Harmonic Series Tunings: Simple Skip-sets

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A. Rational Tunings

· Prime Limit

· Harmonic Series

· Simple Skip-sets

· Skip 2, 5-15 base

· Skip 2, 17-27 base

· Skip 3, 2-20 base

· Skip 3, 22-29 base

· Skip 3, 31-38 base

· Saturated Ratios

· Tetrachords

· Septimal Chromatic

· Hexanies

B. Equal Temperaments

· Octave Repeating

· Non-octave Repeating

· 88c

C. Non-Equal, Non-Rational

· Golden Horagramic

· Lucy Tuning™

· 2pi Roots

A red number in the Rounded Tuning Table column flags it as beyond the +/-99 cent limit set by some hardware synthesizer tuning tables.

23-base · 25-base · 26-base · 28-base · 29-base

22-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
22-55
1	22	1:1	1	0.00	48.32	48	40
2	46	23:22	1.045454545	76.96	25.27	25	77
3	49	49:44	1.113636364	186.33	34.65	35	109
4	25	25:22	1.136363636	221.31	-30.37	-30	35
5	52	13:11	1.181818182	289.21	-62.47	-62	68
6	55	5:4	1.25	386.31	-65.37	-65	97
7	28	14:11	1.272727273	417.51	-134.18	-134	31
8	31	31:22	1.409090909	593.72	-57.97	-58	176
9	34	17:11	1.545454545	753.64	1.95	2	160
10	37	37:22	1.681818182	900.03	48.34	48	146
11	40	20:11	1.818181818	1035.00	83.31	83	135
12	43	43:22	1.954545455	1160.20	108.52	109	125
				1200.00

22-base · 25-base · 26-base · 28-base · 29-base

23-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
23-56
1	23	1:1	1	0.00	77.28	77	77
2	47	47:46	1.02173913	37.23	14.52	15	37
3	50	25:23	1.086956522	144.35	21.64	22	107
4	26	26:23	1.130434783	212.25	-10.46	-10	68
5	53	53:46	1.152173913	245.23	-77.49	-77	33
6	56	28:23	1.217391304	340.55	-82.16	-82	95
7	29	29:23	1.260869565	401.30	-121.41	-121	61
8	32	32:23	1.391304348	571.73	-50.99	-51	170
9	35	35:23	1.52173913	726.87	4.15	4	155
10	38	38:23	1.652173913	869.24	46.52	47	142
11	41	41:23	1.782608696	1000.79	78.07	78	132
12	44	44:23	1.913043478	1123.04	100.33	100	122
				1200.00

22-base · 23-base · 26-base · 28-base · 29-base

25-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
25-58
1	25	1:1	1	0.00	29.77	30	35
2	52	26:25	1.04	67.90	-2.33	-2	68
3	55	11:10	1.1	165.00	-5.23	-5	97
4	28	28:25	1.12	196.20	-74.03	-74	31
5	58	29:25	1.16	256.95	-113.28	-113	61
6	31	31:25	1.24	372.41	-97.82	-98	115
7	34	34:25	1.36	532.33	-37.90	-38	160
8	37	37:25	1.48	678.72	8.49	8	146
9	40	8:5	1.6	813.69	43.46	43	135
10	43	43:25	1.72	938.89	68.66	69	125
11	46	46:25	1.84	1055.65	85.42	85	117
12	49	49:25	1.96	1165.02	94.79	95	109
				1200.00

22-base · 23-base · 25-base · 28-base · 29-base

26-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
26-59
1	26	1:1	1	0.00	53.63	54	68
2	53	53:52	1.019230769	32.98	-13.39	-13	33
3	56	14:13	1.076923077	128.30	-18.07	-18	95
4	29	29:26	1.115384615	189.05	-57.32	-57	61
5	59	59:52	1.134615385	218.64	-127.73	-128	30
6	32	16:13	1.230769231	359.47	-86.90	-87	141
7	35	35:26	1.346153846	514.61	-31.76	-32	155
8	38	19:13	1.461538462	656.99	10.62	11	142
9	41	41:26	1.576923077	788.53	42.16	42	132
10	44	22:13	1.692307692	910.79	64.42	64	122
11	47	47:26	1.807692308	1024.98	78.61	79	114
12	50	25:13	1.923076923	1132.10	85.73	86	107
				1200.00

22-base · 23-base · 25-base · 26-base · 29-base

28-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
28-61
1	28	1:1	1	0.00	25.00	25	31
2	58	29:28	1.035714286	60.75	-14.25	-14	61
3	61	61:56	1.089285714	148.06	-26.94	-27	87
4	31	31:28	1.107142857	176.21	-98.79	-99	28
5	34	17:14	1.214285714	336.13	-38.87	-39	160
6	37	37:28	1.321428571	482.52	7.52	8	146
7	40	10:7	1.428571429	617.49	42.49	42	135
8	43	43:28	1.535714286	742.69	67.69	68	125
9	46	23:14	1.642857143	859.45	84.45	84	117
10	49	49:28	1.75	968.83	93.83	94	109
11	52	13:7	1.857142857	1071.70	96.70	97	103
12	55	55:28	1.964285714	1168.81	93.81	94	97
				1200.00

22-base · 23-base · 25-base · 26-base · 28-base

29-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
29-62
1	29	1:1	1	0.00	53.63	54	61
2	59	59:58	1.017241379	29.59	-16.78	-17	30
3	62	31:29	1.068965517	115.46	-30.91	-31	86
4	32	32:29	1.103448276	170.42	-75.95	-76	55
5	35	35:29	1.206896552	325.56	-20.81	-21	155
6	38	38:29	1.310344828	467.94	21.57	22	142
7	41	41:29	1.413793103	599.49	53.12	53	132
8	44	44:29	1.517241379	721.74	75.37	75	122
9	47	47:29	1.620689655	835.93	89.56	90	114
10	50	50:29	1.724137931	943.05	96.68	97	107
11	53	53:29	1.827586207	1043.93	97.56	98	101
12	56	56:29	1.931034483	1139.25	92.88	93	95
				1200.00

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