Harmonic Series Tunings: Simple Skip-sets

dreamy piano keyboard

DAVID'S HOME PAGE

TUNING PAGES MENU

A. Rational Tunings

· Prime Limit

· Harmonic Series

· Simple Skip-sets

· Skip 2, 5-15 base

· Skip 2, 17-27 base

· Skip 3, 2-10 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.

4-base · 16-base · 17-base · 19-base · 20-base

2-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
2[14]-47
1	2	1:1	1	0.00	45.25	45	170
2	17	17:16	1.0625	104.96	50.21	50	105
3	35	35:32	1.09375	155.14	0.39	0	50
4	38	19:16	1.1875	297.51	42.76	43	142
5	5	5:4	1.25	386.31	31.56	32	89
6	41	41:32	1.28125	429.06	-25.69	-26	43
7	11	11:8	1.375	551.32	-3.43	-3	122
8	23	23:16	1.4375	628.27	-26.48	-26	77
9	47	47:32	1.46875	665.51	-89.24	-89	37
10	26	13:8	1.625	840.53	-14.22	-14	175
11	14	7:4	1.75	968.83	14.08	14	128
12	29	29:16	1.8125	1029.58	-25.17	-25	61
				1200.00

2-base · 16-base · 17-base · 19-base · 20-base

4-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
4[13]-46
1	4	1:1	1	0.00	11.81	12	55
2	34	17:16	1.0625	104.96	16.77	17	105
3	37	37:32	1.15625	251.34	63.15	63	146
4	19	19:16	1.1875	297.51	9.32	9	46
5	10	5:4	1.25	386.31	-1.88	-2	89
6	43	43:32	1.34375	511.52	23.33	23	125
7	22	11:8	1.375	551.32	-36.87	-37	40
8	46	23:16	1.4375	628.27	-59.92	-60	77
9	25	25:16	1.5625	772.63	-15.56	-16	144
10	13	13:8	1.625	840.53	-47.66	-48	68
11	7	7:4	1.75	968.83	-19.36	-19	128
12	31	31:16	1.9375	1145.04	56.85	57	176
				1200.00

2-base · 4-base · 17-base · 19-base · 20-base

16-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
16-49
1	16	1:1	1	0.00	28.00	28	55
2	34	17:16	1.0625	104.96	32.96	33	105
3	37	37:32	1.15625	251.34	79.34	79	146
4	19	19:16	1.1875	297.51	25.51	26	46
5	40	5:4	1.25	386.31	14.31	14	89
6	43	43:32	1.34375	511.52	39.52	40	125
7	22	11:8	1.375	551.32	-20.68	-21	40
8	46	23:16	1.4375	628.27	-43.73	-44	77
9	49	49:32	1.53125	737.65	-34.35	-34	109
10	25	25:16	1.5625	772.63	-99.37	-99	35
11	28	7:4	1.75	968.83	-3.17	-3	196
12	31	31:16	1.9375	1145.04	73.04	73	176
				1200.00

2-base · 4-base · 16-base · 19-base · 20-base

17-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
17-50
1	17	1:1	1	0.00	66.55	67	105
2	35	35:34	1.029411765	50.18	16.74	17	50
3	38	19:17	1.117647059	192.56	59.11	59	142
4	20	20:17	1.176470588	281.36	47.91	48	89
5	41	41:34	1.205882353	324.11	-9.34	-9	43
6	44	22:17	1.294117647	446.36	12.92	13	122
7	23	23:17	1.352941176	523.32	-10.13	-10	77
8	47	47:34	1.382352941	560.55	-72.89	-73	37
9	50	25:17	1.470588235	667.67	-65.77	-66	107
10	26	26:17	1.529411765	735.57	-97.87	-98	68
11	29	29:17	1.705882353	924.62	-8.82	-9	189
12	32	32:17	1.882352941	1095.04	61.60	62	170
				1200.00

2-base · 4-base · 16-base · 17-base · 20-base

19-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
19-52
1	19	1:1	1	0.00	51.58	52	46
2	40	20:19	1.052631579	88.80	40.38	40	89
3	43	43:38	1.131578947	214.00	65.58	66	125
4	22	22:19	1.157894737	253.80	5.38	5	40
5	46	23:19	1.210526316	330.76	-17.66	-18	77
6	49	49:38	1.289473684	440.14	-8.28	-8	109
7	25	25:19	1.315789474	475.11	-73.31	-73	35
8	52	26:19	1.368421053	543.01	-105.41	-105	68
9	28	28:19	1.473684211	671.31	-77.11	-77	128
10	31	31:19	1.631578947	847.52	-0.90	-1	176
11	34	34:19	1.789473684	1007.44	59.02	59	160
12	37	37:19	1.947368421	1153.83	105.41	105	146
				1200.00

2-base · 4-base · 16-base · 17-base · 19-base

20-base, Skip 3
Scale Degree	Harmonic	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Gap in Cents
20-53
1	20	1:1	1	0.00	100.80	101	89
2	41	41:40	1.025	42.75	43.55	44	43
3	44	11:10	1.1	165.00	65.80	66	122
4	23	23:20	1.15	241.96	42.76	43	77
5	47	47:40	1.175	279.19	-20.01	-20	37
6	50	5:4	1.25	386.31	-12.89	-13	107
7	26	13:10	1.3	454.21	-44.99	-45	68
8	53	53:40	1.325	487.19	-112.01	-112	33
9	29	29:20	1.45	643.26	-55.94	-56	156
10	32	8:5	1.6	813.69	14.49	14	170
11	35	7:4	1.75	968.83	69.63	70	155
12	38	19:10	1.9	1111.20	112.00	112	142
				1200.00

· DAVID'S HOME PAGE · TUNING PAGES MENU · TUNING METHODS · HARMONIC SERIES TUNINGS ·

Copyright � 2005 by David J. Finnamore
All rights reserved.
tuning@elvenminstrel.com