Tonality diamond: Difference between revisions
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{{Wikipedia|Tonality diamond}} | {{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: | 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 [[Wikipedia:Height function#Naive height|naive height]], the most common number theoretic height function on rational numbers: <math>H\left(\frac{n}{d}\right) = max(|n|, |d|)</math>; as all rational numbers which are the quotient of two positive odd integers ''n''/''d'' with ''H''(''n''/''d'') ≤ ''q'', [[octave-reduced]]. | ||
== Examples of scales == | == Examples of scales == | ||
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* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/GWS%20Scale%20Study-ModernJazzAtTheCrystalBall%20.mp3 Modern Jazz at the Crystal Ball] by Norbert Oldani in the [[7-limit diamond]]. | * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/GWS%20Scale%20Study-ModernJazzAtTheCrystalBall%20.mp3 Modern Jazz at the Crystal Ball] by Norbert Oldani in the [[7-limit diamond]]. | ||
== | == External links == | ||
* [http://www.tonalsoft.com/enc/t/tonality-diamond.aspx Tonality diamond – arrangement of musical frequency ratios showing the dual identity of each ratio] on [[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] | |||
[[Category:Diamond]] | [[Category:Diamond]] | ||
[[Category:Pitch space]] | [[Category:Pitch space]] | ||
Revision as of 07:48, 26 February 2023
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 naive height, the most common number theoretic height function on rational numbers: [math]\displaystyle{ H\left(\frac{n}{d}\right) = max(|n|, |d|) }[/math]; as all rational numbers which are the quotient of two positive odd integers n/d with H(n/d) ≤ q, octave-reduced.
Examples of scales
Music
- Modern Jazz at the Crystal Ball by Norbert Oldani in the 7-limit diamond.