Prime equal division: Difference between revisions

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* Making a chain of any interval of the ''n''-equal division, one can reach every tone in ''n'' steps. (For composite edos, this works with intervals that are co-prime to ''n'', for example, 5 degrees of 12edo).

For these or similar reasons, some musicians do not like prime equal divisions (e.g. the makers of [[Armodue]]) and others love them.

For these or similar reasons, some musicians do not like prime equal divisions (e.g. the makers of [[Armodue (theory)|Armodue]]) and others love them.

Primality may be desirable if you want, for example, a whole tone scale that is ''not'' absolutely uniform. In this case you might like [[19edo]] (with whole tone scale 3 3 3 3 3 4, [[mos scale]] of type [[1L 5s]]) or [[17edo]] (with whole tone scale 3 3 3 3 3 2, mos scale of type [[5L 1s]]). In general, making a chain of any interval of a prime ''n''-equal division, thus treating the interval as the generator of a mos scale, one can reach every tone in ''n'' steps. For composite equal divisions, this will only work with intervals that are co-prime to the edo, for example 5 degrees of [[12edo]] (which generates the diatonic scale and a cycle of fifths that closes at 12 tones) but not 4 out of 12 (which generates a much smaller cycle of [[3edo]]).

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 * Making a chain of any interval of the ''n''-equal division, one can reach every tone in ''n'' steps. (For composite edos, this works with intervals that are co-prime to ''n'', for example, 5 degrees of 12edo).
-For these or similar reasons, some musicians do not like prime equal divisions (e.g. the makers of [[Armodue]]) and others love them.
+For these or similar reasons, some musicians do not like prime equal divisions (e.g. the makers of [[Armodue (theory)|Armodue]]) and others love them.
 Primality may be desirable if you want, for example, a whole tone scale that is ''not'' absolutely uniform. In this case you might like [[19edo]] (with whole tone scale 3 3 3 3 3 4, [[mos scale]] of type [[1L 5s]]) or [[17edo]] (with whole tone scale 3 3 3 3 3 2, mos scale of type [[5L 1s]]). In general, making a chain of any interval of a prime ''n''-equal division, thus treating the interval as the generator of a mos scale, one can reach every tone in ''n'' steps. For composite equal divisions, this will only work with intervals that are co-prime to the edo, for example 5 degrees of [[12edo]] (which generates the diatonic scale and a cycle of fifths that closes at 12 tones) but not 4 out of 12 (which generates a much smaller cycle of [[3edo]]).