11edo: Difference between revisions

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* 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 does not have acceptable approximations of harmonics 3 and 5, so the simplest accurate interpretation of it is as a 2.7.11 subgroup temperament. On this subgroup it tempers out [[352/343]] allowing for 3 [[7/4]] to equal [[11/8]]. 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 does not have acceptable approximations of harmonics 3 and 5, so the simplest accurate interpretation of it using only primes is as a 2.7.11 subgroup temperament. On this subgroup it tempers out [[352/343]] allowing for 3 [[7/4]] to equal [[11/8]], relating to the [[5L 1s]] scale of 11edo. 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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 * 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.
-edo does not have acceptable approximations of harmonics 3 and 5, so the simplest accurate interpretation of it is as a 2.7.11 subgroup temperament. On this subgroup it tempers out [[352/343]] allowing for 3 [[7/4]] to equal [[11/8]]. 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 does not have acceptable approximations of harmonics 3 and 5, so the simplest accurate interpretation of it using only primes is as a 2.7.11 subgroup temperament. On this subgroup it tempers out [[352/343]] allowing for 3 [[7/4]] to equal [[11/8]], relating to the [[5L 1s]] scale of 11edo. 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]].