11edo: Difference between revisions

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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 concordant. 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.

<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 concordant. 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]] 2.9.15.7.11.17 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 8:9:11:14:15:16:17 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.

11EDO is the largest EDO that patently alternates with an undivided 9/8 in a [[Well tempered nonet|wtn]].

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| 10.909¢

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== 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.

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 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 concordant. 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.
+<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 concordant. 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]] 2.9.15.7.11.17 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 8:9:11:14:15:16:17 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.
 EDO is the largest EDO that patently alternates with an undivided 9/8 in a [[Well tempered nonet|wtn]].
@@ Line 69: / Line 69: @@
 | 10.909¢
 |}
 == Notation ==
 EDO 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.