Harmony of 23edo: Difference between revisions

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If you take a look at the intervals of [[23edo]], you~~'ll~~ find that this system does not contain good representations of the ~~harmonics~~ 3, 5, 7, 11, or 13, which appear as central in most just intonation systems. Rather than ~~trivialize 23edo by calling~~ it "atonal" or "inharmonic", ~~you should~~ consider the higher-limit harmonies that could serve as useful sonorities, perhaps even ~~'consonances'~~, in the context of careful composition. 23edo contains intervals which approach very well the harmonics 9, 17, 21, 23, 33, 35, 55, 79 ~~&~~ 117. Let's compare the ~~cents~~ values to see how close 23edo intervals come to these harmonics (and other intervals):

If you take a look at the intervals of [[23edo]], you will find that this system does not contain good representations of the [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], or [[13/1|13]], which appear as central in most [[just intonation]] systems. Rather than it ''atonal'' or ''inharmonic'', we could consider the higher-limit harmonies that could serve as useful sonorities, perhaps even [[consonance]]s, in the context of careful composition. 23edo contains intervals which approach very well the harmonics [[9/1|9]], [[17/1|17]], [[21/1|21]], [[23/1|23]], [[33/1|33]], [[35/1|35]], [[55/1|55]], [[79/1|79]] and [[117/1|117]]. Let us compare the [[cent]]s values to see how close 23edo intervals come to these harmonics (and other intervals):

{| class="wikitable"

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	If you take a look at the intervals of [[23edo]], you~~'ll~~ find that this system does not contain good representations of the ~~harmonics~~ 3, 5, 7, 11, or 13, which appear as central in most just intonation systems. Rather than ~~trivialize 23edo by calling~~ it "atonal" or "inharmonic", ~~you should~~ consider the higher-limit harmonies that could serve as useful sonorities, perhaps even ~~'consonances'~~, in the context of careful composition. 23edo contains intervals which approach very well the harmonics 9, 17, 21, 23, 33, 35, 55, 79 ~~&~~ 117. Let's compare the ~~cents~~ values to see how close 23edo intervals come to these harmonics (and other intervals):		If you take a look at the intervals of [[23edo]], you will find that this system does not contain good representations of the [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], or [[13/1\|13]], which appear as central in most [[just intonation]] systems. Rather than it ''atonal'' or ''inharmonic'', we could consider the higher-limit harmonies that could serve as useful sonorities, perhaps even [[consonance]]s, in the context of careful composition. 23edo contains intervals which approach very well the harmonics [[9/1\|9]], [[17/1\|17]], [[21/1\|21]], [[23/1\|23]], [[33/1\|33]], [[35/1\|35]], [[55/1\|55]], [[79/1\|79]] and [[117/1\|117]]. Let us compare the [[cent]]s values to see how close 23edo intervals come to these harmonics (and other intervals):

	{\| class="wikitable"		{\| class="wikitable"