24edo: Difference between revisions

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The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. Expanding this, one will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.

Its step, at 50 cents, is notable for being generally seen as one of the most dissonant intervals possible (as such, ~~the~~ harmonic entropy ~~model [ {{nowrap|''~~a~~'' {{=}} 2}} {{nowrap|''s'' {{=}} 1%}} <-- get rid of these] is generally tuned so the~~ peak ~~occurs at~~ around this point). Intervals less than 40 cents tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60 cents are often perceived as having less "tension", and thus are also considered to be more consonant.

Its step, at 50 cents, is notable for being generally seen as one of the most dissonant intervals possible (as such, typical harmonic entropy models show a peak around this point). Intervals less than 40 cents tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60 cents are often perceived as having less "tension", and thus are also considered to be more consonant.

=== Prime harmonics ===

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 The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24&nbsp;subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. Expanding this, one will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.
-Its step, at 50 cents, is notable for being generally seen as one of the most dissonant intervals possible (as such, the harmonic entropy model [ {{nowrap|''a'' {{=}} 2}} {{nowrap|''s'' {{=}} 1%}} <-- get rid of these] is generally tuned so the peak occurs at around this point). Intervals less than 40 cents tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60 cents are often perceived as having less "tension", and thus are also considered to be more consonant.
+Its step, at 50 cents, is notable for being generally seen as one of the most dissonant intervals possible (as such, typical harmonic entropy models show a peak around this point). Intervals less than 40 cents tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60 cents are often perceived as having less "tension", and thus are also considered to be more consonant.
 === Prime harmonics ===