24edo: Difference between revisions
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== Theory == | == Theory == | ||
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 [[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. | ||
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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 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 [[Just intonation subgroup|subgroup]] temperament, on which it is quite accurate. | 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 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 [[Just intonation subgroup|subgroup]] temperament, on which it is quite accurate. | ||
=== Prime harmonics === | |||
{{harmonics in equal|24}} | |||
24edo is the 6th [[highly composite EDO]]. | === Subsets and supersets === | ||
24edo is the 6th [[highly composite EDO]]. Its divisors are {{EDOs|1, 2, 3, 4, 6, 8, 12}}. | |||
== Notation == | == Notation == | ||