19ed7

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19ed7

20ed7 →

Prime factorization	19 (prime)
Step size	177.307 ¢
Octave	7\19ed7 (1241.15 ¢)
Twelfth	11\19ed7 (1950.37 ¢)
Consistency limit	5
Distinct consistency limit	5

Division of the 7th harmonic into 19 equal parts (19ed7) is related to the 11-limit wollemia temperament, which is a cluster temperament with seven clusters of notes in an octave. The step size is about 177.3066 cents, corresponding to 6.7679 edo.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	177.3066	10/9
2	354.6133	11/9, 60/49, 49/40, 27/22
3	531.9199	49/36, 15/11
4	709.2265	3/2
5	886.5331	5/3
6	1063.8398	13/7
7	1241.1464	49/24, 45/22
8	1418.4530	25/11, 91/40
9	1595.7596	98/39
10	1773.0663	39/14
11	1950.3729	40/13, 77/25
12	2127.6795	24/7
13	2304.9861	49/13
14	2482.2928	21/5
15	2659.5994	14/3
16	2836.9060	77/15, 36/7
17	3014.2127	154/27, 40/7, 63/11
18	3191.5193	63/10
19	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of harmonics in 19ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+41.1	+48.4	+82.3	+50.6	-87.7	+0.0	-53.9	-80.5	-85.6	-73.3	-46.6
	Relative (%)	+23.2	+27.3	+46.4	+28.5	-49.5	+0.0	-30.4	-45.4	-48.3	-41.3	-26.3
Steps (reduced)		7 (7)	11 (11)	14 (14)	16 (16)	17 (17)	19 (0)	20 (1)	21 (2)	22 (3)	23 (4)	24 (5)

Approximation of harmonics in 19ed7

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.9	+41.1	-78.3	-12.7	+59.6	-39.3	+44.4	-44.4	+48.4	-32.1	+68.2
	Relative (%)	-4.4	+23.2	-44.2	-7.2	+33.6	-22.2	+25.0	-25.1	+27.3	-18.1	+38.5
Steps (reduced)		25 (6)	26 (7)	26 (7)	27 (8)	28 (9)	28 (9)	29 (10)	29 (10)	30 (11)	30 (11)	31 (12)

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