Superparticular ratio: Difference between revisions
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{{Wikipedia|Superparticular ratio}} | {{Wikipedia|Superparticular ratio}} | ||
In mathematics, a '''superparticular ratio''', also called an '''epimoric ratio''' or '''delta-1 ratio''', is the [[ratio]] of two consecutive integer numbers. | In mathematics, a '''superparticular ratio''', also called an '''epimoric ratio''' or '''delta-1 ratio''', is the [[ratio]] of two consecutive integer numbers (1:2, 2:3, 3:4...). | ||
More particularly, the ratio takes the form: | More particularly, the ratio takes the form: | ||
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[[Kite Giedraitis]] has proposed a [[delta-N ratio|delta-''N'']] terminology (where ''delta'' means difference, here the difference between the numerator and the denominator). Thus delta-1 is an alternative term for superparticular, delta-2 is for ratios of the form <math>\frac{n+2}{n}</math>, likewise delta-3, delta-4, etc. | [[Kite Giedraitis]] has proposed a [[delta-N ratio|delta-''N'']] terminology (where ''delta'' means difference, here the difference between the numerator and the denominator). Thus delta-1 is an alternative term for superparticular, delta-2 is for ratios of the form <math>\frac{n+2}{n}</math>, likewise delta-3, delta-4, etc. | ||
[[Kyle Gann]]'s 1992 composition ''[https://www.kylegann.com/Super.html Superparticular Woman]'' bears the namesake of this term, and indeed originated from a melody which uses superparticular ratios 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, and 5/4, "seven pitches which lie within only 221 cents (a slightly large whole-step)"<ref>https://www.kylegann.com/Super.html</ref>. | |||
== Etymology == | == Etymology == | ||