25edt

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25edt

26edt →

Prime factorization	52
Step size	76.0782 ¢
Octave	16\25edt (1217.25 ¢)
Consistency limit	6
Distinct consistency limit	6

25 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 25edt or 25ed3), is a nonoctave tuning system that divides the interval of 3/1 into 25 equal parts of about 76.1 ¢ each. Each step represents a frequency ratio of 3^1/25, or the 25th root of 3.

It corresponds to 15.7732 edo, or 16 equal divisions of a stretched octave (1217.25 ¢) and a tritave twin of the Armodue/Hornbostel flat third-tone system:

• 6th = 1065.095 ¢
• squared = 2130.19 cents = 228.235 ¢
• cubed = 1293.33 ¢
• fourth power = 2358.425 ¢ → 456.47 ¢

Intervals

Degree	Cents	Hekts	Armodue name
1	76.08	52	1#/2bb
2	152.16	104	1x/2b
3	228.235	156	2
4	304.31	208	2#/3bb
5	380.39	260	2x/3b
6	456.47	312	3
7	532.55	364	3#/4b
8	608.625	416	4
9	684.70	468	4#/5bb
10	760.78	520	4x/5b
11	836.86	572	5
12	912.94	624	5#/6bb
13	989.02	676	5x/6b
14	1065.095	728	6
15	1141.17	780	6#/7bb
16	1217.25	832	6x/7b
17	1293.33	884	7
18	1369.41	936	7#/8b
19	1445.485	988	8
20	1521.56	1040	8#/9bb
21	1597.64	1092	8x/9b
22	1673.72	1144	9
23	1749.80	1196	9#/1bb
24	1825.88	1248	9x/1b
25	1901.955	1300	1

Harmonics

Approximation of prime harmonics in 25edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+17.3	+0.0	+28.6	-21.4	+33.0	-28.0	-36.0	-0.3	-26.7	+28.4	-10.9
	Relative (%)	+22.7	+0.0	+37.6	-28.1	+43.4	-36.8	-47.3	-0.4	-35.1	+37.4	-14.4
Steps (reduced)		16 (16)	25 (0)	37 (12)	44 (19)	55 (5)	58 (8)	64 (14)	67 (17)	71 (21)	77 (2)	78 (3)

Approximation of prime harmonics in 25edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-12.9	+37.6	+31.2	+29.4	-26.5	+16.1	+34.5	+24.2	-0.1	+27.9	-32.8
	Relative (%)	-17.0	+49.4	+41.0	+38.6	-34.8	+21.2	+45.3	+31.8	-0.1	+36.6	-43.1
Steps (reduced)		82 (7)	85 (10)	86 (11)	88 (13)	90 (15)	93 (18)	94 (19)	96 (21)	97 (22)	98 (23)	99 (24)