EDO: Difference between revisions

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== Approaches to exploring EDOs ==

If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise.

If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise. [[Macrotonal EDO]]s have a step size larger than that of 12edo, and thus have fewer than 12 steps per octave, so they may be preferable to those who want simplicity.

If you're a classically trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to the perfect fifth ([[3/2]]) can be rewarding. Classical music also relies on the fact that [[5/4]] is the major third of the diatonic scale, which occurs only when [[81/80]], the syntonic comma, is [[tempered out]]. EDOs {{EDOs| 12, 19, 24, 26, 31, 36, 38, 43, 45, 48, and 50}} temper out 81/80, and are thus [[meantone]] systems. EDOs {{EDOs| 17, 22, 27, 29, 34, 39, 41, 44, 46, 49, 51, and 53}} have an accurate perfect fifth, but do not temper out 81/80, and thus require new ways of thinking about harmony. Many EDOs, such as {{EDOs| 12, 17, 19, 22, 26, 27, 29, 31, 39, 41, 43, 45, 46, 49, and 53 }}, can be notated with some variant on the [[chain-of-fifths notation|A–G "circle of fifths" notation]], while other EDOs, including {{EDOs| 24, 34, 36, 38, 44, 48, or 51}}, involve multiple such circles.

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 == Approaches to exploring EDOs ==
-If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise.
+If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise. [[Macrotonal EDO]]s have a step size larger than that of 12edo, and thus have fewer than 12 steps per octave, so they may be preferable to those who want simplicity.
 If you're a classically trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to the perfect fifth ([[3/2]]) can be rewarding. Classical music also relies on the fact that [[5/4]] is the major third of the diatonic scale, which occurs only when [[81/80]], the syntonic comma, is [[tempered out]]. EDOs {{EDOs| 12, 19, 24, 26, 31, 36, 38, 43, 45, 48, and 50}} temper out 81/80, and are thus [[meantone]] systems. EDOs {{EDOs| 17, 22, 27, 29, 34, 39, 41, 44, 46, 49, 51, and 53}} have an accurate perfect fifth, but do not temper out 81/80, and thus require new ways of thinking about harmony. Many EDOs, such as {{EDOs| 12, 17, 19, 22, 26, 27, 29, 31, 39, 41, 43, 45, 46, 49, and 53 }}, can be notated with some variant on the [[chain-of-fifths notation|A–G "circle of fifths" notation]], while other EDOs, including {{EDOs| 24, 34, 36, 38, 44, 48, or 51}}, involve multiple such circles.