764edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
m Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave" |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 8: | Line 8: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|764|columns= | {{Harmonics in equal|764|columns=11}} | ||
{{Harmonics in equal|764|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 764edo (continued)}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 764 factors into {{ | Since 764 factors into primes as {{nowrap| 2<sup>2</sup> × 191 }}, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s ([[16808edo|22\16808]]). | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 19: | Line 20: | ||
! 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 27: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 1211 -764 }} | ||
| {{ | | {{Mapping| 764 1211 }} | ||
| −0.0439 | | −0.0439 | ||
| 0.0439 | | 0.0439 | ||
| Line 33: | Line 34: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 38 -2 -15 }}, {{monzo| 25 -48 22 }} | ||
| {{ | | {{Mapping| 764 1211 1774 }} | ||
| −0.0399 | | −0.0399 | ||
| 0.0363 | | 0.0363 | ||
| Line 41: | Line 42: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 52734375/52706752, {{monzo| 31 -6 -2 -6 }} | | 4375/4374, 52734375/52706752, {{monzo| 31 -6 -2 -6 }} | ||
| {{ | | {{Mapping| 764 1211 1774 2145 }} | ||
| −0.0552 | | −0.0552 | ||
| 0.0412 | | 0.0412 | ||
| Line 48: | Line 49: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 4375/4374, 131072/130977, 35156250/35153041 | | 3025/3024, 4375/4374, 131072/130977, 35156250/35153041 | ||
| {{ | | {{Mapping| 764 1211 1774 2145 2643 }} | ||
| −0.0436 | | −0.0436 | ||
| 0.0435 | | 0.0435 | ||
| Line 55: | Line 56: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 10549994/10546875 | | 1716/1715, 2080/2079, 3025/3024, 4096/4095, 10549994/10546875 | ||
| {{ | | {{Mapping| 764 1211 1774 2145 2643 2827 }} | ||
| −0.0267 | | −0.0267 | ||
| 0.0548 | | 0.0548 | ||
| Line 62: | Line 63: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 1716/1715, 2080/2079, 2431/2430, 2500/2499, 4096/4095, 4914/4913 | | 1716/1715, 2080/2079, 2431/2430, 2500/2499, 4096/4095, 4914/4913 | ||
| {{ | | {{Mapping| 764 1211 1774 2145 2643 2827 3123 }} | ||
| −0.0327 | | −0.0327 | ||
| 0.0528 | | 0.0528 | ||
| Line 69: | Line 70: | ||
| 2.3.5.7.11.13.17.23 | | 2.3.5.7.11.13.17.23 | ||
| 1716/1715, 2080/2079, 2024/2023, 2431/2430, 2500/2499, 3520/3519, 4096/4095 | | 1716/1715, 2080/2079, 2024/2023, 2431/2430, 2500/2499, 3520/3519, 4096/4095 | ||
| {{ | | {{Mapping| 764 1211 1774 2145 2643 2827 3123 3456 }} | ||
| −0.0286 | | −0.0286 | ||
| 0.0506 | | 0.0506 | ||
| Line 81: | Line 82: | ||
|+ 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 97: | Line 98: | ||
| 435.08 | | 435.08 | ||
| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor (temperament)|Supermajor]] | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 106: | Line 107: | ||
|- | |- | ||
| 2 | | 2 | ||
| 277\764<br | | 277\764<br>(105\764) | ||
| 435.08<br | | 435.08<br>(164.92) | ||
| 9/7<br | | 9/7<br>(11/10) | ||
| [[Semisupermajor]] | | [[Semisupermajor]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct | ||
[[Category:Abigail]] | [[Category:Abigail]] | ||