Tonality diamond: Difference between revisions
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The q-[[Odd limit|odd-limit]] '''tonality diamond''' is the [[ | The q-[[Odd limit|odd-limit]] '''tonality diamond''' is the [[diamond]] function applied to the odd numbers from 1 to q: diamond({1, 3, 5, ..., q}). Another way of defining it is in terms of the most common number theoretic height function on rational numbers: H(N/M) = max(|M|, |N|); as all rational numbers which are the quotient of two positive odd integers N/M with H(N/M) ≤ q, [[octave-reduce|reduced to the octave]]. | ||
== | == See also == | ||
*[https://en.wikipedia.org/wiki/Tonality_diamond Tonality diamond - Wikipedia, the free encyclopedia] | * [[Diamonds]] - related, todo | ||
*[http://www.tonalsoft.com/enc/t/tonality-diamond.aspx tonality diamond - arrangement of musical frequency ratios showing the dual identity of each ratio] | * [https://en.wikipedia.org/wiki/Tonality_diamond Tonality diamond - Wikipedia, the free encyclopedia] | ||
* [http://www.tonalsoft.com/enc/t/tonality-diamond.aspx tonality diamond - arrangement of musical frequency ratios showing the dual identity of each ratio] | |||
[[Category: | [[Category:Diamond]] | ||
[[Category:Stub]] | [[Category:Stub]] | ||
[[Category: | [[Category:Theory]] | ||
Revision as of 09:27, 25 October 2018
The q-odd-limit tonality diamond is the diamond function applied to the odd numbers from 1 to q: diamond({1, 3, 5, ..., q}). Another way of defining it is in terms of the most common number theoretic height function on rational numbers: H(N/M) = max(|M|, |N|); as all rational numbers which are the quotient of two positive odd integers N/M with H(N/M) ≤ q, reduced to the octave.