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

· Skip 4, 15-25 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.

17-base · 19-base · 21-base · 23-base · 25-base

15-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
15-59
1	15	1:1	1	0.00	-55.67	-56	29
2	31	31:30	1.033333333	56.77	-98.91	-99	57
3	35	7:6	1.166666667	266.87	11.20	11	210
4	19	19:15	1.266666667	409.24	53.57	54	142
5	39	13:10	1.3	454.21	-1.46	-1	45
6	43	43:30	1.433333333	623.25	67.57	68	169
7	23	23:15	1.533333333	740.01	84.33	84	117
8	47	47:30	1.566666667	777.24	21.56	22	37
9	51	17:10	1.7	918.64	62.97	63	141
10	27	9:5	1.8	1017.60	61.92	62	99
11	55	11:6	1.833333333	1049.36	-6.31	-6	32
12	59	59:30	1.966666667	1170.90	15.23	15	122
				1200.00

15-base · 19-base · 21-base · 23-base · 25-base

17-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
17-61
1	17	1:1	1	0.00	-64.16	-64	52
2	37	37:34	1.088235294	146.39	-17.77	-18	146
3	41	41:34	1.205882353	324.11	59.95	60	178
4	21	21:17	1.235294118	365.83	1.67	2	42
5	45	45:34	1.323529412	485.27	21.11	21	119
6	49	49:34	1.441176471	632.70	68.54	69	147
7	25	25:17	1.470588235	667.67	3.51	4	35
8	53	53:34	1.558823529	768.55	4.39	4	101
9	57	57:34	1.676470588	894.51	30.36	30	126
10	29	29:17	1.705882353	924.62	-39.54	-40	30
11	61	61:34	1.794117647	1011.93	-52.23	-52	87
12	33	33:17	1.941176471	1148.32	-15.84	-16	136
				1200.00

15-base · 17-base · 21-base · 23-base · 25-base

19-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
19-63
1	19	1:1	1	0.00	28.53	29	142
2	39	39:38	1.026315789	44.97	-26.50	-26	45
3	43	43:38	1.131578947	214.00	42.54	43	169
4	23	23:19	1.210526316	330.76	59.29	59	117
5	47	47:38	1.236842105	367.99	-3.48	-3	37
6	51	51:38	1.342105263	509.40	37.93	38	141
7	27	27:19	1.421052632	608.35	36.88	37	99
8	55	55:38	1.447368421	640.12	-31.35	-31	32
9	59	59:38	1.552631579	761.66	-9.81	-10	122
10	31	31:19	1.631578947	847.52	-23.95	-24	86
11	63	63:38	1.657894737	875.22	-96.25	-96	28
12	35	35:19	1.842105263	1057.63	-13.84	-14	182
				1200.00

15-base · 17-base · 19-base · 23-base · 25-base

21-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
21-65
1	21	1:1	1	0.00	18.18	18	42
2	45	15:14	1.071428571	119.44	37.62	38	119
3	49	7:6	1.166666667	266.87	85.05	85	147
4	25	25:21	1.19047619	301.85	20.02	20	35
5	53	53:42	1.261904762	402.72	20.90	21	101
6	57	19:14	1.357142857	528.69	46.86	47	126
7	29	29:21	1.380952381	558.80	-23.03	-23	30
8	61	61:42	1.452380952	646.10	-35.72	-36	87
9	65	65:42	1.547619048	756.06	-25.76	-26	110
10	33	11:7	1.571428571	782.49	-99.33	-99	26
11	37	37:21	1.761904762	980.56	-1.26	-1	198
12	41	41:21	1.952380952	1158.28	76.46	76	178
				1200.00

15-base · 17-base · 19-base · 21-base · 25-base

23-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
23-67
1	23	1:1	1	0.00	77.48	77	117
2	47	47:46	1.02173913	37.23	14.71	15	37
3	51	51:46	1.108695652	178.64	56.11	56	141
4	27	27:23	1.173913043	277.59	55.07	55	99
5	55	55:46	1.195652174	309.36	-13.17	-13	32
6	59	59:46	1.282608696	430.90	8.37	8	122
7	31	31:23	1.347826087	516.76	-5.76	-6	86
8	63	63:46	1.369565217	544.46	-78.06	-78	28
9	67	67:46	1.456521739	651.03	-71.49	-71	107
10	35	35:23	1.52173913	726.87	-95.66	-96	76
11	39	39:23	1.695652174	914.21	-8.32	-8	187
12	43	43:23	1.869565217	1083.24	60.72	61	169
				1200.00

15-base · 17-base · 19-base · 21-base · 23-base

25-base, Skip 4
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
25-69
1	25	1:1	1	0.00	38.40	38	35
2	53	53:50	1.06	100.88	39.28	39	101
3	57	57:50	1.14	226.84	65.24	65	126
4	29	29:25	1.16	256.95	-4.65	-5	30
5	61	61:50	1.22	344.26	-17.34	-17	87
6	65	13:10	1.3	454.21	-7.38	-7	110
7	33	33:25	1.32	480.65	-80.95	-81	26
8	69	69:50	1.38	557.60	-103.99	-104	77
9	37	37:25	1.48	678.72	-82.88	-83	121
10	41	41:25	1.64	856.43	-5.16	-5	178
11	45	9:5	1.8	1017.60	56.00	56	161
12	49	49:25	1.96	1165.02	103.43	103	147
				1200.00

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