Tonality diamond: Difference between revisions
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imported partd from Diamonds, now diamond function |
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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]]. | 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]]. | ||
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== Examples of scales == | == Examples of scales == | ||
* [[diamond5]] | * [[diamond5]] | ||
Revision as of 11:54, 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.
Examples of scales
Music
- Modern Jazz at the Crystal Ball by Norbert Oldani in the 7-limit diamond.