935edo: Difference between revisions
→Regular temperament properties: + table of rank-2 temps |
Note a subset edo for providing some of its primes |
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== Theory == | == Theory == | ||
935edo is a very strong [[23-limit]] system, and is [[consistent]] through to the [[27-odd-limit]]. It does reasonably well in the higher limits, though the sharply tuned [[11/1|11]] and [[23/1|23]] and the flatly tuned [[29/1|29]] and [[31/1|31]] create inconsistencies together, those being [[29/22]], [[29/23]], [[31/22]], [[31/23]] and their [[octave complement]]s; it is otherwise consistent to the [[39-odd-limit]]. It is a [[zeta peak edo]]. | 935edo is a very strong [[23-limit]] system, and is [[consistent]] through to the [[27-odd-limit]]. It does reasonably well in the higher limits, though the sharply tuned [[11/1|11]] and [[23/1|23]] and the flatly tuned [[29/1|29]] and [[31/1|31]] create inconsistencies together, those being [[29/22]], [[29/23]], [[31/22]], [[31/23]] and their [[octave complement]]s; it is otherwise consistent to the [[39-odd-limit]]. Its tuning of [[7/1|7]], [[11/1|11]], [[13/1|13]], and [[23/1|23]] comes from [[187edo]]. It is a [[zeta peak edo]]. | ||
As an equal temperament, it [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[alphatricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[117649/117612]], [[151263/151250]], [[161280/161051]] in the [[11-limit]]; [[2080/2079]], [[4096/4095]], [[4225/4224]] in the [[13-limit]]; [[2058/2057]], [[2500/2499]], [[4914/4913]] in the [[17-limit]]; [[2432/2431]], [[3136/3135]], [[3250/3249]], [[4200/4199]] in the 19-limit; and [[2025/2024]], [[2300/2299]], [[2646/2645]] among others in the 23-limit. | As an equal temperament, it [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[alphatricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} ([[astro comma]]) in the [[5-limit]]; [[4375/4374]] and 52734375/52706752 in the [[7-limit]]; [[117649/117612]], [[151263/151250]], [[161280/161051]] in the [[11-limit]]; [[2080/2079]], [[4096/4095]], [[4225/4224]] in the [[13-limit]]; [[2058/2057]], [[2500/2499]], [[4914/4913]] in the [[17-limit]]; [[2432/2431]], [[3136/3135]], [[3250/3249]], [[4200/4199]] in the [[19-limit]]; and [[2025/2024]], [[2300/2299]], [[2646/2645]] among others in the 23-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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| {{Monzo| -38 5 13 }} | | {{Monzo| -38 5 13 }} | ||
| [[Astro]] | | [[Astro]] | ||
|- | |||
| 1 | |||
| 339\935 | |||
| 435.08 | |||
| 9/7 | |||
| [[Supermajor (temperament)|Supermajor]] | |||
|- | |- | ||
| 1 | | 1 | ||
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| 104/75 | | 104/75 | ||
| [[Alphatrillium]] | | [[Alphatrillium]] | ||
|- | |- | ||
| 17 | | 17 | ||