13edf: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
{| class="wikitable" | == Theory == | ||
13edf corresponds to 22.2236[[edo]]. It is nearly identical to every ninth step of [[200edo]], but not quite similar to [[22edo]]; the octave is compressed by 12.076{{c}}, a deviation that is small but significant enough to create a discrepancy for the [[7/1|7th]] and [[11/1|11th]] harmonics. | |||
== Harmonics == | |||
{{Harmonics in equal|13|3|2|intervals=prime|columns=8}} | |||
{{Harmonics in equal|13|3|2|start=9|intervals=prime|columns=8}} | |||
== Intervals == | |||
{| class="wikitable mw-collapsible" | |||
|+ style="font-size: 105%;" | Intervals of 13edf | |||
|- | |||
! Degree | |||
! Cents | |||
! Corresponding JI intervals | |||
(even if inconsistent) | |||
! Comments | |||
|- | |||
! colspan="2" | 0 | |||
| '''exact [[1/1]]''' | |||
| | |||
|- | |||
| 1 | |||
| 53.9965 | |||
| [[33/32]] | |||
| pseudo-[[25/24]] | |||
|- | |||
| 2 | |||
| 107.9931 | |||
| [[17/16]], 117/110, [[16/15]] | |||
| | |||
|- | |||
| 3 | |||
| 161.9896 | |||
| [[11/10]] | |||
| | |||
|- | |||
| 4 | |||
| 215.9862 | |||
| [[17/15]] | |||
| | |||
|- | |- | ||
| | | | 5 | ||
| | | | 269.9827 | ||
| [[7/6]] | |||
| | |||
|- | |- | ||
| | | | 6 | ||
| | | | 323.9792 | ||
| [[77/64]] | |||
| pseudo-[[6/5]] | |||
|- | |- | ||
| | | | 7 | ||
| | | | 377.9758 | ||
| [[56/45]] | |||
| pseudo-[[5/4]] | |||
|- | |- | ||
| | | | 8 | ||
| | | | 431.9723 | ||
| [[9/7]] | |||
| | |||
|- | |- | ||
| | | | 9 | ||
| | | | 485.9688 | ||
| [[45/34]] | |||
| pseudo-[[4/3]] | |||
|- | |- | ||
| | | | 10 | ||
| | | | 539.9654 | ||
| [[15/11]] | |||
| | |||
|- | |- | ||
| | | | 11 | ||
| | | | 593.9619 | ||
| [[55/39]], [[24/17]] | |||
| | |||
|- | |- | ||
| | | | 12 | ||
| | | | 647.9585 | ||
| [[16/11]] | |||
| | |||
|- | |- | ||
| | | | 13 | ||
| | | | 701.9550 | ||
| '''exact [[3/2]]''' | |||
| just perfect fifth | |||
|- | |- | ||
| | | | 14 | ||
| | | | 755.9515 | ||
| [[99/64]] | |||
| | |||
|- | |- | ||
| | | | 15 | ||
| | | | 809.9481 | ||
| [[51/32]], [[8/5]] | |||
| | |||
|- | |- | ||
| | | | 16 | ||
| | | | 863.9446 | ||
| [[33/20]] | |||
| | |||
|- | |- | ||
| | | | 17 | ||
| | | | 917.9412 | ||
| [[17/10]] | |||
| | |||
|- | |- | ||
| | | | 18 | ||
| | | | 971.9377 | ||
| [[7/4]] | |||
| | |||
|- | |- | ||
| | | | 19 | ||
| | | | 1025.9342 | ||
| [[29/16]] | |||
| pseudo-[[9/5]] | |||
|- | |- | ||
| | | | 20 | ||
| | | | 1079.9308 | ||
| [[28/15]] | |||
| pseudo-[[15/8]] | |||
|- | |- | ||
| | | | 21 | ||
| | | | 1133.9273 | ||
| [[52/27]], [[27/14]] | |||
| | |||
|- | |- | ||
| | | | 22 | ||
| | | | 1187.9238 | ||
| [[135/68]] | |||
| pseudo-[[octave]] | |||
|- | |- | ||
| | | | 23 | ||
| | | | 1241.9204 | ||
| [[45/44|45/22]] | |||
| | |||
|- | |- | ||
| | | | 24 | ||
| | | | 1295.9169 | ||
| [[19/18|19/9]], [[18/17|36/17]] | |||
| | |||
|- | |- | ||
| | | | 25 | ||
| | | | 1349.9135 | ||
| [[12/11|24/11]] | |||
| | |||
|- | |- | ||
| | | | 26 | ||
| | | | 1403.9100 | ||
| '''exact [[9/4]]''' | |||
| pythagorean major ninth | |||
|} | |} | ||
== Instruments == | |||
A [[Lumatone mapping for 13edf]] is available. | |||
== Music == | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/watch?v=8oDt4CfjOyw&list=WL&index=340 ''13ed(3/2) improv''] (2026) | |||
== See also == | |||
* [[22edo]] — 13edf is fairly close to 22.2edo. | |||
{{stub}} | |||
[[Category:22edo]] | |||