Kleismic: Difference between revisions
m Text replacement - "Prime-optimized" to "Norm-based" Tags: Mobile edit Mobile web edit |
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| Pergen = (P8, P12/6) | | Pergen = (P8, P12/6) | ||
| Color name = Tribiyoti | | Color name = Tribiyoti | ||
| Odd limit 1 = 5 | Mistuning 1 = 1.35 | Complexity 1 = | | Odd limit 1 = 5 | Mistuning 1 = 1.35 | Complexity 1 = 7 | ||
| Odd limit 2 = (2.3.5.13) 15 | Mistuning 2 = 2.35 | Complexity 2 = | | Odd limit 2 = (2.3.5.13) 15 | Mistuning 2 = 2.35 | Complexity 2 = 15 | ||
}} | }} | ||
'''Kleismic''', alternatively called '''hanson''' in the [[5-limit]], is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[kleismic family]], [[generator|generated]] by a [[6/5|classical minor third (6/5)]], six of which stacked are equated to the [[3/1|perfect twelfth (3/1)]], and thereby characterized by the vanishing of the [[15625/15552|kleisma]] ([[ratio]]: 15625/15552, {{monzo|legend=1| -6 -5 6 }}). | '''Kleismic''', alternatively called '''hanson''' in the [[5-limit]], is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[kleismic family]], [[generator|generated]] by a [[6/5|classical minor third (6/5)]], six of which stacked are equated to the [[3/1|perfect twelfth (3/1)]], and thereby characterized by the vanishing of the [[15625/15552|kleisma]] ([[ratio]]: 15625/15552, {{monzo|legend=1| -6 -5 6 }}). | ||
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Most of these extensions can also incorporate prime 11 (and thereby reach the full 13-limit) by tempering out [[385/384]], equating the ~6/5 generator to [[77/64]]. This works well since the optimal tunings of cata's ~6/5 are usually intermediate between [[Just_intonation|just]] 6/5 (just flat of [[19edo]]) and 77/64 (just sharp of [[15edo]]). | Most of these extensions can also incorporate prime 11 (and thereby reach the full 13-limit) by tempering out [[385/384]], equating the ~6/5 generator to [[77/64]]. This works well since the optimal tunings of cata's ~6/5 are usually intermediate between [[Just_intonation|just]] 6/5 (just flat of [[19edo]]) and 77/64 (just sharp of [[15edo]]). | ||
For technical data, see [[Kleismic family #Kleismic a.k.a. hanson]]. | For technical data, see [[Kleismic family #Kleismic a.k.a. hanson]]. | ||
== Interval chain == | == Interval chain == | ||