Tonality diamond: Difference between revisions
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The q-odd-limit '''tonality diamond''' is the [[Diamonds|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]]. | The q-[[Odd limit|odd-limit]] '''tonality diamond''' is the [[Diamonds|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]]. | ||
==Links== | |||
*[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:diamond]] | |||
[[Category: | [[Category:Stub]] | ||
[[Category:theory]] | [[Category:theory]] | ||
Revision as of 18:34, 23 September 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.