369edo: 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" |
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=== Divisors === | === Divisors === | ||
Since 369 factors into {{ | Since 369 factors into primes as {{nowrap| 3<sup>2</sup> × 41 }}, 369edo has subset edos {{EDOs| 3, 9, 41, and 123 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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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 | ||
|- | |- | ||
| Line 26: | Line 26: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 32 -7 -9 }}, {{monzo| 1 -27 18 }} | ||
| {{ | | {{Mapping| 369 585 857 }} | ||
| −0.1991 | | −0.1991 | ||
| 0.1409 | | 0.1409 | ||
| Line 34: | Line 34: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 4375/4374, {{monzo| 32 -7 -9 }} | | 2401/2400, 4375/4374, {{monzo| 32 -7 -9 }} | ||
| {{ | | {{Mapping| 369 585 857 1036 }} | ||
| −0.1743 | | −0.1743 | ||
| 0.1294 | | 0.1294 | ||
| Line 41: | Line 41: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 4000/3993, 4375/4374, 5632/5625 | | 2401/2400, 4000/3993, 4375/4374, 5632/5625 | ||
| {{ | | {{Mapping| 369 585 857 1036 1277 }} | ||
| −0.2277 | | −0.2277 | ||
| 0.1576 | | 0.1576 | ||
| Line 48: | Line 48: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 1575/1573, 2080/2079, 2200/2197, 2401/2400, 3584/3575 | | 1575/1573, 2080/2079, 2200/2197, 2401/2400, 3584/3575 | ||
| {{ | | {{Mapping| 369 585 857 1036 1277 1366 }} (369f) | ||
| −0.2685 | | −0.2685 | ||
| 0.1703 | | 0.1703 | ||
| Line 58: | Line 58: | ||
|+ 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 | ||
|- | |- | ||
| Line 83: | Line 83: | ||
|- | |- | ||
| 9 | | 9 | ||
| 77\369<br | | 77\369<br>(5\369) | ||
| 250.41<br | | 250.41<br>(16.26) | ||
| 140/121<br | | 140/121<br>(100/99) | ||
| [[ | | [[Ennealimmapine]] | ||
|- | |- | ||
| 9 | | 9 | ||
| 97\369<br | | 97\369<br>(15\369) | ||
| 315.45<br | | 315.45<br>(48.78) | ||
| 6/5<br | | 6/5<br>(36/35) | ||
| [[Ennealimmal]] | | [[Ennealimmal]] / enneabiotic | ||
|- | |- | ||
| 9 | | 9 | ||
| 68\369<br | | 68\369<br>(14\369) | ||
| 221.14<br | | 221.14<br>(45.53) | ||
| 25/22<br | | 25/22<br>(77/75) | ||
| [[Quadraennealimmal]] | | [[Quadraennealimmal]] | ||
|- | |- | ||
| 41 | | 41 | ||
| 55\369<br | | 55\369<br>(1\369) | ||
| 178.86<br | | 178.86<br>(3.25) | ||
| 567/512<br | | 567/512<br>(352/351) | ||
| [[Hemicountercomp]] | | [[Hemicountercomp]] | ||
|} | |} | ||
<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 | ||
[[Category:Semiporwellismic]] | [[Category:Semiporwellismic]] | ||