1637edo: Difference between revisions
m →Theory: nullity-1 temps are best given by commas |
m +comma |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1637edo is [[consistent]] to the [[7-odd-limit]], but the error of its [[harmonic]] [[3/1|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. In the 2.5.11.17.23.43 subgroup it tempers out [[10880/10879]]. | 1637edo is [[consistent]] to the [[7-odd-limit]], but the error of its [[harmonic]] [[3/1|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. In the 2.5.11.17.23.43 subgroup it tempers out [[4301/4300]] and [[10880/10879]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 13: | Line 13: | ||
== 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" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.9 | | 2.9 | ||
| Line 39: | Line 40: | ||
| {{monzo|-7 -2 13 -6}}, {{monzo|-24 12 0 -5}}, {{monzo|22 5 -3 -11}} | | {{monzo|-7 -2 13 -6}}, {{monzo|-24 12 0 -5}}, {{monzo|22 5 -3 -11}} | ||
| {{mapping|1637 5189 3801 4596}} | | {{mapping|1637 5189 3801 4596}} | ||
| | | −0.0141 | ||
| 0.0488 | | 0.0488 | ||
| 6.66 | | 6.66 | ||
| Line 46: | Line 47: | ||
| 2359296/2358125, 820125/819896, 50014503/50000000, 275653125/275365888 | | 2359296/2358125, 820125/819896, 50014503/50000000, 275653125/275365888 | ||
| {{mapping|1637 5189 3801 4596 5663}} | | {{mapping|1637 5189 3801 4596 5663}} | ||
| | | −0.0075 | ||
| 0.0456 | | 0.0456 | ||
| 6.22 | | 6.22 | ||
| Line 53: | Line 54: | ||
| 4096/4095, 67392/67375, 3720087/3718000, 225000/224939, 6125625/6117748 | | 4096/4095, 67392/67375, 3720087/3718000, 225000/224939, 6125625/6117748 | ||
| {{mapping|1637 5189 3801 4596 5663 6058}} | | {{mapping|1637 5189 3801 4596 5663 6058}} | ||
| | | −0.0188 | ||
| 0.0487 | | 0.0487 | ||
| 6.64 | | 6.64 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "Kasivo" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/6QCT4t1o2dd1CMDgdmlSAv Spotify] | [https://francium223.bandcamp.com/track/kasivo Bandcamp] | [https://www.youtube.com/watch?v=X-OVkgCF8IY YouTube] – in Kaguyic, 1637edo tuning | |||