373edo: 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 == | ||
373edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 through 13 all tuned flat. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; 2401/2400 ([[breedsma]]), 65625/65536 ([[horwell comma]]), and 43046721/42875000 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the 13-limit, enabling [[squbemic chords]] and [[sinbadmic chords]]. It also [[support]]s the [[ | 373edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 through 13 all tuned flat. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the [[5-limit]]; 2401/2400 ([[breedsma]]), 65625/65536 ([[horwell comma]]), and 43046721/42875000 in the [[7-limit]]; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the [[11-limit]]; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the [[13-limit]], enabling [[squbemic chords]] and [[sinbadmic chords]]. It also [[support]]s the [[hemitert]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
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|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -591 373 }} | ||
| {{ | | {{Mapping| 373 591 }} | ||
| +0.1939 | | +0.1939 | ||
| 0.1939 | | 0.1939 | ||
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|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 8 14 -13 }}, {{monzo| -51 19 9 }} | ||
| {{ | | {{Mapping| 373 591 866 }} | ||
| +0.1658 | | +0.1658 | ||
| 0.1632 | | 0.1632 | ||
| Line 42: | Line 42: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 65625/65536, 43046721/42875000 | | 2401/2400, 65625/65536, 43046721/42875000 | ||
| {{ | | {{Mapping| 373 591 866 1047 }} | ||
| +0.1654 | | +0.1654 | ||
| 0.1413 | | 0.1413 | ||
| Line 49: | Line 49: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 8019/8000, 65625/65536 | | 2401/2400, 3025/3024, 8019/8000, 65625/65536 | ||
| {{ | | {{Mapping| 373 591 866 1047 1290 }} | ||
| +0.2008 | | +0.2008 | ||
| 0.1449 | | 0.1449 | ||
| Line 56: | Line 56: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 | | 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 | ||
| {{ | | {{Mapping| 373 591 866 1047 1290 1380 }} | ||
| +0.2056 | | +0.2056 | ||
| 0.1327 | | 0.1327 | ||
| Line 66: | Line 66: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| 315.28 | | 315.28 | ||
| 6/5 | | 6/5 | ||
| [[ | | [[Counterpara]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 108: | Line 108: | ||
| [[Untriton]] (5-limit) | | [[Untriton]] (5-limit) | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||