11edo: Difference between revisions

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| ja = 11平均律

}}__FORCETOC__

==~~11 tone equal temperament~~==

==Theory==

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Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving Orgone[7] on the whites. The superfluous Ab can be made a note of [[22edo|22edo]], a tuning known as "elevenplus".

~~==Tuning==~~

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

<ul><li>The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The "major second," at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."</li><li>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.</li><li>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.</li></ul>

<ul><li>The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The "major second," at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."</li><li>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.</li><li>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.</li></ul>11edo provides the same tuning on the [[k*N_subgroups|2*11 subgroup]] 2.9.15.7.11 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.

~~==Subgroup==~~

11edo provides the same tuning on the [[k*N_subgroups|2*11 subgroup]] 2.9.15.7.11 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.

==Notation==

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The second approach preserves the ''harmonic'' meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 11edo "on the fly".

The 11edo solfege in the table is derived from [[22edo_Solfege|22edo solfege]].

{| class="wikitable"

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[[File:Sagittal11EDO.jpg|alt=Sagittal11EDO.jpg|Sagittal11EDO.jpg]]

These are heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.

These are all heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.

'''Pentatonic 5th-generated:''' '''D * * E G * * A C * * D''' (generator = wide 3/2 = 7\11 = perfect 5thoid)

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|}

==Intervals==

==JI Intervals==

{| class="wikitable"

|-

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[[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]]

~~==11edo solfege==~~

~~An 11edo solfege system can easily be applied from the [[22edo_Solfege|22edo solfege]] system.~~

~~A chromatic scale would thus be sung: '''do ra re me mo fu su lo la ta ti do'''.~~

==MOS Scales==

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==Instruments==

11-edo ukulele:

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

~~==11edo Instant Ensemble==~~

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.

==~~11edo Zine==~~

==Music==

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

~~==Compositions~~==

[[File:11EDO-improv.mp3]]

''[http://xenharmony.wikispaces.com/space/showimage/11EDO-improv.mp3 First Piece Ever]'' by [[George_Secor|George Secor]], 1970. Apparently the first piece ever written for 11edo.

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<ul><li>''[http://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike_Battaglia_FAQ|Mike Battaglia]] - youtube</li></ul>

==11edo Zine==

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

[[Category:11-tone]]

@@ Line 5: / Line 5: @@
 | ja = 11平均律
 }}__FORCETOC__
-==11 tone equal temperament==
+==Theory==
 -tone equal temperament, or 11[[EDO|edo]], divides the [[Octave|octave]] into eleven equal steps of approximately 109.09 [[cent|cents]]. It is the fifth [[prime_numbers|prime]] edo, after [[2edo|2edo]], [[3edo|3edo]], [[5edo|5edo]], and [[7edo|7edo]].
@@ Line 11: / Line 11: @@
 Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving Orgone[7] on the whites. The superfluous Ab can be made a note of [[22edo|22edo]], a tuning known as "elevenplus".
-==Tuning==
 Compared to 12edo, the intervals of 11edo are stretched:
-<ul><li>The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The "major second," at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."</li><li>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.</li><li>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.</li></ul>
+<ul><li>The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The "major second," at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."</li><li>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.</li><li>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.</li></ul>11edo provides the same tuning on the [[k*N_subgroups|2*11 subgroup]] 2.9.15.7.11 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.
-==Subgroup==
-edo provides the same tuning on the [[k*N_subgroups|2*11 subgroup]] 2.9.15.7.11 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.
 ==Notation==
@@ Line 24: / Line 20: @@
 The second approach preserves the ''harmonic'' meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 11edo "on the fly".
+The 11edo solfege in the table is derived from [[22edo_Solfege|22edo solfege]].
 {| class="wikitable"
@@ Line 192: / Line 190: @@
 [[File:Sagittal11EDO.jpg|alt=Sagittal11EDO.jpg|Sagittal11EDO.jpg]]
-These are heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.
+These are all heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.
 '''<u>Pentatonic 5th-generated:</u>''' '''D * * E G * * A C * * D'''  (generator = wide 3/2 = 7\11 = perfect 5thoid)
@@ Line 328: / Line 326: @@
 |}
-==Intervals==
+==JI Intervals==
 {| class="wikitable"
 |-
@@ Line 412: / Line 410: @@
 [[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]]
-==11edo solfege==
-An 11edo solfege system can easily be applied from the [[22edo_Solfege|22edo solfege]] system.
-A chromatic scale would thus be sung: '''do ra re me mo fu su lo la ta ti do'''.
 ==MOS Scales==
@@ Line 432: / Line 425: @@
 ==Instruments==
+-edo ukulele:
 [[File:11-edo-ukulele.JPG|alt=11-edo-ukulele.JPG|404x304px|11-edo-ukulele.JPG]]
-==11edo Instant Ensemble==
 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.
-==11edo Zine==
+==Music==
-There is an 11edo Zine! As far as we know, 11edo is the first xenharmonic tuning system to have its own zine. See [[11edo_Zine|11edo Zine]].
-==Compositions==
 [[File:11EDO-improv.mp3]]
 <span style=""><span style=""><span style="">''[http://xenharmony.wikispaces.com/space/showimage/11EDO-improv.mp3 First Piece Ever]''</span></span></span> by [[George_Secor|George Secor]], 1970. Apparently the first piece ever written for 11edo.
@@ Line 490: / Line 481: @@
 <ul><li><span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]''</span></span></span>, [[Mike_Battaglia_FAQ|Mike Battaglia]] - youtube</li></ul>
+==11edo Zine==
+There is an 11edo Zine! As far as we know, 11edo is the first xenharmonic tuning system to have its own zine. See [[11edo_Zine|11edo Zine]].
 [[Category:11-tone]]