Generator gronut/Mathematics: Difference between revisions
From Xenharmonic Reference
mNo edit summary |
mNo edit summary |
||
| Line 5: | Line 5: | ||
Let <math>m > 1</math> and <math>n > m, \gcd(n, m) = 1</math> be integer edos and fix a generator <math>g, 2 \leq g \leq m - 2</math> with <math>\gcd(g, m) = 1.</math> Let <math>h</math> be the modular inverse of <math>g</math> modulo <math>m.</math> | Let <math>m > 1</math> and <math>n > m, \gcd(n, m) = 1</math> be integer edos and fix a generator <math>g, 2 \leq g \leq m - 2</math> with <math>\gcd(g, m) = 1.</math> Let <math>h</math> be the modular inverse of <math>g</math> modulo <math>m.</math> | ||
Consider the "cylinder" <math>\mathbb{Z}/m \times [0, 1 | Consider the "cylinder" <math>\mathbb{Z}/m \times [0, 1)</math> with coordinates <math>(x, y)</math> = (along "longitude", along "meridian"). The <math>(n, g\backslash m)</math>-'''gronut''' is constructed as follows: | ||
# Glue the | # Glue the intervals <math>[0, 1)</math> end to end, making a (continuous) circle of circumference <math>m</math> | ||
# Take <math>n</math> equally spaced points on said circle | # Take <math>n</math> equally spaced points on said circle | ||
Revision as of 01:32, 20 October 2026
This is a technical or mathematical page. While the subject may be of some relevance to music, the page treats the subject in technical language.
(Under construction)
Let and be integer edos and fix a generator with Let be the modular inverse of modulo
Consider the "cylinder" with coordinates = (along "longitude", along "meridian"). The -gronut is constructed as follows:
- Glue the intervals end to end, making a (continuous) circle of circumference
- Take equally spaced points on said circle
