Tonality diamond: Difference between revisions
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has to be reworked together with Diamonds |
imported partd from Diamonds, now diamond function |
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The q-[[Odd limit|odd-limit]] '''tonality diamond''' is the [[diamond]] | 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]]. | ||
== Examples of scales == | |||
* [[diamond5]] | |||
* [[diamond7]] | |||
* [[diamond9]] | |||
* [[diamond11]] | |||
* [[diamond13]] | |||
* [[diamond15]] | |||
* [[diamond9plus-marvel]] | |||
== Music == | |||
* [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]]. | |||
== See also == | == See also == | ||
Revision as of 11:52, 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.