Quasisuper: Difference between revisions
Re-introduce supra based on quasisupra. Also note its relation to machine |
expand MOS scales |
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| Line 8: | Line 8: | ||
| Generator tuning = 708.3 | | Generator tuning = 708.3 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]] | | MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]] | ||
| Pergen = (P8, P5) | | Pergen = (P8, P5) | ||
| Color name = Sasaguti | | Color name = Sasaguti | ||
| Odd limit 1 = 9 | Mistuning 1 = 13.7 | Complexity 1 = 17 | | Odd limit 1 = 9 | Mistuning 1 = 13.7 | Complexity 1 = 17 | ||
| Odd limit 2 = | | Odd limit 2 = 11-limit 15 | Mistuning 2 = 14.9 | Complexity 2 = 17 | ||
}} | }} | ||
'''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. | '''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. | ||