Odd limit: Difference between revisions
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== Mathematical Definition == | == Mathematical Definition == | ||
The '''q''' '''odd limit''', where ''q'' is an odd positive integer, consists of everything of the form <code>2^i*u/v</code>, or <math>2^\mathbb Z\frac u v</math>, where ''u'' and ''v'' are odd positive integers less than or equal to q. It may be identified with the [[ | The '''q''' '''odd limit''', where ''q'' is an odd positive integer, consists of everything of the form <code>2^i*u/v</code>, or <math>2^\mathbb Z\frac u v</math>, where ''u'' and ''v'' are odd positive integers less than or equal to q. It may be identified with the [[Tonality diamond|q-limit diamond]]. Examples: some ratios in the 9-limit are: 3/2, 5/4, 7/6, 10/7, 12/7, 9/8 and 14/9. But not 11/9 (11 is a prime greater than 9) nor 15/7 (since 15 is 3*5, both less then 9, but with product greater than 9). | ||
== Odd limit of a ratio == | == Odd limit of a ratio == | ||