Equal Divisions of the Fifth

Compiled by X. J. Scott, 1/25/2001.

Tuning	step size (cents)	commonest variant(s)	step size (cents)	discovered by	recipes
3rd root of 3/2	233.985	subset of Alpha	3 * 77.965 = 233.895	Wendy Carlos
4th root of 3/2	175.489	subset of 88cET, subset of Gamma	2 * 88.000 = 176.000, 5 * 35.1 = 175.5	traditional Georgian
5th root of 3/2	140.391	subset of Gamma	4 * 35.1 = 140.4	Wendy Carlos
6th root of 3/2	116.993	---	---	X. J. Scott
7th root of 3/2	100.279	Pythagorean, 12tET	100.279, 100.000	Serge Cordier
8th root of 3/2	87.744	88 cET	88.000 or 88.075	Gary Morrison
9th root of 3/2	77.995	Alpha	77.965	Wendy Carlos
10th root of 3/2	70.196	Subset of Gamma, 17tET	2 * 35.1 = 70.2, 70.588	Wendy Carlos
11th root of 3/2	63.814	Beta, 19tET	63.833, 63.158	Wendy Carlos
12th root of 3/2	58.496	---	---	X. J. Scott
13th root of 3/2	53.997	22tET	54.546	X. J. Scott
14th root of 3/2	50.139	Quarter Tone Scale	50.000	Traditional
15th root of 3/2	46.797	---	---	X. J. Scott
16th root of 3/2	43.872	---	---	X. J. Scott
17th root of 3/2	41.291	29tET	41.379	X. J. Scott
18th root of 3/2	38.998	31tET	38.710	X. J. Scott
19th root of 3/2	36.945	---	---	X. J. Scott
20th root of 3/2	35.098	Gamma	35.1	Wendy Carlos

Revisions:

2007/12/30 — Added LMSO Recipes

2009/05/17 — Added octave variants

2011/04/13 — Added links