653edo: Difference between revisions
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Cleanup; linking; clarify the title row of the rank-2 temp table; -redundant categories |
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== Theory == | == Theory == | ||
653edo is | 653edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo| 39 -29 3 }} ([[tricot 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. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 24: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 1035 -653 }} | | {{monzo| 1035 -653 }} | ||
| | | {{mapping| 653 1035 }} | ||
| -0.0113 | | -0.0113 | ||
| 0.0113 | | 0.0113 | ||
| Line 31: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }} | | {{monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }} | ||
| | | {{mapping| 653 1035 1516 }} | ||
| +0.0503 | | +0.0503 | ||
| 0.0875 | | 0.0875 | ||
| Line 38: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }} | | 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }} | ||
| | | {{mapping| 653 1035 1516 1833 }} | ||
| +0.0709 | | +0.0709 | ||
| 0.0838 | | 0.0838 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617 | | 2401/2400, 3025/3024, 65625/65536, 1953125/1948617 | ||
| | | {{mapping| 653 1035 1516 1833 2259 }} | ||
| +0.0576 | | +0.0576 | ||
| 0.0795 | | 0.0795 | ||
| Line 52: | Line 52: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536 | | 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536 | ||
| | | {{mapping| 653 1035 1516 1833 2259 2416 }} | ||
| +0.0801 | | +0.0801 | ||
| 0.0882 | | 0.0882 | ||
| Line 59: | Line 59: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976 | | 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976 | ||
| | | {{mapping| 653 1035 1516 1833 2259 2416 2669 }} | ||
| +0.0759 | | +0.0759 | ||
| 0.0823 | | 0.0823 | ||
| Line 66: | Line 66: | ||
| 2.3.5.7.11.13.17.19 | | 2.3.5.7.11.13.17.19 | ||
| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400 | | 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400 | ||
| | | {{mapping| 653 1035 1516 1833 2259 2416 2669 2774 }} | ||
| +0.0608 | | +0.0608 | ||
| 0.0867 | | 0.0867 | ||
| Line 76: | Line 76: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 105: | Line 105: | ||
| [[Tricot]] | | [[Tricot]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
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