User:Contribution/Exploring Selected Modes in 19-EDO

Rank-2 5-limit temperaments

Period	Generator	Temperaments	5-limit commas
19\19	1\19	Unicorn	1594323/1562500
19\19	2\19	Negri	16875/16384
19\19	3\19	Unsmate	17578125/16777216
19\19	4\19	Hogzilla	4428675/4194304
19\19	5\19	Kleismic	15625/15552
19\19	6\19	Magic	3125/3072
19\19	7\19	Sensi	78732/78125
19\19	8\19	Meantone	81/80
19\19	9\19	Stump	273375/262144

MOS Modes

Period	Generator	Modes	Names
19\19	2\19	2 2 2 2 2 1 2 2 2 2	Negri[10]
19\19	3\19	1 2 1 2 1 2 1 2 1 2 1 2 1	Unsmate[13]
19\19	4\19	3 1 3 1 3 1 3 1 3	Hogzilla[9]
		1 2 1 1 2 1 2 1 1 2 1 1 2 1	Hogzilla[14]
19\19	5\19	1 3 1 1 3 1 3 1 1 3 1	Kleismic[11]
		1 2 1 1 1 2 1 1 1 2 1 1 1 2 1	Kleismic[15]
19\19	6\19	1 4 1 1 4 1 1 1 4 1	Magic[10]
		1 1 3 1 1 1 3 1 1 1 3 1 1	Magic[13]
		1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1	Magic[16]
19\19	7\19	2 1 2 2 2 1 2 2 2 1 2	Sensi[11]
19\19	8\19	2 1 2 1 2 2 1 2 1 2 1 2	Meantone[12]
1\19	1\19	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1	19edo

Mapping

sharpness = 1 L = 3 ; s = 2

Degree	Notation	Approximate Ratios	Approximate Ratios	Notation	Degree
0	P1	1/1	2/1	P8	19
1	A1, d2			A7, d8	18
2	m2	16/15, 15/14, 14/13, 13/12	24/13, 13/7, 28/15, 15/8	M7	17
3	M2	10/9, 9/8	16/9, 9/5	m7	16
4	A2, d3	8/7, 15/13, 7/6	12/7, 26/15, 7/4	A6, d7	15
5	m3	6/5	5/3	M6	14
6	M3	16/13, 5/4	8/5, 13/8	m6	13
7	A3, d4	9/7, 13/10	20/13, 14/9	A5, d6	12
8	P4	4/3	3/2	P5	11
9	A4	18/13, 7/5	10/7, 13/9	d5	10