Odd limit: Difference between revisions
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It's not hard to get the maths, but an easier description at the beginning could not harm |
u and v must not be 0 |
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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 integers less than or equal to q. It may be identified with the [[Diamonds|q-limit diamond]]. | 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 [[Diamonds|q-limit diamond]]. | ||
== Examples == | == Examples == | ||
Revision as of 11:37, 25 October 2018
The q odd limit, where q is an odd positive integer, consists of everything of the form 2^i*u/v, or [math]\displaystyle{ 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 q-limit diamond.
Examples
some ratios in the 9-limit are: 3/2, 5/4, 7/6, 10/7, 12/7, 9/8, 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)
See also
- p-limit - or prime harmonic limit
- 1-odd-limit
- 3-odd-limit
- 5-odd-limit
- 7-odd-limit
- 9-odd-limit
- 11-odd-limit
- 13-odd-limit
- 15-odd-limit
- Limit (music) - Wikipedia, the free encyclopedia (covers also the distinction between odd-limit and prime-limit)