20ed7

← 19ed7

20ed7

21ed7 →

Prime factorization	22 × 5
Step size	168.441¢
Octave	7\20ed7 (1179.09¢)
Twelfth	11\20ed7 (1852.85¢)
Consistency limit	4
Distinct consistency limit	4

Division of the 7th harmonic into 20 equal parts (20ed7) is related to the meantone temperament. The step size is about 168.4413 cents, corresponding to 7.1241 edo.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	168.4413	11/10
2	336.8826	17/14
3	505.3239	91/68
4	673.7652	28/19, 96/65, 65/44, 34/23
5	842.2065	13/8
6	1010.6478	70/39
7	1179.0891	77/39
8	1347.5304	24/11
9	1515.9717	12/5
10	1684.4130	119/45, 45/17
11	1852.8542	35/12
12	2021.2955	77/24
13	2189.7368	39/11
14	2358.1781	39/10
15	2526.6194	56/13
16	2695.0607	19/4
17	2863.5020	68/13
18	3031.9433	98/17
19	3200.3846	70/11
20	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of prime harmonics in 20ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-20.9	-49.1	+77.2	+0.0	+59.7	-61.1	-20.2	-44.3	-38.2	+65.9	-49.6
	Relative (%)	-12.4	-29.2	+45.8	+0.0	+35.5	-36.2	-12.0	-26.3	-22.7	+39.1	-29.4
Steps (reduced)		7 (7)	11 (11)	17 (17)	20 (0)	25 (5)	26 (6)	29 (9)	30 (10)	32 (12)	35 (15)	35 (15)

Approximation of prime harmonics in 20ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-19.0	-28.3	+57.7	+72.1	+32.6	+15.4	-42.4	-36.3	+31.7	-16.4	+15.3
	Relative (%)	-11.3	-16.8	+34.3	+42.8	+19.3	+9.1	-25.1	-21.6	+18.8	-9.7	+9.1
Steps (reduced)		37 (17)	38 (18)	39 (19)	40 (0)	41 (1)	42 (2)	42 (2)	43 (3)	44 (4)	44 (4)	45 (5)

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