11edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
== Theory == | |||
11edf corresponds to 18.8046…[[edo]]. It is similar to [[19edo]], and nearly identical to [[Carlos Beta]]. Unlike 19edo, which is [[consistent]] to the [[integer limit|10-integer-limit]], 11edf is only consistent to the 7-integer-limit. | |||
While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo. At 510.51{{c}}, it is 12.47{{c}} sharper than just and 3.7{{c}} flat of that of [[7edo]]. | While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo. At 510.51{{c}}, it is 12.47{{c}} sharper than just and 3.7{{c}} flat of that of [[7edo]]. | ||
11edf represents the upper bound of the [[phoenix]] tuning range. | 11edf represents the upper bound of the [[phoenix]] tuning range. It benefits from all the desirable properties of phoenix tuning systems. | ||
== Harmonics == | === Harmonics === | ||
{{Harmonics in equal|11|3|2| | {{Harmonics in equal|11|3|2|intervals=integer|columns=11}} | ||
{{Harmonics in equal|11|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edf (continued)}} | |||
=== Subsets and supersets === | |||
11edf is the fifth [[prime equal division|prime edf]], past [[7edf]] and before [[13edf]]. It does not contain any nontrivial subset edfs. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
! | ! # | ||
! | ! Cents | ||
! | ! Approximate ratios | ||
|- | |- | ||
| | | 0 | ||
| | | 0.0 | ||
| [[1/1]] | |||
|- | |- | ||
| 1 | | 1 | ||
| 63. | | 63.8 | ||
| | | [[21/20]], [[25/24]], [[27/26]], [[28/27]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 127. | | 127.6 | ||
| [[14/13]] | | [[13/12]], [[14/13]], [[15/14]], [[16/15]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 191. | | 191.4 | ||
| [[9/8]], [[10/9]] | |||
| | |||
|- | |- | ||
| 4 | | 4 | ||
| 255. | | 255.3 | ||
| [[7/6]], ''[[8/7]]'' | |||
| | |||
|- | |- | ||
| 5 | | 5 | ||
| 319. | | 319.1 | ||
| 6/5 | | [[6/5]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 382. | | 382.9 | ||
| 5/4 | | [[5/4]] | ||
|- | |- | ||
| 7 | | 7 | ||
| 446. | | 446.7 | ||
| [[9/7]] | |||
| | |||
|- | |- | ||
| 8 | | 8 | ||
| 510. | | 510.5 | ||
| [[4/3]] | |||
| | |||
|- | |- | ||
| 9 | | 9 | ||
| 574. | | 574.3 | ||
| | | [[7/5]] | ||
|- | |- | ||
| 10 | | 10 | ||
| 638. | | 638.1 | ||
| | | [[13/9]] | ||
|- | |- | ||
| 11 | | 11 | ||
| | | 702.0 | ||
| | | [[3/2]] | ||
|- | |- | ||
| 12 | | 12 | ||
| 765. | | 765.8 | ||
| 14/9 | | [[14/9]] | ||
|- | |- | ||
| 13 | | 13 | ||
| 828. | | 828.6 | ||
| 21/13 | | [[8/5]], [[13/8]], [[21/13]] | ||
|- | |- | ||
| 14 | | 14 | ||
| 893. | | 893.4 | ||
| [[5/3]] | |||
| | |||
|- | |- | ||
| 15 | | 15 | ||
| 956. | | 956.2 | ||
| [[7/4]] | |||
| | |||
|- | |- | ||
| 16 | | 16 | ||
| 1020. | | 1020.0 | ||
| 9/5 | | [[9/5]] | ||
|- | |- | ||
| 17 | | 17 | ||
| 1084. | | 1084.8 | ||
| 15/8 | | [[15/8]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 1148. | | 1148.7 | ||
| [[27/14]], [[35/18]] | |||
| | |||
|- | |- | ||
| 19 | | 19 | ||
| 1211. | | 1211.5 | ||
| [[2/1]] | |||
| | |||
|- | |- | ||
| 20 | | 20 | ||
| 1276. | | 1276.3 | ||
| | | [[21/10]], [[25/12]], [[27/13]] | ||
|- | |- | ||
| 21 | | 21 | ||
| 1340. | | 1340.1 | ||
| 13/6 | | [[13/6]] | ||
|- | |- | ||
| 22 | | 22 | ||
| 1403. | | 1403.9 | ||
| | | [[9/4]] | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "McGarfyGarf" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/2iaicUkq6EcjcGM8RioFZj Spotify] | [https://francium223.bandcamp.com/track/mcgarfygarf Bandcamp] | [https://www.youtube.com/watch?v=sI8X6PNOiXE YouTube] | |||
== See also == | |||
* [[19edo]] – relative edo | |||
* [[30edt]] – relative edt | |||
* [[49ed6]] – relative ed6 | |||
* [[53ed7]] – relative ed7 | |||
* [[68ed12]] – relative ed12 | |||
* [[93ed30]] – relative ed30 | |||