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 (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, reduced to the octave.
Examples of scales
Music
- Modern Jazz at the Crystal Ball by Norbert Oldani in the 7-limit diamond.