Tonality diamond: Difference between revisions

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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]].
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]].


== Examples of scales ==
== Examples of scales ==