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

32-base · 34-base · 35-base · 37-base · 38-base

31-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
31-64
1	31	1:1	1	0.00	-45.77	-46	28
2	64	32:31	1.032258065	54.96	-90.81	-91	55
3	34	34:31	1.096774194	159.92	-85.85	-86	105
4	37	37:31	1.193548387	306.31	-39.47	-39	146
5	40	40:31	1.290322581	441.28	-4.50	-4	135
6	43	43:31	1.387096774	566.48	20.71	21	125
7	46	46:31	1.483870968	683.24	37.46	37	117
8	49	49:31	1.580645161	792.62	46.84	47	109
9	52	52:31	1.677419355	895.49	49.72	50	103
10	55	55:31	1.774193548	992.60	46.82	47	97
11	58	58:31	1.870967742	1084.54	38.77	39	92
12	61	61:31	1.967741935	1171.85	26.08	26	87
				1200.00

31-base · 34-base · 35-base · 37-base · 38-base

32-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
32-65
1	32	1:1	1	0.00	-25.71	-26	55
2	65	65:64	1.015625	26.84	-98.87	-99	27
3	35	35:32	1.09375	155.14	-70.57	-71	128
4	38	19:16	1.1875	297.51	-28.20	-28	142
5	41	41:32	1.28125	429.06	3.35	3	132
6	44	11:8	1.375	551.32	25.61	26	122
7	47	47:32	1.46875	665.51	39.79	40	114
8	50	25:16	1.5625	772.63	46.92	47	107
9	53	53:32	1.65625	873.50	47.79	48	101
10	56	7:4	1.75	968.83	43.11	43	95
11	59	59:32	1.84375	1059.17	33.46	33	90
12	62	31:16	1.9375	1145.04	19.32	19	86
				1200.00

31-base · 32-base · 35-base · 37-base · 38-base

34-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
34-67
1	34	1:1	1	0.00	-97.04	-97	26
2	37	37:34	1.088235294	146.39	-50.65	-51	146
3	40	20:17	1.176470588	281.36	-15.69	-16	135
4	43	43:34	1.264705882	406.56	9.52	10	125
5	46	23:17	1.352941176	523.32	26.28	26	117
6	49	49:34	1.441176471	632.70	35.65	36	109
7	52	26:17	1.529411765	735.57	38.53	39	103
8	55	55:34	1.617647059	832.68	35.63	36	97
9	58	29:17	1.705882353	924.62	27.58	28	92
10	61	61:34	1.794117647	1011.93	14.89	15	87
11	64	32:17	1.882352941	1095.04	-2.00	-2	83
12	67	67:34	1.970588235	1174.35	-22.69	-23	79
				1200.00

31-base · 32-base · 34-base · 37-base · 38-base

35-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
35-68
1	35	1:1	1	0.00	-82.32	-82	50
2	38	38:35	1.085714286	142.37	-39.95	-40	142
3	41	41:35	1.171428571	273.92	-8.40	-8	132
4	44	44:35	1.257142857	396.18	13.86	14	122
5	47	47:35	1.342857143	510.37	28.05	28	114
6	50	10:7	1.428571429	617.49	35.17	35	107
7	53	53:35	1.514285714	718.36	36.05	36	101
8	56	8:5	1.6	813.69	31.37	31	95
9	59	59:35	1.685714286	904.03	21.71	22	90
10	62	62:35	1.771428571	989.90	7.58	8	86
11	65	13:7	1.857142857	1071.70	-10.62	-11	82
12	68	68:35	1.942857143	1149.82	-32.50	-33	78
				1200.00

31-base · 32-base · 34-base · 35-base · 38-base

37-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
37-70
1	37	1:1	1	0.00	-54.84	-55	96
2	40	40:37	1.081081081	134.97	-19.87	-20	135
3	43	43:37	1.162162162	260.17	5.34	5	125
4	46	46:37	1.243243243	376.93	22.09	22	117
5	49	49:37	1.324324324	486.31	31.47	31	109
6	52	52:37	1.405405405	589.18	34.35	34	103
7	55	55:37	1.486486486	686.29	31.45	31	97
8	58	58:37	1.567567568	778.23	23.40	23	92
9	61	61:37	1.648648649	865.54	10.70	11	87
10	64	64:37	1.72972973	948.66	-6.18	-6	83
11	67	67:37	1.810810811	1027.96	-26.87	-27	79
12	70	70:37	1.891891892	1103.80	-51.04	-51	76
				1200.00

31-base · 32-base · 34-base · 35-base · 37-base

38-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
38-71
1	38	1:1	1	0.00	-41.99	-42	118
2	41	41:38	1.078947368	131.55	-10.44	-10	132
3	44	22:19	1.157894737	253.80	11.81	12	122
4	47	47:38	1.236842105	367.99	26.00	26	114
5	50	25:19	1.315789474	475.11	33.12	33	107
6	53	53:38	1.394736842	575.99	34.00	34	101
7	56	28:19	1.473684211	671.31	29.32	29	95
8	59	59:38	1.552631579	761.66	19.67	20	90
9	62	31:19	1.631578947	847.52	5.53	6	86
10	65	65:38	1.710526316	929.33	-12.66	-13	82
11	68	34:19	1.789473684	1007.44	-34.55	-35	78
12	71	71:38	1.868421053	1082.18	-59.81	-60	75
				1200.00

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