Conference napalm::commusic_v1

993.0. "Yamaha 4op FM Frequency Ratio Charts" by ECADSR::SHERMAN (Correct as always, King Friday ...) Tue Oct 27 1987 02:20

The following charts were taken off my TX81Z and are more 'complete'
charts than what's in note 819.  Mostly, I found myself trying to get
a particular frequency ratio and couldn't get exactly what I wanted
very easily.  So, I made the charts.

Using either chart, the way to get the ratio you want is to decrement
the coarse and fine adjustments down to 0.50 (hold the decrement down
for a few seconds), then add the number of button pushes in coarse and fine 
to get to the desired ratio.  

This first chart is a 2-d array by increasing coarse (CRS) and fine
(FIN) adjustments.  The second is separated from the first by a line of
*'s, so do a search for * to get to the second chart.  The second chart 
has the same information as the first, but it is sorted by ascending ratio 
(RTO).  The second chart will probably be most useful if working from 
scratch.


CRS			FIN->
|
v 0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

0 0.50	0.56	0.62	0.68	0.75	0.81	0.87	0.93	-	-	-	-	-	-	-	-

1 0.71	0.79	0.88	0.96	1.05	1.14	1.23	1.32	-	-	-	-	-	-	-	-

2 0.78	0.88	0.98	1.07	1.17	1.27	1.37	1.47	-	-	-	-	-	-	-	-

3 0.87	0.97	1.08	1.18	1.29	1.40	1.51	1.62	-	-	-	-	-	-	-	-

4 1.00	1.06	1.12	1.18	1.25	1.31	1.37	1.43	1.50	1.56	1.62	1.68	1.75	1.81	1.87	1.93

5 1.41	1.49	1.58	1.67	1.76	1.85	1.93	2.02	2.11	2.20	2.29	2.37	2.46	2.55	2.64	2.73

6 1.57	1.66	1.76	1.86	1.96	2.06	2.15	2.25	2.35	2.45	2.55	2.64	2.74	2.84	2.94	3.04

7 1.73	1.83	1.94	2.05	2.16	2.27	2.37	2.48	2.59	2.70	2.81	2.91	3.02	3.13	3.24	3.35

8 2.00	2.06	2.12	2.18	2.25	2.31	2.37	2.43	2.50	2.56	2.62	2.68	2.75	2.81	2.87	2.93

9 2.82	2.90	2.99	3.08	3.17	3.26	3.34	3.43	3.52	3.61	3.70	3.78	3.87	3.96	4.05	4.14

10 3.00	3.06	3.12	3.18	3.25	3.31	3.37	3.43	3.50	3.56	3.62	3.68	3.75	3.81	3.87	3.93

11 3.14	3.23	3.33	3.43	3.53	3.63	3.72	3.82	3.92	4.02	4.12	4.21	4.31	4.41	4.51	4.61

12 3.46	3.56	3.67	3.78	3.89	4.00	4.10	4.21	4.32	4.43	4.54	4.64	4.75	4.86	4.97	5.08

13 4.00	4.06	4.12	4.18	4.25	4.31	4.37	4.43	4.50	4.56	4.62	4.68	4.75	4.81	4.87	4.93

14 4.24	4.31	4.40	4.49	4.58	4.67	4.75	4.84	4.93	5.02	5.11	5.19	5.28	5.37	5.46	5.55

15 4.71	4.80	4.90	5.00	5.10	5.20	5.29	5.39	5.49	5.59	5.69	5.78	5.88	5.98	6.08	6.18

16 5.00	5.06	5.12	5.18	5.25	5.31	5.37	5.43	5.50	5.56	5.62	5.68	5.75	5.81	5.87	5.93

17 5.19	5.29	5.40	5.51	5.62	5.73	5.83	5.94	6.05	6.16	6.27	6.37	6.48	6.59	6.70	6.81

18 5.65	5.72	5.81	5.90	5.99	6.08	6.16	6.25	6.34	6.43	6.52	6.60	6.69	6.78	6.87	6.96

19 6.00	6.06	6.12	6.18	6.25	6.31	6.37	6.43	6.50	6.56	6.62	6.68	6.75	6.81	6.87	6.93

20 6.28	6.37	6.47	6.57	6.67	6.77	6.86	6.96	7.06	7.16	7.26	7.35	7.45	7.55	7.65	7.75

21 6.92	7.02	7.13	7.24	7.35	7.46	7.56	7.67	7.78	7.89	8.00	8.10	8.21	8.32	8.43	8.54

22 7.00	7.06	7.12	7.18	7.25	7.31	7.37	7.43	7.50	7.56	7.62	7.68	7.75	7.81	7.87	7.93

23 7.07	7.13	7.22	7.31	7.40	7.49	7.57	7.66	7.75	7.84	7.93	8.01	8.10	8.19	8.28	8.37

24 7.85	7.94	8.04	8.14	8.24	8.34	8.43	8.53	8.63	8.73	8.83	8.92	9.02	9.12	9.22	9.32

25 8.00	8.06	8.12	8.18	8.25	8.31	8.37	8.43	8.50	8.56	8.62	8.68	8.75	8.81	8.87	8.93

26 8.48	8.54	8.63	8.72	8.81	8.90	8.98	9.07	9.16	9.25	9.34	9.42	9.51	9.60	9.69	9.78

27 8.65	8.75	8.86	8.97	9.08	9.19	9.29	9.40	9.51	9.62	9.73	9.83	9.94	10.05	10.16	10.27

28 9.00	9.06	9.12	9.18	9.25	9.31	9.37	9.43	9.50	9.56	9.62	9.68	9.75	9.81	9.87	9.93

29 9.42	9.51	9.61	9.71	9.81	9.91	10.00	10.10	10.20	10.30	10.40	10.49	10.59	10.69	10.79	10.89

30 9.89	9.95	10.04	10.13	10.22	10.31	10.39	10.48	10.57	10.66	10.75	10.83	10.92	11.01	11.10	11.19

31 10.00 10.06	10.12	10.18	10.25	10.31	10.37	10.43	10.50	10.56	10.62	10.68	10.75	10.81	10.87	10.93	

32 10.38 10.48	10.59	10.70	10.81	10.92	11.02	11.13	11.24	11.35	11.45	11,56	11.67	11.78	11.89	12.00	

33 10.99 11.08	11.18	11.28	11.38	11.48	11.57	11.67	11.77	11.87	11.97	12.06	12.16	12.26	12.36	12.46	

34 11.00 11.06	11.12	11.18	11.25	11.31	11.37	11.43	11.50	11.56	11.62	11.68	11.75	11.81	11.87	11.93	

35 11.30 11.36	11.45	11.54	11.63	11.72	11.80	11.89	11.98	12.07	12.16	12.24	12.33	12.42	12.51	12.60	

36 12.00 12.06	12.12	12.18	12.25	12.31	12.37	12.43	12.50	12.56	12.62	12.68	12.75	12.81	12.87	12.93	

37 12.11 12.21	12.32	12.43	12.54	12.65	12.75	12.86	12.97	13.08	13.19	13.29	13.40	13.51	13.62	13.73	

38 12.56 12.65	12.75	12.85	12.95	13.05	13.14	13.24	13.34	13.44	13.54	13.63	13.73	13.83	13.93	14.03	

39 12.72 12.77	12.86	12.95	13.04	13.13	13.21	13.30	13.39	13.48	13.57	13.65	13.74	13.83	13.92	14.01	

40 13.00 13.06	13.12	13.18	13.25	13.31	13.37	13.43	13.50	13.56	13.62	13.68	13.75	13.81	13.87	13.93	

41 13.84 13.94	14.05	14.16	14.27	14.38	14.48	14.59	14.70	14.81	14.92	15.02	15.13	15.24	15.35	15.46	

42 14.00 14.06	14.12	14.18	14.25	14.31	14.37	14.43	14.50	14.56	14.62	14.68	14.75	14.81	14.87	14.93	

43 14.10 14.18	14.27	14.36	14.45	14.54	14.62	14.71	14.80	14.89	14.98	15.06	15.15	15.24	15.33	15.42	

44 14.13 14.22	14.32	14.42	14.52	14.62	14.71	14.81	14.91	15.01	15.11	15.20	15.30	15.40	15.50	15.60	

45 15.00 15.06	15.12	15.18	15.25	15.31	15.37	15.43	15.50	15.56	15.62	15.68	15.75	15.81	15.87	15.93	

46 15.55 15.59	15.68	15.77	15.86	15.95	16.03	16.12	16.21	16.30	16.39	16.47	16.56	16.65	16.74	16.83	

47 15.57 15.67	15.78	15.89	16.00	16.11	16.21	16.32	16.43	16.54	16.65	16.75	16.86	16.97	17.08	17.19	

48 15.70 15.79	15.89	15.99	16.09	16.19	16.28	16.38	16.48	16.58	16.68	16.77	16.87	16.97	17.07	17.17	

49 16.96 17.00	17.09	17.18	17.27	17.36	17.44	17.53	17.62	17.71	17.80	17.88	17.97	18.06	18.15	18.24	

50 17.27 17.36	17.46	17.56	17.66	17.76	17.85	17.95	18.05	18.15	18.25	18.34	18.44	18.54	18.64	18.74	

51 17.30 17.40	17.51	17.62	17.73	17.84	17.94	18.05	18.16	18.27	18.38	18.48	18.59	18.70	18.81	18.92	

52 18.37 18.41	18.50	18.59	18.68	18.77	18.85	18.94	19.03	19.12	19.21	19.29	19.38	19.47	19.56	19.65	

53 18.84 18.93	19.03	19.13	19.23	19.33	19.42	19.52	19.62	19.72	19.82	19.91	20.01	20.11	20.21	20.31	

54 19.03 19.13	19.24	19.35	19.46	19.57	19.67	19.78	19.89	20.00	20.11	20.21	20.32	20.43	20.54	20.65	

55 19.78 19.82	19.91	20.00	20.09	20.18	20.26	20.35	20.44	20.53	20.62	20.70	20.79	20.88	20.97	21.06	

56 20.41 20.50	20.60	20.70	20.80	20.90	20.99	21.09	21.19	21.29	21.39	21.48	21.58	21.68	21.78	21.88	

57 20.76 20.86	20.97	21.08	21.19	21.30	21.40	21.51	21.62	21.73	21.84	21.94	22.05	22.16	22.27	22.38	

58 21.20 21.23	21.32	21.41	21.50	21.59	21.67	21.76	21.85	21.94	22.03	22.11	22.20	22.29	22.38	22.47	
 
59 21.98 22.07	22.17	22.27	22.37	22.47	22.56	22.66	22.76	22.86	22.96	23.05	23.15	23.25	23.35	23.45	

60 22.49 22.59	22.70	22.81	22.92	23.03	23.13	23.24	23.35	23.46	23.57	23.67	23.78	23.89	24.00	24.11	

61 23.55 23.64	23.74	23.84	23.94	24.04	24.13	24.23	24.33	24.43	24.53	24.62	24.72	24.82	24.92	25.02	

62 24.22 24.32	24.43	24.54	24.65	24.76	24.86	24.97	25.08	25.19	25.30	25.40	25.51	25.62	25.73	25.84	

63 25.95 26.05	26.16	26.27	26.38	26.49	26.59	26.70	26.81	26.92	27.03	27.13	27.24	27.35	27.46	27.57	

********************************************************************************

RTO	CRS	FIN

0.50	0	0
0.56	0	1
0.62	0	2
0.68	0	3
0.71	1	0
0.75	0	4
0.78	2	0
0.79	1	1
0.81	0	5
0.87	0	6
0.87	3	0
0.88	1	2
0.88	2	1
0.93	0	7
0.96	1	3
0.97	3	1
0.98	2	2
1.00	4	0
1.05	1	4
1.06	4	1
1.07	2	3
1.08	3	2
1.12	4	2
1.14	1	5
1.17	2	4
1.18	3	3
1.18	4	3
1.23	1	6
1.25	4	4
1.27	2	5
1.29	3	4
1.31	4	5
1.32	1	7
1.37	2	6
1.37	4	6
1.40	3	5
1.41	5	0
1.43	4	7
1.47	2	7
1.49	5	1
1.50	4	8
1.51	3	6
1.56	4	9
1.57	6	0
1.58	5	2
1.62	3	7
1.62	4	10
1.66	6	1
1.67	5	3
1.68	4	11
1.73	7	0
1.75	4	12
1.76	5	4
1.76	6	2
1.81	4	13
1.83	7	1
1.85	5	5
1.86	6	3
1.87	4	14
1.93	4	15
1.93	5	6
1.94	7	2
1.96	6	4
10.00	29	6
10.00	31	0
10.04	30	2
10.05	27	13
10.06	31	1
10.10	29	7
10.12	31	2
10.13	30	3
10.16	27	14
10.18	31	3
10.20	29	8
10.22	30	4
10.25	31	4
10.27	27	15
10.30	29	9
10.31	30	5
10.31	31	5
10.37	31	6
10.38	32	0
10.39	30	6
10.40	29	10
10.43	31	7
10.48	30	7
10.48	32	1
10.49	29	11
10.50	31	8
10.56	31	9
10.57	30	8
10.59	29	12
10.59	32	2
10.62	31	10
10.66	30	9
10.68	31	11
10.69	29	13
10.70	32	3
10.75	30	10
10.75	31	12
10.79	29	14
10.81	31	13
10.81	32	4
10.83	30	11
10.87	31	14
10.89	29	15
10.92	30	12
10.92	32	5
10.93	31	15
10.99	33	0
11,56	32	11
11.00	34	0
11.01	30	13
11.02	32	6
11.06	34	1
11.08	33	1
11.10	30	14
11.12	34	2
11.13	32	7
11.18	33	2
11.18	34	3
11.19	30	15
11.24	32	8
11.25	34	4
11.28	33	3
11.30	35	0
11.31	34	5
11.35	32	9
11.36	35	1
11.37	34	6
11.38	33	4
11.43	34	7
11.45	32	10
11.45	35	2
11.48	33	5
11.50	34	8
11.54	35	3
11.56	34	9
11.57	33	6
11.62	34	10
11.63	35	4
11.67	32	12
11.67	33	7
11.68	34	11
11.72	35	5
11.75	34	12
11.77	33	8
11.78	32	13
11.80	35	6
11.81	34	13
11.87	33	9
11.87	34	14
11.89	32	14
11.89	35	7
11.93	34	15
11.97	33	10
11.98	35	8
12.00	32	15
12.00	36	0
12.06	33	11
12.06	36	1
12.07	35	9
12.11	37	0
12.12	36	2
12.16	33	12
12.16	35	10
12.18	36	3
12.21	37	1
12.24	35	11
12.25	36	4
12.26	33	13
12.31	36	5
12.32	37	2
12.33	35	12
12.36	33	14
12.37	36	6
12.42	35	13
12.43	36	7
12.43	37	3
12.46	33	15
12.50	36	8
12.51	35	14
12.54	37	4
12.56	36	9
12.56	38	0
12.60	35	15
12.62	36	10
12.65	37	5
12.65	38	1
12.68	36	11
12.72	39	0
12.75	36	12
12.75	37	6
12.75	38	2
12.77	39	1
12.81	36	13
12.85	38	3
12.86	37	7
12.86	39	2
12.87	36	14
12.93	36	15
12.95	38	4
12.95	39	3
12.97	37	8
13.00	40	0
13.04	39	4
13.05	38	5
13.06	40	1
13.08	37	9
13.12	40	2
13.13	39	5
13.14	38	6
13.18	40	3
13.19	37	10
13.21	39	6
13.24	38	7
13.25	40	4
13.29	37	11
13.30	39	7
13.31	40	5
13.34	38	8
13.37	40	6
13.39	39	8
13.40	37	12
13.43	40	7
13.44	38	9
13.48	39	9
13.50	40	8
13.51	37	13
13.54	38	10
13.56	40	9
13.57	39	10
13.62	37	14
13.62	40	10
13.63	38	11
13.65	39	11
13.68	40	11
13.73	37	15
13.73	38	12
13.74	39	12
13.75	40	12
13.81	40	13
13.83	38	13
13.83	39	13
13.84	41	0
13.87	40	14
13.92	39	14
13.93	38	14
13.93	40	15
13.94	41	1
14.00	42	0
14.01	39	15
14.03	38	15
14.05	41	2
14.06	42	1
14.10	43	0
14.12	42	2
14.13	44	0
14.16	41	3
14.18	42	3
14.18	43	1
14.22	44	1
14.25	42	4
14.27	41	4
14.27	43	2
14.31	42	5
14.32	44	2
14.36	43	3
14.37	42	6
14.38	41	5
14.42	44	3
14.43	42	7
14.45	43	4
14.48	41	6
14.50	42	8
14.52	44	4
14.54	43	5
14.56	42	9
14.59	41	7
14.62	42	10
14.62	43	6
14.62	44	5
14.68	42	11
14.70	41	8
14.71	43	7
14.71	44	6
14.75	42	12
14.80	43	8
14.81	41	9
14.81	42	13
14.81	44	7
14.87	42	14
14.89	43	9
14.91	44	8
14.92	41	10
14.93	42	15
14.98	43	10
15.00	45	0
15.01	44	9
15.02	41	11
15.06	43	11
15.06	45	1
15.11	44	10
15.12	45	2
15.13	41	12
15.15	43	12
15.18	45	3
15.20	44	11
15.24	41	13
15.24	43	13
15.25	45	4
15.30	44	12
15.31	45	5
15.33	43	14
15.35	41	14
15.37	45	6
15.40	44	13
15.42	43	15
15.43	45	7
15.46	41	15
15.50	44	14
15.50	45	8
15.55	46	0
15.56	45	9
15.57	47	0
15.59	46	1
15.60	44	15
15.62	45	10
15.67	47	1
15.68	45	11
15.68	46	2
15.70	48	0
15.75	45	12
15.77	46	3
15.78	47	2
15.79	48	1
15.81	45	13
15.86	46	4
15.87	45	14
15.89	47	3
15.89	48	2
15.93	45	15
15.95	46	5
15.99	48	3
16.00	47	4
16.03	46	6
16.09	48	4
16.11	47	5
16.12	46	7
16.19	48	5
16.21	46	8
16.21	47	6
16.28	48	6
16.30	46	9
16.32	47	7
16.38	48	7
16.39	46	10
16.43	47	8
16.47	46	11
16.48	48	8
16.54	47	9
16.56	46	12
16.58	48	9
16.65	46	13
16.65	47	10
16.68	48	10
16.74	46	14
16.75	47	11
16.77	48	11
16.83	46	15
16.86	47	12
16.87	48	12
16.96	49	0
16.97	47	13
16.97	48	13
17.00	49	1
17.07	48	14
17.08	47	14
17.09	49	2
17.17	48	15
17.18	49	3
17.19	47	15
17.27	49	4
17.27	50	0
17.30	51	0
17.36	49	5
17.36	50	1
17.40	51	1
17.44	49	6
17.46	50	2
17.51	51	2
17.53	49	7
17.56	50	3
17.62	49	8
17.62	51	3
17.66	50	4
17.71	49	9
17.73	51	4
17.76	50	5
17.80	49	10
17.84	51	5
17.85	50	6
17.88	49	11
17.94	51	6
17.95	50	7
17.97	49	12
18.05	50	8
18.05	51	7
18.06	49	13
18.15	49	14
18.15	50	9
18.16	51	8
18.24	49	15
18.25	50	10
18.27	51	9
18.34	50	11
18.37	52	0
18.38	51	10
18.41	52	1
18.44	50	12
18.48	51	11
18.50	52	2
18.54	50	13
18.59	51	12
18.59	52	3
18.64	50	14
18.68	52	4
18.70	51	13
18.74	50	15
18.77	52	5
18.81	51	14
18.84	53	0
18.85	52	6
18.92	51	15
18.93	53	1
18.94	52	7
19.03	52	8
19.03	53	2
19.03	54	0
19.12	52	9
19.13	53	3
19.13	54	1
19.21	52	10
19.23	53	4
19.24	54	2
19.29	52	11
19.33	53	5
19.35	54	3
19.38	52	12
19.42	53	6
19.46	54	4
19.47	52	13
19.52	53	7
19.56	52	14
19.57	54	5
19.62	53	8
19.65	52	15
19.67	54	6
19.72	53	9
19.78	54	7
19.78	55	0
19.82	53	10
19.82	55	1
19.89	54	8
19.91	53	11
19.91	55	2
2.00	8	0
2.02	5	7
2.05	7	3
2.06	6	5
2.06	8	1
2.11	5	8
2.12	8	2
2.15	6	6
2.16	7	4
2.18	8	3
2.20	5	9
2.25	6	7
2.25	8	4
2.27	7	5
2.29	5	10
2.31	8	5
2.35	6	8
2.37	5	11
2.37	7	6
2.37	8	6
2.43	8	7
2.45	6	9
2.46	5	12
2.48	7	7
2.50	8	8
2.55	5	13
2.55	6	10
2.56	8	9
2.59	7	8
2.62	8	10
2.64	5	14
2.64	6	11
2.68	8	11
2.70	7	9
2.73	5	15
2.74	6	12
2.75	8	12
2.81	7	10
2.81	8	13
2.82	9	0
2.84	6	13
2.87	8	14
2.90	9	1
2.91	7	11
2.93	8	15
2.94	6	14
2.99	9	2
20.00	54	9
20.00	55	3
20.01	53	12
20.09	55	4
20.11	53	13
20.11	54	10
20.18	55	5
20.21	53	14
20.21	54	11
20.26	55	6
20.31	53	15
20.32	54	12
20.35	55	7
20.41	56	0
20.43	54	13
20.44	55	8
20.50	56	1
20.53	55	9
20.54	54	14
20.60	56	2
20.62	55	10
20.65	54	15
20.70	55	11
20.70	56	3
20.76	57	0
20.79	55	12
20.80	56	4
20.86	57	1
20.88	55	13
20.90	56	5
20.97	55	14
20.97	57	2
20.99	56	6
21.06	55	15
21.08	57	3
21.09	56	7
21.19	56	8
21.19	57	4
21.20	58	0
21.23	58	1
21.29	56	9
21.30	57	5
21.32	58	2
21.39	56	10
21.40	57	6
21.41	58	3
21.48	56	11
21.50	58	4
21.51	57	7
21.58	56	12
21.59	58	5
21.62	57	8
21.67	58	6
21.68	56	13
21.73	57	9
21.76	58	7
21.78	56	14
21.84	57	10
21.85	58	8
21.88	56	15
21.94	57	11
21.94	58	9
21.98	59	0
22.03	58	10
22.05	57	12
22.07	59	1
22.11	58	11
22.16	57	13
22.17	59	2
22.20	58	12
22.27	57	14
22.27	59	3
22.29	58	13
22.37	59	4
22.38	57	15
22.38	58	14
22.47	58	15
22.47	59	5
22.49	60	0
22.56	59	6
22.59	60	1
22.66	59	7
22.70	60	2
22.76	59	8
22.81	60	3
22.86	59	9
22.92	60	4
22.96	59	10
23.03	60	5
23.05	59	11
23.13	60	6
23.15	59	12
23.24	60	7
23.25	59	13
23.35	59	14
23.35	60	8
23.45	59	15
23.46	60	9
23.55	61	0
23.57	60	10
23.64	61	1
23.67	60	11
23.74	61	2
23.78	60	12
23.84	61	3
23.89	60	13
23.94	61	4
24.00	60	14
24.04	61	5
24.11	60	15
24.13	61	6
24.22	62	0
24.23	61	7
24.32	62	1
24.33	61	8
24.43	61	9
24.43	62	2
24.53	61	10
24.54	62	3
24.62	61	11
24.65	62	4
24.72	61	12
24.76	62	5
24.82	61	13
24.86	62	6
24.92	61	14
24.97	62	7
25.02	61	15
25.08	62	8
25.19	62	9
25.30	62	10
25.40	62	11
25.51	62	12
25.62	62	13
25.73	62	14
25.84	62	15
25.95	63	0
26.05	63	1
26.16	63	2
26.27	63	3
26.38	63	4
26.49	63	5
26.59	63	6
26.70	63	7
26.81	63	8
26.92	63	9
27.03	63	10
27.13	63	11
27.24	63	12
27.35	63	13
27.46	63	14
27.57	63	15
3.00	10	0
3.02	7	12
3.04	6	15
3.06	10	1
3.08	9	3
3.12	10	2
3.13	7	13
3.14	11	0
3.17	9	4
3.18	10	3
3.23	11	1
3.24	7	14
3.25	10	4
3.26	9	5
3.31	10	5
3.33	11	2
3.34	9	6
3.35	7	15
3.37	10	6
3.43	10	7
3.43	11	3
3.43	9	7
3.46	12	0
3.50	10	8
3.52	9	8
3.53	11	4
3.56	10	9
3.56	12	1
3.61	9	9
3.62	10	10
3.63	11	5
3.67	12	2
3.68	10	11
3.70	9	10
3.72	11	6
3.75	10	12
3.78	12	3
3.78	9	11
3.81	10	13
3.82	11	7
3.87	10	14
3.87	9	12
3.89	12	4
3.92	11	8
3.93	10	15
3.96	9	13
4.00	12	5
4.00	13	0
4.02	11	9
4.05	9	14
4.06	13	1
4.10	12	6
4.12	11	10
4.12	13	2
4.14	9	15
4.18	13	3
4.21	11	11
4.21	12	7
4.24	14	0
4.25	13	4
4.31	11	12
4.31	13	5
4.31	14	1
4.32	12	8
4.37	13	6
4.40	14	2
4.41	11	13
4.43	12	9
4.43	13	7
4.49	14	3
4.50	13	8
4.51	11	14
4.54	12	10
4.56	13	9
4.58	14	4
4.61	11	15
4.62	13	10
4.64	12	11
4.67	14	5
4.68	13	11
4.71	15	0
4.75	12	12
4.75	13	12
4.75	14	6
4.80	15	1
4.81	13	13
4.84	14	7
4.86	12	13
4.87	13	14
4.90	15	2
4.93	13	15
4.93	14	8
4.97	12	14
5.00	15	3
5.00	16	0
5.02	14	9
5.06	16	1
5.08	12	15
5.10	15	4
5.11	14	10
5.12	16	2
5.18	16	3
5.19	14	11
5.19	17	0
5.20	15	5
5.25	16	4
5.28	14	12
5.29	15	6
5.29	17	1
5.31	16	5
5.37	14	13
5.37	16	6
5.39	15	7
5.40	17	2
5.43	16	7
5.46	14	14
5.49	15	8
5.50	16	8
5.51	17	3
5.55	14	15
5.56	16	9
5.59	15	9
5.62	16	10
5.62	17	4
5.65	18	0
5.68	16	11
5.69	15	10
5.72	18	1
5.73	17	5
5.75	16	12
5.78	15	11
5.81	16	13
5.81	18	2
5.83	17	6
5.87	16	14
5.88	15	12
5.90	18	3
5.93	16	15
5.94	17	7
5.98	15	13
5.99	18	4
6.00	19	0
6.05	17	8
6.06	19	1
6.08	15	14
6.08	18	5
6.12	19	2
6.16	17	9
6.16	18	6
6.18	15	15
6.18	19	3
6.25	18	7
6.25	19	4
6.27	17	10
6.28	20	0
6.31	19	5
6.34	18	8
6.37	17	11
6.37	19	6
6.37	20	1
6.43	18	9
6.43	19	7
6.47	20	2
6.48	17	12
6.50	19	8
6.52	18	10
6.56	19	9
6.57	20	3
6.59	17	13
6.60	18	11
6.62	19	10
6.67	20	4
6.68	19	11
6.69	18	12
6.70	17	14
6.75	19	12
6.77	20	5
6.78	18	13
6.81	17	15
6.81	19	13
6.86	20	6
6.87	18	14
6.87	19	14
6.92	21	0
6.93	19	15
6.96	18	15
6.96	20	7
7.00	22	0
7.02	21	1
7.06	20	8
7.06	22	1
7.07	23	0
7.12	22	2
7.13	21	2
7.13	23	1
7.16	20	9
7.18	22	3
7.22	23	2
7.24	21	3
7.25	22	4
7.26	20	10
7.31	22	5
7.31	23	3
7.35	20	11
7.35	21	4
7.37	22	6
7.40	23	4
7.43	22	7
7.45	20	12
7.46	21	5
7.49	23	5
7.50	22	8
7.55	20	13
7.56	21	6
7.56	22	9
7.57	23	6
7.62	22	10
7.65	20	14
7.66	23	7
7.67	21	7
7.68	22	11
7.75	20	15
7.75	22	12
7.75	23	8
7.78	21	8
7.81	22	13
7.84	23	9
7.85	24	0
7.87	22	14
7.89	21	9
7.93	22	15
7.93	23	10
7.94	24	1
8.00	21	10
8.00	25	0
8.01	23	11
8.04	24	2
8.06	25	1
8.10	21	11
8.10	23	12
8.12	25	2
8.14	24	3
8.18	25	3
8.19	23	13
8.21	21	12
8.24	24	4
8.25	25	4
8.28	23	14
8.31	25	5
8.32	21	13
8.34	24	5
8.37	23	15
8.37	25	6
8.43	21	14
8.43	24	6
8.43	25	7
8.48	26	0
8.50	25	8
8.53	24	7
8.54	21	15
8.54	26	1
8.56	25	9
8.62	25	10
8.63	24	8
8.63	26	2
8.65	27	0
8.68	25	11
8.72	26	3
8.73	24	9
8.75	25	12
8.75	27	1
8.81	25	13
8.81	26	4
8.83	24	10
8.86	27	2
8.87	25	14
8.90	26	5
8.92	24	11
8.93	25	15
8.97	27	3
8.98	26	6
9.00	28	0
9.02	24	12
9.06	28	1
9.07	26	7
9.08	27	4
9.12	24	13
9.12	28	2
9.16	26	8
9.18	28	3
9.19	27	5
9.22	24	14
9.25	26	9
9.25	28	4
9.29	27	6
9.31	28	5
9.32	24	15
9.34	26	10
9.37	28	6
9.40	27	7
9.42	26	11
9.42	29	0
9.43	28	7
9.50	28	8
9.51	26	12
9.51	27	8
9.51	29	1
9.56	28	9
9.60	26	13
9.61	29	2
9.62	27	9
9.62	28	10
9.68	28	11
9.69	26	14
9.71	29	3
9.73	27	10
9.75	28	12
9.78	26	15
9.81	28	13
9.81	29	4
9.83	27	11
9.87	28	14
9.89	30	0
9.91	29	5
9.93	28	15
9.94	27	12
9.95	30	1

Geez, I didn't realize that the TZ had this capability.  The 4-op DX's only
provide for "course" adjustment.  The "fine" adjustment must be linked in some
way to the "alternate tuning" capabilities of the beast.

Todd.

    Actually, if by 'alternate tuning' you are referring to scaling,
    that's a whole 'nuther feature.  Has more to do with how the keyboard
    input is interpreted and is separately programmable for each voice.  
    For example, most stuff is octavian scaled, but other scaling is available.
    I'm not real familiar with this, yet. It seems to be a feature of
    the later Yamaha stuff.  I can provide more details if there is interest.
    
    The next thing I plan to do is go through all the voices and figure
    out what they are doing to some small extent.  For example, I plan
    to see about grouping voices by algorithm, frequency ratios and 
    operator amplitudes.  I should be able to develop some general 
    guidelines for how to generate voice patches from scratch.  I 
    just don't feel right about paying somebody $20+ for patches ...
    Naturally, I'll keep you folks posted.
    
    Steve

    There are some terms being bandied about here that are bound to
    cause some confusion....
    
    The CRS and FIN parameters on the TZ allow you to set the frequency
    of the operator as a function of 440 hz. This is what the DX line
    does. The TZ expands on it by use of the FIN parameter, allowing
    you to tweak the ratio of any operator. Note that the increments
    of fine change size as a function of the coarse setting. A low
    (say, 1.00) CRS setting allows small adjustments via FIN. As the
    CRS frequency increases so does the size of the FIN steps.

    Do not confuse the frequency of an operator with the frequency
    of a note. They be different beasts.
    
    Scaling is refered to by Yamaha as the ability to vary the output
    of an operator as a function of what note is played. This is used
    to simulate the differences in timbre an instrument displays at
    opposing ends of it's range. It has nothing to do with common or
    alternative tunings.
    
    The alternative tuning function of the TZ defines what frequency
    a key will produce when pressed. The equal-tempered tuning we all
    know and love divides 1200 cents (1 octave) into 12 equal steps
    of 100 cents each. The alternative tuning allows you to define
    these steps to any size you want. They do not have to be equal.
    For example, I've taken an octave and defined each key to be
    1/12 of the distance between it and a reference key....
    
    Sounds horrible, but I can do it....
    
    Edd
    
                

    Yeah, there may be some confusion in terms.  I'm trying to follow
    Yamaha's definitions.  The CRS and FIN adjustments for the TZ 
    are in either FIX or RTO mode for each operator.  In FIX you get control 
    over a fixed frequency, and with RTO the control is based on frequency 
    that can be varied from the keyboard (based on the 440 Hz A).  Turns 
    out that even this can be diddled with using detune, master tune
    and transpose settings.  

    By selecting FIX mode, you can pick one frequency for an operator
    and adjust it using CRS and FIN.  The manual shows that in this
    mode the CRS and FIN tend to operate a bit more intuitively than
    in RTO mode.  For that reason, I haven't done any charting with 
    operators in FIX mode.

    I don't remember offhand what all is included in the set of
    adjustments that Yamaha refers to as 'scaling'.  But, there is a 
    'scale' control for the voice patch, the default being octavian.
    I haven't played with this much, yet.
    
    Hey, all my stuff is at home ...
        
    Steve

    The scaling parameters are 'rate' and 'level'.
    
    I did some diddling with FIX and RTO over the weekend. They may
    not be as mutually exclusive as we suspect. Setting the FIX RANGE
    seems to have an effect on what RTO values are available. More
    on this as I figure it out.
    
    Aren't the alternative tuning parameters refered to as MICROTUNE?
    
    What a beast to work with. The DX-21 programmer module makes it
    *almost* bearable....;^)
    
    Edd

    Hmmm.  I'll have to check on that idea about the RTO values changing
    with the FIX frequency.  The values in this chart were calculated
    with FIX frequency set to 255 Hz.  If they change with the FIX
    frequency, I may need to generate more charts >:(.  Too bad I can't
    just do it via algorithm.  But, the good side may be that it will
    be possible to get almost any frequency ratio.  Or, this may be
    a cover problem:  a subset of FIX frequencies may result in complete
    coverege of all possible frequency ratios.  I'll check into it tonight.
     
    FWIW - The TZ really is a beast.  In addition to it being FM, there
    are those extra waveforms, making it tough to master.  But, I don't
    think anyone doubts that it has all kinds of potential.  I feel that
    if the thing can be mastered, the results will make the presets look 
    pretty lame and the sounds will rival the best stuff out there,
    i.e.; I won't be as tempted to pick up a D-50 or a sampler or anything 
    else that happens to come along.  I sometimes get the
    feeling that we get so interested in the new hardware that we don't
    take the time to realize much of the potential of the current stuff.
    
    Steve

    
    
    Steve
        

    re: .-1  You got it.  The biggest problem with the yamaha stuff
    is the damned inaccessability of all the parameters (the TZ must
    be at least three orders of magnitude worse in this respect than
    the DX7)
    
    Is there any method to that huge frequency chart's madness?
    
    The DX7 has coarse and fine frequency adjustments.  When in ratio
    mode, the fine adds increments of .01 times the coarse value.
    
    So if your coarse frequency is set to 1.0, then each increment of
    the fine frequency adds .1 to the frequency.
    
    It works the same for fixed operators.  If your coarse frequency
    is 100.0Hz, then each increment adds 1Hz.
    
    There has got to be an algorithm for the TZ, because it would be a
    waste of memory (not to mention programming effort) to have a table of
    all those values!  (Of course, I've been wrong before)
    
                     
    Steph
     

    
    I recieved a Yamaha technical paper that explains the relation between
    coarse freq. step and fine freq. step. I don't know much about the
    TZ but I will write some data from the paper if you want to. It's 
    something about chorus effects and the ear resonances. 
    
    I passed by .0 and figure out the same thought of Steph... Why not
    an algorithm?
    
    Anyway, have fun extracting then 1100 lines of .0
    
    
    Orlando

    Actually I'm only half right.  The ratioed stuff is correct, but I must
    have been halucinating pretty bad the day I played with the fixed
    frequency stuff.
    
    Its real algorithm is as follows: 
    
    f_fixed = 10 ^ f_coarse_index * (1/100) ^ f_fine_index
    
    f_coarse_index and f_fine_index are the numeric internal
    representations of these parameters.  That is, the f_coarse on a
    DX7 has 4 discrete values (1, 10, 100, 1000)>  The f_fine has 100
    discrete values.
    
    I'm sure the TZs is similar (but I'm too lazy to actually check
    your data).  Perhaps  the TZ has a different number of internal
    steps for the fine parameter, in which case the exponential base
    should be (1/n) where n is the number of steps.
    
    I derived the formula based on simple number theory.  I dunno about
    chorusing and psycho-acoustics....  (even though the fields are
    related).
    
    Steph

    Well, I've diddled with the FIX frequencies and have observed no
    variations form the chart.  If any deviation is observed, I'd
    appreciate having it pointed out. 
    
    Looking into my manual, 'scaling' allows setting of rate scaling
    (basically controls how much higher range notes get faster attack
    and decay, more like acoustic instruments) and level scaling (controls
    how much higher range notes get lower sustain values, again to emulate
    acoustic instruments).  Note that this 'scaling' is done for each
    operator in a voice.
    
    As far as the 'other' kind of scale, each voice can have microtuning.
    There are 11 preset scales and 2 user-programmable.  The 11 preset
    scales are:
    
    	1. Equal
    	2. Pure (major)
    	3. Pure (minor)
    	4. Mean tone
    	5. Pythagorean
    	6. Werckmeister
    	7. Kirnberger
    	8. Vallotti & Young
    	9. 1/4 Shift Equal
    	10. 1/4 Tone
    	11. 1/8 Tone
    
    You can use one of these to start and then diddle with the tuning
    of each note between C#-1 and C7 (the full range of the instrument).
    The result can then be saved in one of the user-programmable slots.
    Pretty powerful stuff, but I haven't played with it much, yet.
    
    As far as FIX mode goes, after the select frequency is chosen for
    an operator, CRS steps from a lower to an upper limit in chunks
    and FIN steps with smaller units.  So, it is more intuitive than
    in RTO mode.  There could well be an algorithm, but if I have the
    chart, I don't need the algorithm to set up a particular ratio.
    
    Now... on to tearing apart the presets!

    
    Steve
    

    I bungled it again.  (I must have been falling asleep):
    
    
    	f_fixed = 10 ^ (f_coarse_index + (f_fine_index/100))
    
    f_coarse_index = 0-3   f_fine_index = 0-99.
    
    
    You want a formula because you are going to write a patch editor
    for your favorite computer, and you don't want to type all that
    stuff in.  (Still, I'm impressed.)
    
    Steph
    

Geez, now if we could just figure out the FM math behind operator four's
feedback capabilities.  If we had this, I could model an entire 4-op
patch at any given point in time, and plot the waveform accordingly.

You every seen operator 4's output on a scope with the feedback cranked
up to 7?  Yuck!

Todd.

    Yeah, it gets very bushy.  I think what's happening is that it starts
    wrapping around the FM sine table and therefore starts jumping.
    	
    I learned a lot just playing with the DX100 and a scope.