1277edo: Difference between revisions
Review. The listing of temps was particularly lame. |
|||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
1277edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752 and {{monzo|51 -13 -1 -10}} in the 7-limit; | 1277edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1277edo is the 206th [[prime | 1277edo is the 206th [[prime edo]]. [[2554edo]], which divides the edostep in two, is the smallest edo [[distinctly consistent]] through the [[41-odd-limit]], and provides correction for harmonics 11 through 41. | ||
[[2554edo]], which divides the edostep in two, is the smallest | |||
== 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|2024 -1277}} | | {{monzo| 2024 -1277 }} | ||
|{{mapping|1277 2024}} | | {{mapping| 1277 2024 }} | ||
| -0.0009 | | -0.0009 | ||
| 0.0009 | | 0.0009 | ||
| 0.10 | | 0.10 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|54 -37 2}}, {{monzo|-67 -9 35}} | | {{monzo| 54 -37 2 }}, {{monzo| -67 -9 35 }} | ||
|{{mapping|1277 2024 2965}} | | {{mapping| 1277 2024 2965 }} | ||
| +0.0132 | | +0.0132 | ||
| 0.0199 | | 0.0199 | ||
| 2.12 | | 2.12 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 52734375/52706752, {{monzo|51 -13 -1 -10}} | | 4375/4374, 52734375/52706752, {{monzo| 51 -13 -1 -10 }} | ||
|{{mapping|1277 2024 2965 3585}} | | {{mapping| 1277 2024 2965 3585 }} | ||
| +0.0093 | | +0.0093 | ||
| 0.0186 | | 0.0186 | ||
| 1.98 | | 1.98 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|4375/4374, 759375/758912 | | 4375/4374, 151263/151250, 759375/758912, 2097152/2096325 | ||
|{{mapping|1277 2024 2965 3585 4418}} | | {{mapping| 1277 2024 2965 3585 4418 }} | ||
| -0.0092 | | -0.0092 | ||
| 0.0405 | | 0.0405 | ||
| Line 62: | Line 60: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|265\1277 | | 265\1277 | ||
|249.021 | | 249.021 | ||
|{{monzo|-27 11 3 1}} | | {{monzo| -27 11 3 1 }} | ||
|[[Monzismic]] | | [[Monzismic]] | ||
|- | |- | ||
|1 | | 1 | ||
|380\1277 | | 380\1277 | ||
|357.087 | | 357.087 | ||
|768/625 | | 768/625 | ||
|[[Dodifo]] | | [[Dodifo]] | ||
|- | |- | ||
|1 | | 1 | ||
|463\1277 | | 463\1277 | ||
|435.082 | | 435.082 | ||
|9/7 | | 9/7 | ||
|[[Supermajor]] | | [[Supermajor]] | ||
|} | |} | ||
<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 | ||