95edt

← 94edt

95edt

96edt →

Prime factorization	5 × 19
Step size	20.0206 ¢
Octave	60\95edt (1201.23 ¢) (→ 12\19edt)
Consistency limit	10
Distinct consistency limit	10

95 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 95edt or 95ed3), is a nonoctave tuning system that divides the interval of 3/1 into 95 equal parts of about 20 ¢ each. Each step represents a frequency ratio of 3^1/95, or the 95th root of 3.

Theory

95edt is related to 60edo (tenth-tone tuning), but with the perfect twelfth rather than the octave being just. The octave is about 1.23 cents stretched. Like 60edo, 95edt is consistent to the 10-integer-limit. While it tunes prime 2 and 13 sharp, the 5 and 7 remain flat but less so, and the 17 is practically pure, which may be seen as an improvement in intonation over 60edo.

Harmonics

Approximation of harmonics in 95edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	-3.45	+1.23	-5.37	+3.70	+0.00	-2.22	-7.06	+2.47
	Relative (%)	+6.2	+0.0	+12.3	-17.2	+6.2	-26.8	+18.5	+0.0	-11.1	-35.3	+12.3
Steps (reduced)		60 (60)	95 (0)	120 (25)	139 (44)	155 (60)	168 (73)	180 (85)	190 (0)	199 (9)	207 (17)	215 (25)

Approximation of harmonics in 95edt (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+4.04	-4.13	-3.45	+4.94	+0.09	+1.23	+7.73	-0.98	-5.37	-5.82	-2.70	+3.70
	Relative (%)	+20.2	-20.6	-17.2	+24.7	+0.4	+6.2	+38.6	-4.9	-26.8	-29.1	-13.5	+18.5
Steps (reduced)		222 (32)	228 (38)	234 (44)	240 (50)	245 (55)	250 (60)	255 (65)	259 (69)	263 (73)	267 (77)	271 (81)	275 (85)

Subsets and supersets

Since 95 factors into primes as 5 × 19, 95edt has subset edt's 5edt and 19edt.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	20	13.7
2	40	27.4	42/41, 43/42
3	60.1	41.1	29/28, 30/29
4	80.1	54.7	22/21, 43/41
5	100.1	68.4	18/17, 35/33
6	120.1	82.1	15/14
7	140.1	95.8	13/12
8	160.2	109.5	34/31
9	180.2	123.2	10/9, 41/37
10	200.2	136.8	37/33
11	220.2	150.5	25/22, 42/37
12	240.2	164.2	23/20, 31/27
13	260.3	177.9	36/31, 43/37
14	280.3	191.6	20/17
15	300.3	205.3	25/21
16	320.3	218.9
17	340.3	232.6	28/23, 39/32
18	360.4	246.3	16/13
19	380.4	260
20	400.4	273.7	29/23, 34/27
21	420.4	287.4	37/29
22	440.5	301.1	31/24, 40/31
23	460.5	314.7	30/23, 43/33
24	480.5	328.4	29/22, 33/25, 37/28
25	500.5	342.1	4/3
26	520.5	355.8	27/20
27	540.6	369.5	26/19, 41/30
28	560.6	383.2	29/21
29	580.6	396.8	7/5
30	600.6	410.5	17/12, 41/29
31	620.6	424.2	43/30
32	640.7	437.9	29/20, 42/29
33	660.7	451.6	22/15, 41/28
34	680.7	465.3	37/25, 40/27, 43/29
35	700.7	478.9	3/2
36	720.7	492.6	41/27
37	740.8	506.3	23/15, 43/28
38	760.8	520	31/20
39	780.8	533.7	11/7
40	800.8	547.4	27/17
41	820.8	561.1	37/23
42	840.9	574.7	13/8
43	860.9	588.4	23/14
44	880.9	602.1
45	900.9	615.8	32/19, 37/22
46	920.9	629.5	17/10
47	941	643.2	31/18, 43/25
48	961	656.8
49	981	670.5	30/17, 37/21
50	1001	684.2	41/23
51	1021	697.9
52	1041.1	711.6	31/17, 42/23
53	1061.1	725.3	24/13
54	1081.1	738.9	28/15, 43/23
55	1101.1	752.6	17/9
56	1121.2	766.3	21/11
57	1141.2	780	29/15
58	1161.2	793.7	43/22
59	1181.2	807.4
60	1201.2	821.1	2/1
61	1221.3	834.7
62	1241.3	848.4	41/20, 43/21
63	1261.3	862.1	29/14
64	1281.3	875.8
65	1301.3	889.5	36/17
66	1321.4	903.2	15/7
67	1341.4	916.8
68	1361.4	930.5
69	1381.4	944.2	20/9
70	1401.4	957.9	9/4
71	1421.5	971.6	25/11
72	1441.5	985.3	23/10
73	1461.5	998.9
74	1481.5	1012.6	40/17
75	1501.5	1026.3
76	1521.6	1040	41/17
77	1541.6	1053.7	39/16
78	1561.6	1067.4	32/13, 37/15
79	1581.6	1081.1
80	1601.6	1094.7
81	1621.7	1108.4
82	1641.7	1122.1	31/12
83	1661.7	1135.8
84	1681.7	1149.5	37/14
85	1701.7	1163.2
86	1721.8	1176.8	27/10
87	1741.8	1190.5	41/15
88	1761.8	1204.2	36/13
89	1781.8	1217.9	14/5
90	1801.9	1231.6	17/6
91	1821.9	1245.3	43/15
92	1841.9	1258.9	29/10
93	1861.9	1272.6	41/14
94	1881.9	1286.3
95	1902	1300	3/1

See also

• 35edf – relative edf
• 60edo – relative edo
• 139ed5 – relative ed5
• 155edt – relative ed6