Tonality diamond: Difference between revisions
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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]]. | ||
__TOC__ | __TOC__ | ||
== Examples of scales == | == Examples of scales == | ||
* [[diamond5]] | * [[diamond5]] | ||