24edo: Difference between revisions

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The [[5-limit]] approximations in 24edo are the same as those in 12edo, therefore 24edo offers nothing new as far as approximating the 5-limit is concerned.

The 7th harmonic-based intervals ([[7/4]], [[7/5]] and [[7/6]]) are almost as bad in 24edo as in 12edo. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12edo requires high-degree tunings like [[36edo|36et]], [[72edo|72et]], [[84edo|84et]] or [[156edo|156et]]. However, it should be noted that 24edo, like [[22edo]], ''does'' temper out the [[quartisma]], linking the otherwise sub-par 7-limit harmonies with those of the 11-limit.

The 7th harmonic-based intervals ([[7/4]], [[7/5]] and [[7/6]]) are almost as bad in 24edo as in 12edo. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12edo requires high-degree tunings like [[36edo|36et]], [[72edo|72et]], [[84edo|84et]] or [[156edo|156et]]. However, it should be noted that 24edo, like [[22edo]], ''does'' temper out the [[quartisma]], linking the otherwise sub-par [[7-limit]] harmonies with those of the [[11-limit]].

Speaking of 11-limit representation in 24edo, the 11th harmonic, and most intervals derived from it, (11/10, 11/9, 11/8, 11/6, 12/11, 15/11, 16/11, 18/11, 20/11) are very well approximated in this EDO. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth.

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 The [[5-limit]] approximations in 24edo are the same as those in 12edo, therefore 24edo offers nothing new as far as approximating the 5-limit is concerned.
-The 7th harmonic-based intervals ([[7/4]], [[7/5]] and [[7/6]]) are almost as bad in 24edo as in 12edo. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12edo requires high-degree tunings like [[36edo|36et]], [[72edo|72et]], [[84edo|84et]] or [[156edo|156et]].  However, it should be noted that 24edo, like [[22edo]], ''does'' temper out the [[quartisma]], linking the otherwise sub-par 7-limit harmonies with those of the 11-limit.
+The 7th harmonic-based intervals ([[7/4]], [[7/5]] and [[7/6]]) are almost as bad in 24edo as in 12edo. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12edo requires high-degree tunings like [[36edo|36et]], [[72edo|72et]], [[84edo|84et]] or [[156edo|156et]].  However, it should be noted that 24edo, like [[22edo]], ''does'' temper out the [[quartisma]], linking the otherwise sub-par [[7-limit]] harmonies with those of the [[11-limit]].
 Speaking of 11-limit representation in 24edo, the 11th harmonic, and most intervals derived from it, (11/10, 11/9, 11/8, 11/6, 12/11, 15/11, 16/11, 18/11, 20/11) are very well approximated in this EDO. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth.