99edt

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99 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 99edt or 99ed3), is a nonoctave tuning system that divides the interval of 3/1 into 99 equal parts of about 19.2 ¢ each. Each step represents a frequency ratio of 3^1/99, or the 99th root of 3.

← 98edt

99edt

100edt →

Prime factorization	32 × 11
Step size	19.2117 ¢
Octave	62\99edt (1191.12 ¢)
Consistency limit	3
Distinct consistency limit	3

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	19.2	13.1
2	38.4	26.3
3	57.6	39.4	30/29, 31/30
4	76.8	52.5
5	96.1	65.7	19/18, 37/35
6	115.3	78.8	31/29
7	134.5	91.9	27/25
8	153.7	105.1
9	172.9	118.2	21/19
10	192.1	131.3	19/17
11	211.3	144.4	35/31
12	230.5	157.6
13	249.8	170.7	15/13
14	269	183.8	7/6
15	288.2	197	13/11
16	307.4	210.1	37/31
17	326.6	223.2	35/29
18	345.8	236.4	11/9
19	365	249.5	21/17, 37/30
20	384.2	262.6
21	403.4	275.8
22	422.7	288.9	37/29
23	441.9	302
24	461.1	315.2
25	480.3	328.3	29/22, 33/25
26	499.5	341.4
27	518.7	354.5
28	537.9	367.7	15/11
29	557.1	380.8	29/21
30	576.4	393.9
31	595.6	407.1	31/22
32	614.8	420.2
33	634	433.3
34	653.2	446.5
35	672.4	459.6	31/21
36	691.6	472.7
37	710.8	485.9
38	730	499	29/19
39	749.3	512.1
40	768.5	525.3	39/25
41	787.7	538.4
42	806.9	551.5	43/27
43	826.1	564.6	29/18
44	845.3	577.8	31/19
45	864.5	590.9
46	883.7	604	5/3
47	902.9	617.2
48	922.2	630.3	29/17
49	941.4	643.4	31/18, 43/25
50	960.6	656.6
51	979.8	669.7	37/21
52	999	682.8	41/23
53	1018.2	696	9/5
54	1037.4	709.1
55	1056.6	722.2	35/19
56	1075.9	735.4
57	1095.1	748.5
58	1114.3	761.6
59	1133.5	774.7	25/13
60	1152.7	787.9	35/18, 37/19
61	1171.9	801
62	1191.1	814.1
63	1210.3	827.3
64	1229.5	840.4
65	1248.8	853.5	35/17, 37/18
66	1268	866.7
67	1287.2	879.8
68	1306.4	892.9
69	1325.6	906.1
70	1344.8	919.2	37/17
71	1364	932.3	11/5
72	1383.2	945.5
73	1402.5	958.6
74	1421.7	971.7	25/11
75	1440.9	984.8
76	1460.1	998
77	1479.3	1011.1
78	1498.5	1024.2
79	1517.7	1037.4
80	1536.9	1050.5	17/7
81	1556.1	1063.6	27/11
82	1575.4	1076.8
83	1594.6	1089.9
84	1613.8	1103	33/13
85	1633	1116.2	18/7
86	1652.2	1129.3	13/5
87	1671.4	1142.4
88	1690.6	1155.6
89	1709.8	1168.7
90	1729.1	1181.8	19/7
91	1748.3	1194.9
92	1767.5	1208.1	25/9
93	1786.7	1221.2
94	1805.9	1234.3
95	1825.1	1247.5	43/15
96	1844.3	1260.6	29/10
97	1863.5	1273.7
98	1882.7	1286.9
99	1902	1300	3/1

Harmonics

Approximation of harmonics in 99edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.88	+0.00	+1.46	-0.62	-8.88	-6.78	-7.42	+0.00	-9.50	-1.60	+1.46
	Relative (%)	-46.2	+0.0	+7.6	-3.2	-46.2	-35.3	-38.6	+0.0	-49.4	-8.3	+7.6
Steps (reduced)		62 (62)	99 (0)	125 (26)	145 (46)	161 (62)	175 (76)	187 (88)	198 (0)	207 (9)	216 (18)	224 (26)

Approximation of harmonics in 99edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+3.55	-0.62	+2.92	-5.98	-8.88	-6.42	+0.84	-6.78	+8.74	+8.63
	Relative (%)	-13.7	+18.5	-3.2	+15.2	-31.1	-46.2	-33.4	+4.4	-35.3	+45.5	+44.9
Steps (reduced)		231 (33)	238 (40)	244 (46)	250 (52)	255 (57)	260 (62)	265 (67)	270 (72)	274 (76)	279 (81)	283 (85)