133edt

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133edt

134edt →

Prime factorization	7 × 19
Step size	14.3004¢
Octave	84\133edt (1201.23¢) (→12\19edt)
Consistency limit	10
Distinct consistency limit	10

133 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 133edt or 133ed3), is a nonoctave tuning system that divides the interval of 3/1 into 133 equal parts of about 14.3⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/133, or the 133rd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	14.3	9.8
2	28.6	19.5
3	42.9	29.3	40/39, 41/40, 42/41
4	57.2	39.1	30/29, 31/30
5	71.5	48.9	25/24
6	85.8	58.6	21/20, 41/39
7	100.1	68.4	18/17
8	114.4	78.2	31/29, 47/44
9	128.7	88	14/13
10	143	97.7	25/23, 51/47
11	157.3	107.5	23/21
12	171.6	117.3	32/29
13	185.9	127.1	39/35
14	200.2	136.8	46/41
15	214.5	146.6	43/38
16	228.8	156.4
17	243.1	166.2	23/20, 38/33
18	257.4	175.9	29/25, 36/31
19	271.7	185.7	48/41
20	286	195.5	46/39
21	300.3	205.3	25/21, 44/37
22	314.6	215	6/5
23	328.9	224.8	29/24
24	343.2	234.6	39/32, 50/41
25	357.5	244.4
26	371.8	254.1	31/25
27	386.1	263.9	5/4
28	400.4	273.7	29/23, 34/27
29	414.7	283.5	47/37
30	429	293.2	32/25, 41/32, 50/39
31	443.3	303	31/24
32	457.6	312.8	43/33
33	471.9	322.6	21/16, 46/35
34	486.2	332.3	45/34
35	500.5	342.1
36	514.8	351.9	35/26
37	529.1	361.7
38	543.4	371.4
39	557.7	381.2	29/21, 40/29
40	572	391	32/23, 39/28
41	586.3	400.8
42	600.6	410.5	41/29
43	614.9	420.3
44	629.2	430.1	23/16
45	643.5	439.8	29/20, 45/31
46	657.8	449.6
47	672.1	459.4
48	686.4	469.2	52/35
49	700.7	478.9	3/2
50	715	488.7
51	729.3	498.5	32/21
52	743.6	508.3
53	757.9	518	31/20, 48/31
54	772.2	527.8	25/16
55	786.5	537.6
56	800.8	547.4	27/17
57	815.1	557.1	8/5
58	829.4	566.9	21/13
59	843.7	576.7	44/27
60	858	586.5	23/14, 41/25
61	872.3	596.2	48/29
62	886.6	606
63	900.9	615.8	37/22
64	915.2	625.6	39/23
65	929.5	635.3
66	943.8	645.1	50/29
67	958.1	654.9	40/23, 47/27
68	972.4	664.7
69	986.7	674.4	23/13
70	1001	684.2	41/23
71	1015.3	694
72	1029.6	703.8	29/16
73	1043.9	713.5	42/23
74	1058.2	723.3
75	1072.5	733.1	13/7
76	1086.8	742.9	15/8
77	1101.1	752.6	17/9
78	1115.4	762.4	40/21
79	1129.7	772.2	48/25
80	1144	782	31/16
81	1158.3	791.7	41/21
82	1172.6	801.5
83	1186.9	811.3
84	1201.2	821.1	2/1
85	1215.5	830.8
86	1229.8	840.6
87	1244.1	850.4	41/20
88	1258.4	860.2	31/15
89	1272.7	869.9	48/23
90	1287	879.7
91	1301.3	889.5
92	1315.6	899.2	47/22
93	1329.9	909	28/13
94	1344.2	918.8	50/23
95	1358.5	928.6	46/21
96	1372.8	938.3
97	1387.1	948.1
98	1401.4	957.9
99	1415.7	967.7	34/15, 43/19
100	1430	977.4	16/7
101	1444.3	987.2
102	1458.6	997
103	1472.9	1006.8
104	1487.2	1016.5
105	1501.5	1026.3	50/21
106	1515.8	1036.1	12/5
107	1530.1	1045.9
108	1544.4	1055.6
109	1558.7	1065.4	32/13
110	1573	1075.2
111	1587.3	1085	5/2
112	1601.6	1094.7
113	1615.9	1104.5
114	1630.2	1114.3	41/16
115	1644.5	1124.1	31/12
116	1658.8	1133.8
117	1673.1	1143.6
118	1687.4	1153.4
119	1701.7	1163.2
120	1716	1172.9	35/13
121	1730.4	1182.7
122	1744.7	1192.5
123	1759	1202.3	47/17
124	1773.3	1212	39/14
125	1787.6	1221.8
126	1801.9	1231.6	17/6
127	1816.2	1241.4	20/7
128	1830.5	1251.1
129	1844.8	1260.9	29/10
130	1859.1	1270.7	41/14
131	1873.4	1280.5
132	1887.7	1290.2
133	1902	1300	3/1

Harmonics

Approximation of harmonics in 133edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	+2.27	+1.23	+6.07	+3.70	+0.00	+3.50	-4.20	+2.47
	Relative (%)	+8.6	+0.0	+17.3	+15.9	+8.6	+42.5	+25.9	+0.0	+24.5	-29.4	+17.3
Steps (reduced)		84 (84)	133 (0)	168 (35)	195 (62)	217 (84)	236 (103)	252 (119)	266 (0)	279 (13)	290 (24)	301 (35)

Approximation of harmonics in 133edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.90	-6.99	+2.27	+4.94	+0.09	+1.23	-6.57	+4.74	+6.07	-2.96	+5.88
	Relative (%)	+48.3	-48.9	+15.9	+34.5	+0.6	+8.6	-45.9	+33.1	+42.5	-20.7	+41.1
Steps (reduced)		311 (45)	319 (53)	328 (62)	336 (70)	343 (77)	350 (84)	356 (90)	363 (97)	369 (103)	374 (108)	380 (114)