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

· Skip 4, 3-13 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.

5-base · 7-base · 9-base · 11-base · 13-base

3-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
3-47
1	3	1:1	1	0.00	-111.52	-112	36
2	27	9:8	1.125	203.91	-7.61	-8	204
3	7	7:6	1.166666667	266.87	-44.65	-45	63
4	15	5:4	1.25	386.31	-25.21	-25	119
5	31	31:24	1.291666667	443.08	-68.44	-68	57
6	35	35:24	1.458333333	653.18	41.66	42	210
7	19	19:12	1.583333333	795.56	84.04	84	142
8	39	13:8	1.625	840.53	29.01	29	45
9	43	43:24	1.791666667	1009.56	98.04	98	169
10	11	11:6	1.833333333	1049.36	37.84	38	40
11	23	23:12	1.916666667	1126.32	14.80	15	77
12	47	47:24	1.958333333	1163.55	-47.97	-48	37
				1200.00

3-base · 7-base · 9-base · 11-base · 13-base

5-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
5-49
1	5	1:1	1	0.00	47.13	47	135
2	41	41:40	1.025	42.75	-10.12	-10	43
3	21	21:20	1.05	84.47	-68.41	-68	42
4	45	9:8	1.125	203.91	-48.96	-49	119
5	49	49:40	1.225	351.34	-1.54	-2	147
6	25	5:4	1.25	386.31	-66.56	-67	35
7	13	13:10	1.3	454.21	-98.66	-99	68
8	29	29:20	1.45	643.26	-9.61	-10	189
9	33	33:20	1.65	866.96	114.09	114	224
10	17	17:10	1.7	918.64	65.77	66	52
11	9	9:5	1.8	1017.60	64.72	65	99
12	37	37:20	1.85	1065.03	12.16	12	47
				1200.00

3-base · 5-base · 9-base · 11-base · 13-base

7-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
7-51
1	7	1:1	1	0.00	-53.40	-53	63
2	15	15:14	1.071428571	119.44	-33.95	-34	119
3	31	31:28	1.107142857	176.21	-77.19	-77	57
4	35	5:4	1.25	386.31	32.92	33	210
5	19	19:14	1.357142857	528.69	75.29	75	142
6	39	39:28	1.392857143	573.66	20.26	20	45
7	43	43:28	1.535714286	742.69	89.30	89	169
8	11	11:7	1.571428571	782.49	29.10	29	40
9	23	23:14	1.642857143	859.45	6.05	6	77
10	47	47:28	1.678571429	896.68	-56.71	-57	37
11	51	51:28	1.821428571	1038.08	-15.31	-15	141
12	27	27:14	1.928571429	1137.04	-16.36	-16	99
				1200.00

3-base · 5-base · 7-base · 11-base · 13-base

9-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
9-53
1	9	1:1	1	0.00	31.12	31	99
2	37	37:36	1.027777778	47.43	-21.44	-21	47
3	41	41:36	1.138888889	225.15	56.28	56	178
4	21	7:6	1.166666667	266.87	-2.01	-2	42
5	45	5:4	1.25	386.31	17.44	17	119
6	49	49:36	1.361111111	533.74	64.87	65	147
7	25	25:18	1.388888889	568.72	-0.16	0	35
8	13	13:9	1.444444444	636.62	-32.26	-32	68
9	53	53:36	1.472222222	669.59	-99.28	-99	33
10	29	29:18	1.611111111	825.67	-43.21	-43	156
11	33	11:6	1.833333333	1049.36	80.49	80	224
12	17	17:9	1.888888889	1101.05	32.17	32	52
				1200.00

3-base · 5-base · 7-base · 9-base · 13-base

11-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
11-55
1	11	1:1	1	0.00	31.70	32	40
2	23	23:22	1.045454545	76.96	8.65	9	77
3	47	47:44	1.068181818	114.19	-54.12	-54	37
4	51	51:44	1.159090909	255.59	-12.71	-13	141
5	27	27:22	1.227272727	354.55	-13.76	-14	99
6	55	5:4	1.25	386.31	-81.99	-82	32
7	15	15:11	1.363636364	536.95	-31.35	-31	151
8	31	31:22	1.409090909	593.72	-74.59	-75	57
9	35	35:22	1.590909091	803.82	35.52	36	210
10	19	19:11	1.727272727	946.20	77.89	78	142
11	39	39:22	1.772727273	991.16	22.86	23	45
12	43	43:22	1.954545455	1160.20	91.90	92	169
				1200.00

3-base · 5-base · 7-base · 9-base · 11-base

13-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
13-57
1	13	1:1	1	0.00	-5.56	-6	68
2	53	53:52	1.019230769	32.98	-72.58	-73	33
3	57	57:52	1.096153846	158.94	-46.61	-47	126
4	29	29:26	1.115384615	189.05	-116.51	-117	30
5	33	33:26	1.269230769	412.75	7.19	7	224
6	17	17:13	1.307692308	464.43	-41.13	-41	52
7	37	37:26	1.423076923	610.82	5.26	5	146
8	41	41:26	1.576923077	788.53	82.98	83	178
9	21	21:13	1.615384615	830.25	24.70	25	42
10	45	45:26	1.730769231	949.70	44.14	44	119
11	49	49:26	1.884615385	1097.12	91.57	92	147
12	25	25:13	1.923076923	1132.10	26.54	27	35
				1200.00

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