No-sevens subgroup temperaments: Difference between revisions
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== 2.3.5.13 temperaments == | == 2.3.5.13 temperaments == | ||
=== Majvam === | === Majvam === | ||
: ''For the 5-limit version | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Majvam]].'' | ||
: ''For full 13- and 17-limit extensions, see [[Parkleiness temperaments #Majvamic]] or [[Cataharry temperaments #Majvamoid]].'' | : ''For full 13- and 17-limit extensions, see [[Parkleiness temperaments #Majvamic]] or [[Cataharry temperaments #Majvamoid]].'' | ||
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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 subgroup ==== | ||
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 }} | ||
=== Taylor === | === Taylor === | ||
{{ | {{Main| Schismatic family #Taylor (2.3.5.13) }} | ||
=== Vulture === | |||
: ''For the 5-limit restriction and full 13-limit extension, see [[Vulture family]].'' | |||
This entry is interesting because [[vulture]] and [[buzzard]] unite to the same temperament on the 2.3.5.13.19 subgroup. It results in a surprising decrease in Dirichlet badness, and up to [[octave equivalence]] finds [[13/8]] at 27 generators and [[19/16]] at 41 generators. In this temperament, the [[schisma]] is equated with [[325/324]], [[361/360]], [[513/512]], and [[625/624]]. [[270edo]] is especially ideal, whose step size being between 361/360 and 513/512, with [[217edo]] exaggerating the comma to be slightly sharp of 361/360. Smaller edos such as [[58edo|58]] (58h val), [[111edo|111]], and [[164edo|164]] are also possible. | |||
[[Subgroup]]: 2.3.5.13 | |||
[[Comma list]]: 676/675, 256000/255879 | |||
{{Mapping|legend=2| 1 0 -6 -7 | 0 4 21 27 }} | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1200.0000, ~320/243 = 475.5502 | |||
: [[error map]]: {{val| 0.000 +0.2457 +0.2401 -0.6728 }} | |||
* [[CWE]]: ~2 = 1200.0000, ~320/243 = 475.5543 | |||
: [[error map]]: {{val| 0.000 +0.2622 +0.3266 -0.5616 }} | |||
{{Optimal ET sequence|legend=1| 53, 164, 217, 270 }} | |||
[[Badness]] (Dirichlet): 0.301 | |||
==== 2.3.5.13.19 subgroup ==== | |||
Subgroup: 2.3.5.13.19 | |||
Comma list: 676/675, 1216/1215, 20007/20000 | |||
Sval mapping: {{mapping| 1 0 -6 -7 -12 | 0 4 21 27 41 }} | |||
Optimal tunings: | |||
* CTE: ~2 = 1200.0000, ~320/243 = 475.5498 | |||
* CWE: ~2 = 1200.0000, ~320/243 = 475.5533 | |||
{{Optimal ET sequence|legend=0| 53, 164, 217, 270 }} | |||
Badness (Dirichlet): 0.190 | |||
== 2.3.5.17 temperaments == | == 2.3.5.17 temperaments == | ||