11edo: Difference between revisions

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{{Infobox ET}}

== Theory ==

Compared to 12edo, the intervals of 11edo are stretched:

* The "major third" at 436.36 cents, is quite sharp, and closer to the [[supermajor]] third of frequency ratio [[9/7]] than the simpler third of 5/4.

* The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the [[11/8]] superfourth than the simpler perfect fourth of 4/3.

11edo provides the same tuning on the [[k*N subgroups|2*11 subgroup]] 2.9.15.7.11.17 as does 22edo, and on this subgroup it [[tempering out|tempers out]] the same [[comma]]s as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16:17 [[chord]] and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating [[JI]] chords.

[[File:0-8-16-20 chord.wav|thumb|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]]

=== Ups and downs notation ===

11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

! Solfege

! Approximate Ratios*

! colspan="2" | Up/down notation <br> with major narrower <br> than minor

! [[Smitonic]]<br>(3rd-gen)<br>notation  

|[[File:0-1200 octave.mp3|frameless]]

|}

The ups and downs notations above are heptatonic systems generated by 5ths (~3/2). Alternative notations include pentatonic 5th-generated, octatonic 5th-generated, nonatonic 5th-generated, heptatonic 3rd-generated, and hexatonic 2nd-generated.

== Regular temperament properties ==

=== Uniform maps ===

=== Commas ===

{| class="commatable wikitable center-1 center-2 right-4 center-5"

| Layobi

| Major chroma

|-

| 5

| 31.57

| Lala-tribiyo

|-

| 5

[[File:11edo_approx_2-7-9-11-15-17_2ndsave.png|alt=11edo_approx_2-7-9-11-15-17_2ndsave.png|11edo_approx_2-7-9-11-15-17_2ndsave.png]]

== Scales ==

{{Main|List of 11edo MOS scales}}

Although 11edo has one fewer interval in the octave than 12edo, in terms of [[MOS scale|moment-of-symmetry scales]], it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11 (two degrees of 11edo), 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.

== Instruments ==

[[File:11-edo-ukulele.JPG|alt=11-edo-ukulele.JPG|404x304px|11-edo-ukulele.JPG]]

'''Ensembles'''

In February 2011, [http://oddmusicuc.wordpress.com/ Oddmusic U-C], as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming.

'''Lumatone'''

== Introductory Materials ==

== Music ==

{{Catrel|11edo tracks}}

==== Modern renderings ====

; {{W|Arthur Schutt}}

; [[Francium]]

* "Tostadosto" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/27hl1xKswTuaQG0vIjMHhk Spotify] | [https://francium223.bandcamp.com/track/tostadosto Bandcamp] | [https://www.youtube.com/watch?v=28SOTJvT6sw YouTube]

; [[David Hamill]]

* [https://www.youtube.com/watch?v=fwyM3quEzu4 ''Prelude & Fugue in 11edo, in Four Parts, for Recorder, Organ, Cello''] (2022)

* [https://www.youtube.com/watch?v=qNqDuAq6O5k ''George Secor · 11EDO improvisation (1971)''] (2022)

; [[Mundoworld]]

* [https://www.youtube.com/watch?v=69TiqslCgeg ''Fire Memes'' (with Anthony "Pomp" Pompliano)] – Machine[6] in 11edo tuning

* [https://www.youtube.com/watch?v=MfNLxcbVzs8 ''Theory of Creation''] – Machine[6] in 11edo tuning

; [[User:GlitchyDarkness|No Clue Music]]

=== Unequal Derivatives of 11edo ===

; [[Bryan Deister]]

== Videos ==

* [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ|Mike Battaglia]] - youtube

== See also ==

* [[11edo Zine]] — There is an 11edo Zine! As far as we know, 11edo is the first xenharmonic tuning system to have its own zine.

== Notes ==

[[Category:Listen]]