121edt

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121edt

122edt →

Prime factorization	112
Step size	15.7186¢
Octave	76\121edt (1194.62¢)
Consistency limit	2
Distinct consistency limit	2

121 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 121edt or 121ed3), is a nonoctave tuning system that divides the interval of 3/1 into 121 equal parts of about 15.7⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/121, or the 121st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	15.7	10.7
2	31.4	21.5
3	47.2	32.2	36/35
4	62.9	43
5	78.6	53.7	22/21, 23/22, 45/43
6	94.3	64.5	19/18
7	110	75.2	33/31, 49/46
8	125.7	86
9	141.5	96.7	38/35
10	157.2	107.4	23/21
11	172.9	118.2	21/19
12	188.6	128.9	29/26
13	204.3	139.7
14	220.1	150.4	25/22
15	235.8	161.2	47/41
16	251.5	171.9
17	267.2	182.6	7/6
18	282.9	193.4
19	298.7	204.1
20	314.4	214.9	6/5
21	330.1	225.6	23/19
22	345.8	236.4	11/9
23	361.5	247.1
24	377.2	257.9	41/33
25	393	268.6
26	408.7	279.3	19/15
27	424.4	290.1	23/18
28	440.1	300.8	49/38
29	455.8	311.6
30	471.6	322.3	46/35
31	487.3	333.1
32	503	343.8
33	518.7	354.5	31/23
34	534.4	365.3	49/36
35	550.2	376
36	565.9	386.8	43/31
37	581.6	397.5	7/5
38	597.3	408.3
39	613	419	47/33
40	628.7	429.8
41	644.5	440.5	45/31
42	660.2	451.2
43	675.9	462	31/21, 34/23
44	691.6	472.7
45	707.3	483.5
46	723.1	494.2	38/25, 41/27
47	738.8	505	23/15
48	754.5	515.7	17/11
49	770.2	526.4
50	785.9	537.2
51	801.7	547.9	27/17
52	817.4	558.7
53	833.1	569.4	34/21
54	848.8	580.2	31/19, 49/30
55	864.5	590.9
56	880.2	601.7
57	896	612.4
58	911.7	623.1
59	927.4	633.9
60	943.1	644.6
61	958.8	655.4	47/27
62	974.6	666.1
63	990.3	676.9
64	1006	687.6	34/19
65	1021.7	698.3
66	1037.4	709.1
67	1053.1	719.8
68	1068.9	730.6
69	1084.6	741.3	43/23
70	1100.3	752.1	17/9
71	1116	762.8
72	1131.7	773.6
73	1147.5	784.3	33/17
74	1163.2	795	45/23, 49/25
75	1178.9	805.8
76	1194.6	816.5
77	1210.3	827.3
78	1226.1	838
79	1241.8	848.8	43/21
80	1257.5	859.5	31/15
81	1273.2	870.2
82	1288.9	881
83	1304.6	891.7
84	1320.4	902.5	15/7
85	1336.1	913.2
86	1351.8	924
87	1367.5	934.7
88	1383.2	945.5
89	1399	956.2
90	1414.7	966.9	43/19
91	1430.4	977.7
92	1446.1	988.4
93	1461.8	999.2
94	1477.6	1009.9
95	1493.3	1020.7	45/19
96	1509	1031.4	43/18
97	1524.7	1042.1	41/17
98	1540.4	1052.9
99	1556.1	1063.6	27/11
100	1571.9	1074.4
101	1587.6	1085.1	5/2
102	1603.3	1095.9
103	1619	1106.6
104	1634.7	1117.4	18/7
105	1650.5	1128.1
106	1666.2	1138.8
107	1681.9	1149.6
108	1697.6	1160.3
109	1713.3	1171.1
110	1729.1	1181.8	19/7
111	1744.8	1192.6
112	1760.5	1203.3	47/17
113	1776.2	1214
114	1791.9	1224.8	31/11
115	1807.6	1235.5
116	1823.4	1246.3	43/15
117	1839.1	1257
118	1854.8	1267.8	35/12
119	1870.5	1278.5
120	1886.2	1289.3
121	1902	1300	3/1

Harmonics

Approximation of harmonics in 121edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.38	+0.00	+4.95	-4.12	-5.38	-5.04	-0.43	+0.00	+6.22	-1.60	+4.95
	Relative (%)	-34.3	+0.0	+31.5	-26.2	-34.3	-32.0	-2.8	+0.0	+39.6	-10.2	+31.5
Steps (reduced)		76 (76)	121 (0)	153 (32)	177 (56)	197 (76)	214 (93)	229 (108)	242 (0)	254 (12)	264 (22)	274 (32)

Approximation of harmonics in 121edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.85	+5.30	-4.12	-5.82	-0.74	-5.38	-4.67	+0.84	-5.04	-6.98	-5.34
	Relative (%)	+49.9	+33.7	-26.2	-37.0	-4.7	-34.3	-29.7	+5.3	-32.0	-44.4	-34.0
Steps (reduced)		283 (41)	291 (49)	298 (56)	305 (63)	312 (70)	318 (76)	324 (82)	330 (88)	335 (93)	340 (98)	345 (103)