Tonality diamond: Difference between revisions
m Cleanup |
m n for numerator and d for denominator |
||
| Line 3: | Line 3: | ||
| en = Tonality diamond | | en = 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'' ('' | 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 == | ||