653edo: Difference between revisions
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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== Theory == | == Theory == | ||
653edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]]. | 653edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], and the [[23-odd-limit]] if not for the [[23/13]] and its [[octave complement]] barely missing the mark. Although the [[25/1|25]] is flat enough to create more inconsistencies, the [[29/1|29]] and [[31/1|31]] blend well with the lower primes, together making it a fairly strong [[31-limit]] system. | ||
As an equal temperament, it [[tempering out|tempers out]] {{monzo| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]]; [[875/874]], [[1105/1104]] among others in the [[23-limit]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|653|columns=11}} | {{Harmonics in equal|653|columns=11}} | ||
{{Harmonics in equal|653|columns= | {{Harmonics in equal|653|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 653edo (continued)}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
653edo is the 119th [[prime edo]]. | 653edo is the 119th [[prime edo]]. As such, it does not contain any nontrivial subset edo. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 72: | Line 74: | ||
| 0.0867 | | 0.0867 | ||
| 4.72 | | 4.72 | ||
|- | |||
| 2.3.5.7.11.13.17.19.23 | |||
| 875/874, 1105/1104, 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079 | |||
| {{Mapping| 653 1035 1516 1833 2259 2416 2669 2774 2954 }} | |||
| +0.0489 | |||
| 0.0884 | |||
| 4.81 | |||
|} | |} | ||