17ed7

← 16ed7

17ed7

18ed7 →

Prime factorization	17 (prime)
Step size	198.166¢
Octave	6\17ed7 (1189¢) (semiconvergent)
Twelfth	10\17ed7 (1981.66¢)
Consistency limit	3
Distinct consistency limit	3

Division of the 7th harmonic into 17 equal parts (17ed7) is related to 6 edo, but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 198.1662 cents.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	198.1662	28/25
2	396.3325	49/39, 34/27	pseudo-5/4
3	594.4987	24/17
4	792.6649	30/19, 128/81
5	990.8311	85/48, 39/22
6	1188.9974	143/72, 175/88	pseudo-octave
7	1387.1636	49/22
8	1585.3298	5/2
9	1783.4961	14/5
10	1981.6623	22/7
11	2179.8285	88/25
12	2377.9948	154/39, 320/81, 336/85	pseudo-4/1
13	2576.1610	133/30
14	2774.3272	119/24	pseudo-5/1
15	2972.4934	39/7
16	3170.6597	25/4
17	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of prime harmonics in 17ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-11.0	+79.7	-12.0	+0.0	+10.2	-80.9	+49.2	+54.8	-77.8	-82.8	-0.0
	Relative (%)	-5.6	+40.2	-6.0	+0.0	+5.1	-40.8	+24.8	+27.7	-39.3	-41.8	-0.0
Steps (reduced)		6 (6)	10 (10)	14 (14)	17 (0)	21 (4)	22 (5)	25 (8)	26 (9)	27 (10)	29 (12)	30 (13)

Approximation of prime harmonics in 17ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+90.0	-87.7	+28.0	+72.1	+62.3	+74.8	+17.1	+52.8	-47.5	-95.6	-34.2
	Relative (%)	+45.4	-44.3	+14.1	+36.4	+31.4	+37.8	+8.6	+26.7	-24.0	-48.3	-17.3
Steps (reduced)		32 (15)	32 (15)	33 (16)	34 (0)	35 (1)	36 (2)	36 (2)	37 (3)	37 (3)	37 (3)	38 (4)

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