673edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|673}} == Theory == 673edo is consistent to the 5-odd-limit. Using the 2.3.5.17.19.41 subgroup, it tempers out 4624/46..." |
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 |
||
| (10 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
673edo is the 122nd [[prime EDO]]. [[2019edo]], which triples it, gives a good correction to the [[ | 673edo is the 122nd [[prime EDO]]. [[2019edo]], which triples it, gives a good correction to the [[7-limit]] alongside primes 13 and 23. | ||
== 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]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|1067 -673}} | | {{monzo|1067 -673}} | ||
| {{mapping|673 1067}} | | {{mapping|673 1067}} | ||
| | | −0.1801 | ||
| 0.1801 | | 0.1801 | ||
| 10.10 | | 10.10 | ||
| Line 32: | Line 33: | ||
| {{monzo|32 -7 -9}}, {{monzo|19 -53 28}} | | {{monzo|32 -7 -9}}, {{monzo|19 -53 28}} | ||
| {{mapping|673 1067 1563}} | | {{mapping|673 1067 1563}} | ||
| | | −0.2077 | ||
| 0.1521 | | 0.1521 | ||
| 8.53 | | 8.53 | ||
| Line 39: | Line 40: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 52: | Line 54: | ||
| [[Escapade]] | | [[Escapade]] | ||
|} | |} | ||
<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 == | |||
; [[Francium]] | |||
* "They Unraveled" from ''Scoop'' (2024) – [https://open.spotify.com/track/2VjnkDBShyJekqv4tv7HA8 Spotify] | [https://francium223.bandcamp.com/track/they-unraveled Bandcamp] | [https://www.youtube.com/watch?v=yQCfdPObfKI YouTube] | |||