EDO: Difference between revisions

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=== Size of an EDO ===

When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world.

When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world. i[https://soundcloud.com/scottthompson-3/the-13-edos-of-xmas soundcloud.com/scottthompson-3/the-13-edos-of-xmas] s a humorous demonstration of edos 1-13.

On the other hand, if you use the edo to tune a scale or [[Regular_Temperaments|regular temperament]], the size of the edo does not matter so much (at least conceptually), as you don't need to use all of it. Some of the edos which can be used to tune various temperaments are listed on the [[optimal patent val]] page. Tuning a scale in just intonation by one of these edos can be regarded as automatically tempering it to the corresponding regular temperament.

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 === Size of an EDO ===
-When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world.
+When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world. i[https://soundcloud.com/scottthompson-3/the-13-edos-of-xmas soundcloud.com/scottthompson-3/the-13-edos-of-xmas] s a humorous demonstration of edos 1-13.
 On the other hand, if you use the edo to tune a scale or [[Regular_Temperaments|regular temperament]], the size of the edo does not matter so much (at least conceptually), as you don't need to use all of it. Some of the edos which can be used to tune various temperaments are listed on the [[optimal patent val]] page. Tuning a scale in just intonation by one of these edos can be regarded as automatically tempering it to the corresponding regular temperament.