Matrix-6 LFO ratios

Tuning polyrhythms by ear is fine, as long as it works. But with the M6's discrete LFO speeds, you'll find more often than not that the ratio you want just isn't available for that base rate. I found myself writing down known ratios on random scraps of paper.

These ratios are derived from the LFO-speed data. For each ratio out to 9-limit, I found all sufficiently close approximations -- the quality is measured by the time it takes for the LFOs to beat a full cycle against one another. In practice, the estimated beat rate corresponds only loosely to reality...

lfo-speed ratios out to a factor-limit of nine and a beat rate of 5 mHz:

		beat rate (mHz)
--- 2:1 ---
 63	61	1.0
 62	59	0.1
 61	57	1.5
 60	55	1.2
 59	53	2.7
 58	51	1.4
 57	49	1.0
 49	39	0.9
 48	38	0.7
 41	28	0.2
 40	27	0.3
 37	24	0.3
 25	17	0.1
 7	2	0.0
 3	0	0.0
--- 3:1 ---
 63	59	0.7
 62	56	1.7
 61	53	2.3
 60	50	1.9
 58	45	2.4
 56	42	2.0
 52	36	1.1
 23	13	-3.9
 18	9	0.6
 6	0	0.7
--- 4:1 ---
 63	57	2.5
 62	53	2.8
 61	49	2.5
 57	39	1.9
 54	33	2.8
 52	30	1.4
 44	21	0.7
 43	20	0.7
 22	10	-2.6
 16	4	-1.4
 15	3	-3.6
--- 5:1 ---
 63	55	2.8
 62	50	2.9
 60	43	2.6
 54	29	1.4
 48	22	1.0
 39	16	0.6
 37	15	0.4
 14	1	0.3
--- 6:1 ---
 63	53	3.3
--- 7:1 ---
 63	51	3.2
 62	45	3.6
 58	31	3.0
 49	19	1.4
 38	13	0.6
 25	6	3.4
 21	4	5.0
--- 8:1 ---
 63	49	3.5
 61	39	3.4
 51	19	1.7
 44	15	-4.5
 29	7	-3.3
 27	6	1.4
 15	0	-3.5
--- 9:1 ---
 62	42	3.7
 38	11	0.4
 31	7	-1.1
 29	6	-0.5
 25	4	-2.9
--- 3:2 ---
 63	62	0.5
 61	59	-0.3
 59	56	1.6
 57	53	0.8
 55	50	0.7
 51	45	1.0
 22	18	4.0
 6	3	0.6
--- 5:2 ---
 63	60	1.6
 61	55	1.8
 59	50	2.8
 55	43	1.4
 38	22	0.4
 24	15	0.1
--- 7:2 ---
 63	58	1.7
 61	51	2.1
 59	45	3.4
 51	31	1.6
 39	19	0.5
 17	6	3.3
--- 9:2 ---
 63	56	2.2
 59	42	3.6
 35	15	-2.2
 32	14	2.7
 22	9	4.7
 17	4	-3.0
--- 4:3 ---
 62	61	0.5
 59	57	1.8
 56	53	1.1
 53	49	0.2
 39	34	-4.7
 36	30	0.2
--- 5:3 ---
 62	60	1.1
 59	55	2.1
 56	50	1.2
 50	43	0.8
 29	21	-3.5
 26	19	-2.8
 22	17	-2.2
 18	14	3.2
--- 7:3 ---
 62	58	1.2
 59	51	2.5
 56	45	1.9
 45	31	0.6
 38	23	4.5
 34	20	0.8
 23	15	-3.4
--- 8:3 ---
 62	57	2.0
 59	49	2.8
 53	39	1.0
 49	34	-3.8
 43	26	-4.5
 39	22	4.4
 23	14	-1.3
 15	6	-4.2
 14	5	-0.9
--- 5:4 ---
 61	60	0.6
 57	55	0.3
 53	50	0.1
 36	31	-4.9
 33	29	-1.4
 11	9	4.7
--- 7:4 ---
 61	58	0.7
 57	51	0.6
 53	45	0.8
 43	33	-3.8
--- 9:4 ---
 61	56	1.2
 53	42	0.9
 47	34	-1.9
 44	30	-4.1
 35	21	3.0
 25	16	-1.4
--- 6:5 ---
 60	59	-0.9
 55	53	0.5
 38	35	-4.8
 36	32	-4.2
 35	31	4.3
 25	22	2.4
 2	1	4.9
--- 7:5 ---
 60	58	0.1
 55	51	0.3
 50	45	0.6
 37	30	-3.6
--- 8:5 ---
 60	57	0.9
 55	49	0.7
 44	37	-4.9
 23	18	-4.6
 20	16	0.0
 13	9	0.0
--- 9:5 ---
 60	56	0.6
 50	42	0.8
 41	30	4.1
 35	24	-2.3
 33	23	1.1
 32	22	-4.5
 27	19	-3.4
 23	17	1.6
 14	9	-2.6
--- 7:6 ---
 59	58	1.0
 53	51	-0.2
 41	38	-4.9
 32	29	-3.0
 23	21	1.8
--- 8:7 ---
 58	57	0.8
 51	49	0.4
 42	40	-4.5
 38	36	-3.6
 35	32	-2.9
 34	31	0.2
 27	25	-1.9
 15	14	2.0
 10	8	-0.3
 5	4	4.2
--- 9:7 ---
 58	56	0.5
 45	42	0.2
 43	39	4.6
 39	35	3.6
 38	33	-4.8
 34	29	2.4
 30	26	-2.2
 29	25	-3.9
 15	13	-0.6
 14	12	4.0
 13	11	-0.2
--- 9:8 ---
 57	56	-0.3
 36	33	-1.3
 31	29	2.2
 29	27	-2.0
 20	19	4.4
 17	16	-1.5
 14	13	-2.6
 7	6	2.8

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eli+w3@cs.cmu.edu

19 Jan 2002