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 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.