677edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep. | While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep. | ||
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== 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]] | ||
|{{monzo|-1073 677}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|677 1073}} | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo|-1073 677}} | |||
| {{mapping|677 1073}} | |||
| +0.0110 | | +0.0110 | ||
| 0.0110 | | 0.0110 | ||
| 0.62 | | 0.62 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|38 -2 -15}}, {{monzo|-31 43 -16}} | | {{monzo|38 -2 -15}}, {{monzo|-31 43 -16}} | ||
|{{mapping|677 1073 1572}} | | {{mapping|677 1073 1572}} | ||
| | | −0.0066 | ||
| 0.0264 | | 0.0264 | ||
| 1.49 | | 1.49 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|703125/702464, 589824/588245, 14348907/14336000 | | 703125/702464, 589824/588245, 14348907/14336000 | ||
|{{mapping|677 1073 1572 1901}} | | {{mapping|677 1073 1572 1901}} | ||
| | | −0.0714 | ||
| 0.1145 | | 0.1145 | ||
| 6.46 | | 6.46 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|3025/3024, 24057/24010, 131072/130977, 759375/758912 | | 3025/3024, 24057/24010, 131072/130977, 759375/758912 | ||
|{{mapping|677 1073 1572 1901 2342}} | | {{mapping|677 1073 1572 1901 2342}} | ||
| | | −0.0535 | ||
| 0.1084 | | 0.1084 | ||
| 6.12 | | 6.12 | ||
| Line 61: | Line 63: | ||
=== 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 | |- | ||
! Generator | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br> | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|109\677 | | 109\677 | ||
|193.21 | | 193.21 | ||
|262144/234375 | | 262144/234375 | ||
|[[Luna]] | | [[Luna]] | ||
|- | |- | ||
|1 | | 1 | ||
|125\677 | | 125\677 | ||
|221.57 | | 221.57 | ||
|8388608/7381125 | | 8388608/7381125 | ||
|[[Fortune]] | | [[Fortune]] | ||
|- | |- | ||
|1 | | 1 | ||
|281\677 | | 281\677 | ||
|498.08 | | 498.08 | ||
|4/3 | | 4/3 | ||
|[[Counterschismic]] | | [[Counterschismic]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | |||
; [[Francium]] | |||
* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] | [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] | [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube] | |||
* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] | [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] | [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] | |||
* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] | [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] | [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube] | |||
* "Eggs Of An Oven" from ''Eggs'' (2025) – [https://open.spotify.com/track/0pe7FES4PhYa58UBaQScAS Spotify] | [https://francium223.bandcamp.com/track/eggs-of-an-oven Bandcamp] | [https://www.youtube.com/watch?v=sejOxKdHd8E YouTube] | |||