriate family pages in an effort to include extensions other than incremental-prime-limit; sections for them remain on this page due to extensive linkage. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 7. Many of these have been removed from this page and placed on their appropriate family pages in an effort to include extensions other than incremental-prime-limit; sections for them remain on this page due to extensive linkage. | ||
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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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{{Optimal ET sequence|legend=0| 53, 164, 217, 270 }} | {{Optimal ET sequence|legend=0| 53, 164, 217, 270 }} | ||
Badness ( | Badness (Sintel): 0.190 | ||
== 2.3.5.17 temperaments == | == 2.3.5.17 temperaments == | ||
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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]] | ||