Tonality diamond: Difference between revisions
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The q-[[ | 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'', [[octave reduction|reduced to the octave]]. | ||
== Examples of scales == | == Examples of scales == | ||
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== See also == | == See also == | ||
* [[ | * [[Diamond function]] | ||
* [ | * [[Wikipedia: Tonality diamond]] | ||
* [http://www.tonalsoft.com/enc/t/tonality-diamond.aspx | * [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 05:10, 23 January 2021
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.