28edf

← 27edf

28edf

29edf →

Prime factorization	22 × 7
Step size	25.0698¢
Octave	48\28edf (1203.35¢) (→12\7edf)
Twelfth	76\28edf (1905.31¢) (→19\7edf)
Consistency limit	6
Distinct consistency limit	6

Division of the just perfect fifth into 28 equal parts (28EDF) is related to 48 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 25.0698 cents (corresponding to 47.8663 edo).

It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; 6656/6655, 256000/255879, and 38671875/38614472 in the 13-limit (2.3.5.11.13 subgroup), which is supported by 335, 383, 718, 1053, and 1101 EDOs.

Harmonics

Approximation of prime harmonics in 28edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.4	+3.4	-3.6	-9.5	+10.3	-3.2	+8.7	-8.3	+11.9	+11.7	-3.5
	Relative (%)	+13.4	+13.4	-14.2	-37.8	+41.0	-12.6	+34.8	-33.3	+47.4	+46.6	-13.9
Steps (reduced)		48 (20)	76 (20)	111 (27)	134 (22)	166 (26)	177 (9)	196 (0)	203 (7)	217 (21)	233 (9)	237 (13)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	25.07
2	50.14
3	75.209	21/20, 23/22, 24/23, 26/25, 27/26
4	100.279	17/16, 18/17
5	125.349	14/13, 15/14
6	150.419	12/11
7	175.489	10/9, 11/10, 21/19
8	200.559	9/8
9	225.628	17/15
10	250.698	15/13, 23/20
11	275.768	20/17, 27/23
12	300.838	25/21
13	325.908	6/5
14	350.978	11/9, 27/22
15	376.047	5/4, 26/21
16	401.117	19/15
17	426.187	23/18
18	451.257	13/10, 22/17
19	476.327	25/19
20	501.396	4/3
21	526.466	15/11, 19/14, 23/17, 27/20
22	551.536	11/8, 26/19
23	576.606	7/5
24	601.676	17/12, 24/17
25	626.746	10/7, 13/9, 23/16
26	651.815	16/11, 19/13
27	676.885
28	701.955	3/2

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