Quasisuper: Difference between revisions
m Recategorize |
start article Tag: Removed redirect |
||
| Line 1: | Line 1: | ||
{{Infobox Regtemp | |||
| Title = Quasisuper; quasisupra | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11 | |||
| Comma basis = [[64/63]], [[2430/2401]] (7-limit);<br>[[64/63]], [[99/98]], [[121/120]] (11-limit) | |||
| Edo join 1 = 17c | Edo join 2 = 22 | |||
| Mapping = 1; 1 -13 -2 -6 | |||
| Generator = 3/2 | |||
| Generator tuning = 708.3 | |||
| Optimization method = CWE | |||
| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]] | |||
| Pergen = (P8, P5) | |||
| Color name = Sasaguti | |||
| Odd limit 1 = 9 | Mistuning 1 = 13.7 | Complexity 1 = 17 | |||
| Odd limit 2 = (11-limit) 15 | Mistuning 2 = | Complexity 2 = 17 | |||
}} | |||
'''Quasisuper''' is an alternative extension of [[2.3.7 subgroup|2.3.7]] [[archy]] to prime [[5/1|5]]. This extension maps prime 5 to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo|17c-edo]] to [[22edo|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth. The best extension to the [[11-limit]], '''quasisupra''', uses the [[supra]] mapping of prime [[11/1|11]] to -6 generators, as a diminished fifth (C–G♭). This tempers out [[99/98]] as in supra, as well as [[121/120]] and [[540/539]]. | |||
{{Clear}} | |||
== Interval chain == | |||
In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''. | |||
{| class="wikitable" | |||
|+ style="font-size: 105%" | Intervals of quasisupra (11-limit) | |||
! Generators | |||
! Cents* | |||
! Intervals | |||
|- | |||
| 0 | |||
| 0.0 | |||
| '''1/1''' | |||
|- | |||
| 1 | |||
| 708.3 | |||
| '''3/2''' | |||
|- | |||
| 2 | |||
| 216.6 | |||
| '''8/7''', '''9/8''' | |||
|- | |||
| 3 | |||
| 925.0 | |||
| 12/7 | |||
|- | |||
| 4 | |||
| 433.3 | |||
| 9/7, 14/11 | |||
|- | |||
| 5 | |||
| 1141.6 | |||
| 27/14, 21/11 | |||
|- | |||
| 6 | |||
| 649.9 | |||
| '''16/11''', 22/15 | |||
|- | |||
| 7 | |||
| 158.2 | |||
| 12/11, 11/10 | |||
|- | |||
| 8 | |||
| 866.6 | |||
| 18/11 | |||
|- | |||
| 9 | |||
| 374.9 | |||
| 27/22, 56/45 | |||
|- | |||
| 10 | |||
| 1083.2 | |||
| 28/15 | |||
|- | |||
| 11 | |||
| 591.5 | |||
| 7/5 | |||
|- | |||
| 12 | |||
| 99.8 | |||
| '''16/15''' | |||
|- | |||
| 13 | |||
| 808.2 | |||
| '''8/5''' | |||
|- | |||
| 14 | |||
| 316.5 | |||
| 6/5 | |||
|- | |||
| 15 | |||
| 1024.8 | |||
| 9/5 | |||
|- | |||
| 16 | |||
| 533.1 | |||
| 27/20 | |||
|- | |||
| 17 | |||
| 41.4 | |||
| 81/80, 56/55 | |||
|} | |||
<nowiki/>* in 11-limit [[CWE]] tuning, octave reduced | |||
== Tunings == | |||
{{todo|complete section|inline=1}} | |||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Archytas clan]] | [[Category:Archytas clan]] | ||
[[Category:Nuwell temperaments]] | [[Category:Nuwell temperaments]] | ||