Generator gronut/Mathematics - Revision history

Inthar: /* Gronut */

2026-10-20T13:54:49Z

Gronut

← Older revision		Revision as of 13:54, 20 October 2026
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	== Gronut ==		== Gronut ==
	For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph''' or the '''gronut'''; every vertex of the gronut has degree 6, and the graph forms a triangulation of the torus.		Take the grylinder. For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph''' or the '''gronut'''; every vertex of the gronut has degree 6, and the graph forms a triangulation of the torus.

Inthar at 13:54, 20 October 2026

2026-10-20T13:54:06Z

← Older revision		Revision as of 13:54, 20 October 2026
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	(Under construction)		(Under construction)

	== ~~Definition~~ ==		== Grylinder ==
	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>

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	# Take <math>n</math> equally spaced points on said circle. For sake of canonicality one of the <math>n</math> points is taken to be a "glue point".		# Take <math>n</math> equally spaced points on said circle. For sake of canonicality one of the <math>n</math> points is taken to be a "glue point".
	# Unglue the line segments and put them back at their original positions.		# Unglue the line segments and put them back at their original positions.
	The resulting sequence of embeddings <math>\mathbb{Z}/n \to S^1\to C</math> is called the <math>(n, g\backslash m)</math>-'''~~gronut~~'''.		The resulting sequence of embeddings <math>\mathbb{Z}/n \to S^1\to C</math> is called the <math>(n, g\backslash m)</math>-'''grylinder'''.

	== ~~Straddle generator structure~~ ==		== Gronut ==
	For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut ~~graph~~ has degree 6, and the graph forms a triangulation of the torus.		For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph''' or the '''gronut'''; every vertex of the gronut has degree 6, and the graph forms a triangulation of the torus.

Inthar: /* Straddle generator structure */

2026-10-20T13:34:51Z

Straddle generator structure

← Older revision		Revision as of 13:34, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
	For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6 and the graph forms a triangulation of ~~(something)~~.		For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6, and the graph forms a triangulation of the torus.

Inthar: /* Straddle generator structure */

2026-10-20T13:26:49Z

Straddle generator structure

← Older revision		Revision as of 13:26, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
	For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6 and the graph forms a triangulation of (something).		For each vertex, corresponding to a note of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6 and the graph forms a triangulation of (something).

Inthar: /* Straddle generator structure */

2026-10-20T13:15:20Z

Straddle generator structure

← Older revision		Revision as of 13:15, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
	For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6.		For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6 and the graph forms a triangulation of (something).

Inthar: /* Straddle generator structure */

2026-10-20T13:10:34Z

Straddle generator structure

← Older revision		Revision as of 13:10, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
	For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''.		For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''; every vertex of the gronut graph has degree 6.

Inthar: /* Straddle generator structure */

2026-10-20T13:09:55Z

Straddle generator structure

← Older revision		Revision as of 13:09, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
	For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two ~~generators straddling~~ g\m. The resulting graph is called the '''gronut graph'''.		For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two nearest intervals in n-edo to g\m, which straddle g\m. The resulting graph is called the '''gronut graph'''.

Inthar: /* Straddle generator structure */

2026-10-20T13:09:21Z

Straddle generator structure

← Older revision		Revision as of 13:09, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
	The gronut graph...		For each vertex (note) of n-edo, draw an edge corresponding to 1\n and two edges for the two generators straddling g\m. The resulting graph is called the '''gronut graph'''.

Inthar: /* Straddle generator structure */

2026-10-20T13:00:13Z

Straddle generator structure

← Older revision		Revision as of 13:00, 20 October 2026
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	== Straddle generator structure ==		== Straddle generator structure ==
			The gronut graph...

Inthar: /* Definition */

2026-10-20T02:06:52Z

Definition

← Older revision		Revision as of 02:06, 20 October 2026
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	# Take <math>n</math> equally spaced points on said circle. For sake of canonicality one of the <math>n</math> points is taken to be a "glue point".		# Take <math>n</math> equally spaced points on said circle. For sake of canonicality one of the <math>n</math> points is taken to be a "glue point".
	# Unglue the line segments and put them back at their original positions.		# Unglue the line segments and put them back at their original positions.
	The resulting sequence of embeddings <math>\mathbb{Z}/n \to S^1\to ~~C</math> into <math>~~C</math> is called the <math>(n, g\backslash m)</math>-'''gronut'''.		The resulting sequence of embeddings <math>\mathbb{Z}/n \to S^1\to C</math> is called the <math>(n, g\backslash m)</math>-'''gronut'''.

	== Straddle generator structure ==		== Straddle generator structure ==