445edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|445}} == Theory == 445et is consistent to the 7-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 48828125/48771072, 95703..." |
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== Theory == | == Theory == | ||
445edo is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-141 89}} | | {{monzo| -141 89 }} | ||
|{{mapping|445 705}} | | {{mapping| 445 705 }} | ||
| 0.2623 | | 0.2623 | ||
| 0.2623 | | 0.2623 | ||
| 9.73 | | 9.73 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-28 25 -5}}, {{monzo|-29 -11 20}} | | {{monzo| -28 25 -5 }}, {{monzo| -29 -11 20 }} | ||
|{{mapping|445 705 1033}} | | {{mapping| 445 705 1033 }} | ||
| 0.2748 | | 0.2748 | ||
| 0.2149 | | 0.2149 | ||
| 7.97 | | 7.97 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, | | 2401/2400, 7381125/7340032, 43046721/42875000 | ||
|{{mapping|445 705 1033 1249}} | | {{mapping| 445 705 1033 1249 }} | ||
| 0.2716 | | 0.2716 | ||
| 0.1862 | | 0.1862 | ||
| 6.90 | | 6.90 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|3025/3024 | | 2401/2400, 3025/3024, 8019/8000, 234375/234256 | ||
|{{mapping|445 705 1033 1249 1539}} | | {{mapping| 445 705 1033 1249 1539 }} | ||
| 0.2870 | | 0.2870 | ||
| 0.1694 | | 0.1694 | ||
| Line 60: | Line 60: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|13\445 | | 13\445 | ||
|35.06 | | 35.06 | ||
|1990656/1953125 | | 1990656/1953125 | ||
|[[Gammic]] | | [[Gammic]] (5-limit) | ||
|- | |- | ||
|1 | | 1 | ||
|42\445 | | 42\445 | ||
|113.26 | | 113.26 | ||
|16/15 | | 16/15 | ||
|[[Misneb]] | | [[Misneb]] | ||
|- | |- | ||
|1 | | 1 | ||
|216\445 | | 216\445 | ||
|582.47 | | 582.47 | ||
|7/5 | | 7/5 | ||
|[[Neptune]] | | [[Neptune]] (7-limit) | ||
|- | |- | ||
|5 | | 5 | ||
|185\445<br>(7\445) | | 185\445<br>(7\445) | ||
|498.88<br>(18.88) | | 498.88<br>(18.88) | ||
|4/3<br>(81/80) | | 4/3<br>(81/80) | ||
|[[Pental]] | | [[Pental]] (5-limit) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||