101ed4

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101ed4

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Prime factorization	101 (prime)
Step size	23.7624 ¢
Octave	51\101ed4 (1211.88 ¢)
Twelfth	80\101ed4 (1900.99 ¢)
Consistency limit	1
Distinct consistency limit	1

101 equal divisions of the 4th harmonic (abbreviated 101ed4) is a nonoctave tuning system that divides the interval of 4/1 into 101 equal parts of about 23.8 ¢ each. Each step represents a frequency ratio of 4^1/101, or the 101st root of 4. This tuning has an excellent 3rd harmonic, only about 4% off.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	23.8
2	47.5
3	71.3
4	95	19/18, 37/35
5	118.8
6	142.6	25/23
7	166.3	11/10
8	190.1
9	213.9
10	237.6	31/27, 39/34
11	261.4	43/37
12	285.1
13	308.9
14	332.7
15	356.4	43/35
16	380.2
17	404
18	427.7
19	451.5	35/27
20	475.2
21	499
22	522.8	23/17
23	546.5	37/27
24	570.3
25	594.1
26	617.8	10/7
27	641.6
28	665.3	25/17
29	689.1
30	712.9
31	736.6
32	760.4	45/29
33	784.2	11/7
34	807.9	43/27
35	831.7	21/13
36	855.4
37	879.2
38	903
39	926.7	29/17
40	950.5
41	974.3
42	998
43	1021.8
44	1045.5
45	1069.3	13/7
46	1093.1
47	1116.8
48	1140.6	29/15
49	1164.4	45/23
50	1188.1
51	1211.9
52	1235.6
53	1259.4
54	1283.2	21/10
55	1306.9
56	1330.7	41/19
57	1354.5
58	1378.2
59	1402
60	1425.7	41/18
61	1449.5	30/13
62	1473.3
63	1497
64	1520.8
65	1544.6
66	1568.3
67	1592.1
68	1615.8
69	1639.6
70	1663.4	34/13
71	1687.1	45/17
72	1710.9
73	1734.7	30/11
74	1758.4
75	1782.2
76	1805.9
77	1829.7
78	1853.5
79	1877.2
80	1901	3/1
81	1924.8
82	1948.5
83	1972.3
84	1996	19/6
85	2019.8
86	2043.6
87	2067.3	33/10
88	2091.1
89	2114.9
90	2138.6
91	2162.4
92	2186.1
93	2209.9
94	2233.7
95	2257.4
96	2281.2
97	2305
98	2328.7
99	2352.5	35/9
100	2376.2
101	2400

Harmonics

Approximation of harmonics in 101ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.9	-1.0	+0.0	-6.1	+10.9	+5.4	+11.9	-1.9	+5.8	+7.1	-1.0
	Relative (%)	+50.0	-4.1	+0.0	-25.7	+45.9	+22.9	+50.0	-8.1	+24.3	+29.9	-4.1
Steps (reduced)		51 (51)	80 (80)	101 (0)	117 (16)	131 (30)	142 (41)	152 (51)	160 (59)	168 (67)	175 (74)	181 (80)

Approximation of harmonics in 101ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.0	-6.4	-7.1	+0.0	-9.9	+10.0	+11.4	-6.1	+4.5	-4.8	-10.5
	Relative (%)	+12.8	-27.1	-29.8	+0.0	-41.7	+41.9	+48.0	-25.7	+18.8	-20.1	-44.0
Steps (reduced)		187 (86)	192 (91)	197 (96)	202 (0)	206 (4)	211 (9)	215 (13)	218 (16)	222 (20)	225 (23)	228 (26)