Tonality diamond: Difference between revisions
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{{Wikipedia|Tonality diamond}} | |||
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''/''d'') = max (|''n''|, |''d''|); as all rational numbers which are the quotient of two positive odd integers ''n''/''d'' with ''H'' (''n''/''d'') ≤ ''q'', [[octave reduction|reduced to the octave]]. | 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''/''d'') = max (|''n''|, |''d''|); as all rational numbers which are the quotient of two positive odd integers ''n''/''d'' with ''H'' (''n''/''d'') ≤ ''q'', [[octave reduction|reduced to the octave]]. | ||
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== See also == | == See also == | ||
* [[Diamond function]] | * [[Diamond function]] | ||
* [http://www.tonalsoft.com/enc/t/tonality-diamond.aspx Tonality diamond – arrangement of musical frequency ratios showing the dual identity of each ratio] – Tonalsoft Encyclopedia | * [http://www.tonalsoft.com/enc/t/tonality-diamond.aspx Tonality diamond – arrangement of musical frequency ratios showing the dual identity of each ratio] – Tonalsoft Encyclopedia | ||
[[Category:Diamond]] | [[Category:Diamond]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 15:05, 25 March 2022
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/d) = max (|n|, |d|); as all rational numbers which are the quotient of two positive odd integers n/d with H (n/d) ≤ q, reduced to the octave.
Examples of scales
Music
- Modern Jazz at the Crystal Ball by Norbert Oldani in the 7-limit diamond.