Tonality diamond: Difference between revisions
Jump to navigation
Jump to search
m +toc |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 1: | Line 1: | ||
{{interwiki | |||
| de = Tonalitätsdiamant | |||
| en = Tonality_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]]. | 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]]. | ||
__TOC__ | __TOC__ | ||
== Examples of scales == | == Examples of scales == | ||
* [[diamond5]] | * [[diamond5]] | ||
Revision as of 16:52, 24 December 2019
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.