547edo: 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" |
|||
| (10 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 6: | Line 6: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|547}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
547edo is the 101st [[prime edo]]. 1641edo, which divides edostep in 3, corrects the mapping for the 11-limit. | 547edo is the 101st [[prime edo]]. [[1641edo]], which divides edostep in 3, corrects the mapping for the 11-limit. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.3 | ! rowspan="2" | [[Subgroup]] | ||
|{{ | ! rowspan="2" | [[Comma list]] | ||
|{{ | ! rowspan="2" | [[Mapping]] | ||
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{Monzo| 867 -547 }} | |||
| {{Mapping| 547 867 }} | |||
| −0.0177 | |||
| 0.0177 | | 0.0177 | ||
| 0.81 | | 0.81 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{ | | {{Monzo| 39 -29 3 }}, {{monzo| -29 -11 20 }} | ||
|{{ | | {{Mapping| 547 867 1270 }} | ||
| +0.0180 | | +0.0180 | ||
| 0.0525 | | 0.0525 | ||
| 2.39 | | 2.39 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 4096000/4084101, 23066015625/23018340352 | | 4375/4374, 4096000/4084101, 23066015625/23018340352 | ||
|{{ | | {{Mapping| 547 867 1270 1536 }} | ||
| | | −0.0601 | ||
| 0.1428 | | 0.1428 | ||
| 6.51 | | 6.51 | ||
| Line 45: | Line 47: | ||
=== 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 | ||
|- | |- | ||
|1 | | 1 | ||
|16\547 | | 16\547 | ||
|35.10 | | 35.10 | ||
|1990656/1953125 | | 1990656/1953125 | ||
|[[Gammic]] | | [[Gammic]] | ||
|- | |- | ||
|1 | | 1 | ||
|51\547 | | 51\547 | ||
|111.88 | | 111.88 | ||
|16/15 | | 16/15 | ||
|[[Vavoom]] | | [[Vavoom]] | ||
|- | |- | ||
|1 | | 1 | ||
|101\547 | | 101\547 | ||
|221.57 | | 221.57 | ||
|8388608/7381125 | | 8388608/7381125 | ||
|[[Fortune]] | | [[Fortune]] | ||
|- | |- | ||
|1 | | 1 | ||
|105\547 | | 105\547 | ||
|230.35 | | 230.35 | ||
|8/7 | | 8/7 | ||
|[[Gamera]] | | [[Gamera]] | ||
|- | |- | ||
|1 | | 1 | ||
|258\547 | | 258\547 | ||
|566.00 | | 566.00 | ||
|104/75 | | 104/75 | ||
|[[ | | [[Alphatrillium]] | ||
|} | |} | ||
<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]] | |||
* "Activate!" from ''End Of Sartorius Membranes'' (2024) − [https://open.spotify.com/track/2mVV0wyzlDuuk5KZ1YP8QW Spotify] | [https://francium223.bandcamp.com/track/activate Bandcamp] | [https://www.youtube.com/watch?v=-Oxj8OOUW48 YouTube] | |||
* "IT'S A LEG!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/0oRlaPc8uFZz1Nbgtguh8n Spotify] | [https://francium223.bandcamp.com/track/its-a-leg Bandcamp] | [https://www.youtube.com/watch?v=-aQolexQwY4 YouTube] − in Vavoom, 547edo tuning | |||
* from ''Eggs'' (2025) | |||
** "Steam Eggs with Wikipedia" – [https://open.spotify.com/track/5z903cBQkfYCGMZo2YvBP0 Spotify] | [https://francium223.bandcamp.com/track/steam-eggs-with-wikipedia Bandcamp] | [https://www.youtube.com/watch?v=APOWzIFl1Xk YouTube] | |||
** "Her Name Was Egg." – [https://open.spotify.com/track/5IOaQ1cNTUimE9gvui1qlK Spotify] | [https://francium223.bandcamp.com/track/her-name-was-egg Bandcamp] | [https://www.youtube.com/watch?v=ixFhdiEBB_w YouTube] | |||
[[Category:Listen]] | |||