Quasisuper: Difference between revisions
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{{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]] | ||
Revision as of 10:46, 30 December 2025
Lua error in Module:Infobox_regtemp at line 138: attempt to perform arithmetic on local 'generator_size' (a nil value). Quasisuper is an alternative extension of 2.3.7 archy to prime 5. This extension maps prime 5 to -13 generators, as a double-diminished fifth (C–G𝄫). This extension works in the range 17c-edo to 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 diatonic scale, with a small step of around 60 cents 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 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.
Interval chain
In the following table, odd harmonics and subharmonics 1–15 are in bold.
| 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 |
* in 11-limit CWE tuning, octave reduced
Tunings
|
Todo: complete section |