25ed4

Todo: review See if there’s a better way to reword the theory section’s contents, they’re a bit confusing & unclear

← 23ed4

25ed4

27ed4 →

Prime factorization	52
Step size	96¢
Octave	13\25ed4 (1248¢)
Twelfth	20\25ed4 (1920¢) (→4\5ed4)
Consistency limit	1
Distinct consistency limit	1

25ed4 is the equal division of the double octave into 25 parts of exactly 96 cents each (every second step of 25edo). It corresponds to 12.5edo and is notable as a type of compressed 12edo.

Theory

We could have 12edo with a quarter note, like with 1.5edo, where the 2nd note is the same as the 3rd in 4edo or we could squish the notes and fit in something else.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	96
2	192	10/9, 19/17
3	288	13/11
4	384
5	480	25/19
6	576	7/5
7	672	22/15, 25/17
8	768	14/9
9	864	23/14
10	960	26/15
11	1056
12	1152
13	1248
14	1344
15	1440	23/10
16	1536	17/7, 22/9
17	1632	23/9
18	1728	19/7
19	1824
20	1920
21	2016
22	2112	17/5
23	2208	25/7
24	2304	19/5
25	2400

Harmonics

Approximation of harmonics in 25ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+48.0	+18.0	+0.0	-2.3	-30.0	-8.8	+48.0	+36.1	+45.7	-23.3	+18.0
	Relative (%)	+50.0	+18.8	+0.0	-2.4	-31.2	-9.2	+50.0	+37.6	+47.6	-24.3	+18.8
Steps (reduced)		13 (13)	20 (20)	25 (0)	29 (4)	32 (7)	35 (10)	38 (13)	40 (15)	42 (17)	43 (18)	45 (20)

Approximation of harmonics in 25ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-24.5	+39.2	+15.7	+0.0	-9.0	-11.9	-9.5	-2.3	+9.2	+24.7	+43.7
	Relative (%)	-25.5	+40.8	+16.4	+0.0	-9.3	-12.4	-9.9	-2.4	+9.6	+25.7	+45.5
Steps (reduced)		46 (21)	48 (23)	49 (24)	50 (0)	51 (1)	52 (2)	53 (3)	54 (4)	55 (5)	56 (6)	57 (7)

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