100ed7/3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 99ed7/3

100ed7/3

101ed7/3 →

Prime factorization	22 × 52
Step size	14.6687¢
Octave	82\100ed7/3 (1202.83¢) (→41\50ed7/3)
Twelfth	130\100ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	5
Distinct consistency limit	5

100 equal divisions of 7/3 (abbreviated 100ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 100 equal parts of about 14.7 ¢ each. Each step represents a frequency ratio of (7/3)^1/100, or the 100th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.669
2	29.337
3	44.006	39/38, 40/39
4	58.675
5	73.344
6	88.012	20/19
7	102.681	35/33
8	117.35	15/14, 31/29
9	132.018
10	146.687	25/23, 37/34
11	161.356	34/31
12	176.025	41/37
13	190.693
14	205.362	9/8
15	220.031	25/22
16	234.699
17	249.368	15/13
18	264.037
19	278.705
20	293.374	32/27, 45/38
21	308.043	37/31
22	322.712	41/34
23	337.38
24	352.049
25	366.718
26	381.386
27	396.055	44/35
28	410.724	19/15, 33/26
29	425.393
30	440.061
31	454.73	13/10
32	469.399	21/16
33	484.067	41/31
34	498.736	4/3
35	513.405	35/26
36	528.074	19/14
37	542.742	26/19
38	557.411
39	572.08	39/28
40	586.748
41	601.417	41/29
42	616.086	10/7
43	630.754
44	645.423
45	660.092
46	674.761	34/23
47	689.429
48	704.098	3/2
49	718.767
50	733.435
51	748.104	20/13
52	762.773	14/9
53	777.442
54	792.11	30/19
55	806.779
56	821.448	37/23, 45/28
57	836.116
58	850.785
59	865.454	33/20
60	880.123
61	894.791
62	909.46	22/13
63	924.129	29/17
64	938.797	43/25
65	953.466	26/15, 33/19
66	968.135	7/4
67	982.804
68	997.472	16/9
69	1012.141
70	1026.81	38/21
71	1041.478	31/17
72	1056.147	35/19
73	1070.816	13/7
74	1085.484	43/23
75	1100.153
76	1114.822	40/21
77	1129.491
78	1144.159
79	1158.828	43/22
80	1173.497
81	1188.165
82	1202.834
83	1217.503
84	1232.172
85	1246.84	39/19
86	1261.509
87	1276.178	23/11
88	1290.846	40/19
89	1305.515
90	1320.184	15/7
91	1334.853
92	1349.521
93	1364.19	11/5
94	1378.859
95	1393.527
96	1408.196
97	1422.865	25/11
98	1437.533
99	1452.202	44/19
100	1466.871	7/3

Harmonics

Approximation of harmonics in 100ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.83	+4.98	+5.67	+0.74	-6.86	+4.98	-6.17	-4.71	+3.58	-0.07	-4.02
	Relative (%)	+19.3	+33.9	+38.6	+5.1	-46.7	+33.9	-42.0	-32.1	+24.4	-0.5	-27.4
Steps (reduced)		82 (82)	130 (30)	164 (64)	190 (90)	211 (11)	230 (30)	245 (45)	259 (59)	272 (72)	283 (83)	293 (93)

Approximation of harmonics in 100ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.09	-6.86	+5.72	-3.33	-5.61	-1.88	+7.20	+6.41	-4.71	+2.76	-0.85
	Relative (%)	+27.9	-46.7	+39.0	-22.7	-38.2	-12.8	+49.1	+43.7	-32.1	+18.8	-5.8
Steps (reduced)		303 (3)	311 (11)	320 (20)	327 (27)	334 (34)	341 (41)	348 (48)	354 (54)	359 (59)	365 (65)	370 (70)