576edo: Difference between revisions
Created page with "576edo divides the octave into steps of 2.08<SPAN STYLE="text-decoration:overline">3</SPAN> cents each. ==Theory== {{primes in edo|576|columns=14}} 576edo is an excellent 2.3..." |
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576 is a highly composite number which is equal to 24 squared, which in itself is double the world-predominant [[12edo]]. It's xenharmonic divisors are {{EDOs|8, 9, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, and 288}}. Some of these like 72 and 96 have been put into historical use. Its approximation to the perfect fifth is just one step above the 12edo fifth. | 576 is a highly composite number which is equal to 24 squared, which in itself is double the world-predominant [[12edo]]. It's xenharmonic divisors are {{EDOs|8, 9, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, and 288}}. Some of these like 72 and 96 have been put into historical use. Its approximation to the perfect fifth is just one step above the 12edo fifth. | ||
Because of composition, it may be preferrable to make references to smaller EDOs instead of using the best approximation. For example, using the ⟨576 912 1616 1992] [[val]] for representing the 2.3.7.11 subgroup makes references to 24edo and 36edo: ⟨1\1 7\12 11\24 29\36] when octave reduced. In fact, this approach may be preferrable since | Because of composition, it may be preferrable to make references to smaller EDOs instead of using the best approximation, that is the patent val. For example, using the ⟨576 912 1616 1992] [[val]] for representing the 2.3.7.11 subgroup makes references to 24edo and 36edo: ⟨1\1 7\12 11\24 29\36] when octave reduced. In fact, this approach may be preferrable since the patent val will create sequences that fall aside by 1\576 of each other, which may sound like an untempered comma. | ||
Revision as of 16:59, 21 October 2021
576edo divides the octave into steps of 2.083 cents each.
Theory
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576edo is an excellent 2.3.7 subgroup tuning.
576 is a highly composite number which is equal to 24 squared, which in itself is double the world-predominant 12edo. It's xenharmonic divisors are 8, 9, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, and 288. Some of these like 72 and 96 have been put into historical use. Its approximation to the perfect fifth is just one step above the 12edo fifth.
Because of composition, it may be preferrable to make references to smaller EDOs instead of using the best approximation, that is the patent val. For example, using the ⟨576 912 1616 1992] val for representing the 2.3.7.11 subgroup makes references to 24edo and 36edo: ⟨1\1 7\12 11\24 29\36] when octave reduced. In fact, this approach may be preferrable since the patent val will create sequences that fall aside by 1\576 of each other, which may sound like an untempered comma.