Quasisuper: Difference between revisions
+ link to technical data |
I'm just copypasting ultrapyth for the opening |
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| Odd limit 2 = (11-limit) 15 | Mistuning 2 = 14.9 | Complexity 2 = 17 | | Odd limit 2 = (11-limit) 15 | Mistuning 2 = 14.9 | Complexity 2 = 17 | ||
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'''Quasisuper''' is an alternative extension of [[ | '''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval|prime]] [[5/1|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]]. | |||
For technical data see [[Archytas clan #Quasisuper]]. | |||
== Interval chain == | == Interval chain == | ||
In the following table, odd harmonics and subharmonics | In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''. | ||
{| class="wikitable | {| class="wikitable center-1 right-2" | ||
! # | |||
! | |||
! Cents* | ! Cents* | ||
! | ! Approximate ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 50: | Line 50: | ||
| 5 | | 5 | ||
| 1141.6 | | 1141.6 | ||
| 27/14 | | 21/11, 27/14 | ||
|- | |- | ||
| 6 | | 6 | ||
| Line 58: | Line 58: | ||
| 7 | | 7 | ||
| 158.2 | | 158.2 | ||
| 12/11 | | 11/10, 12/11 | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 78: | Line 78: | ||
| 12 | | 12 | ||
| 99.8 | | 99.8 | ||
| | | 16/15 | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 103: | Line 103: | ||
== Tunings == | == Tunings == | ||
{{ | {{Todo|inline=1|complete section}} | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Archytas clan]] | [[Category:Archytas clan]] | ||
[[Category:Nuwell temperaments]] | [[Category:Nuwell temperaments]] | ||
Revision as of 11:38, 31 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 the archy chain of fifths to superpyth. Like superpyth, it is a temperament generated by a perfect fifth, where stacking two of them reaches the interval of 8/7~9/8, tempering out 64/63. The difference is that 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.
For technical data see Archytas clan #Quasisuper.
Interval chain
In the following table, odd harmonics and subharmonics 1–11 are in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 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 | 21/11, 27/14 |
| 6 | 649.9 | 16/11, 22/15 |
| 7 | 158.2 | 11/10, 12/11 |
| 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 |