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34ed7

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34ed7

35ed7 →

Prime factorization	2 × 17
Step size	99.0831 ¢
Octave	12\34ed7 (1189 ¢) (→ 6\17ed7)
Twelfth	19\34ed7 (1882.58 ¢)
Consistency limit	11
Distinct consistency limit	6

34 equal divisions of the 7th harmonic (abbreviated 34ed7) is a nonoctave tuning system that divides the interval of 7/1 into 34 equal parts of about 99.1 ¢ each. Each step represents a frequency ratio of 7^1/34, or the 34th root of 7. This tuning is a compressed 12edo.

Steps	Cents	Approximate ratios	12edo note names	9\109-based note names
0	0	1/1	C
1	99.1	19/18	C#/Db	^^Db
2	198.2	9/8, 28/25	D	vD
3	297.2	13/11, 19/16, 25/21	D#/Eb	^Eb
4	396.3	24/19	E	vvE
5	495.4	4/3	F
6	594.5		F#/Gb	^^Gb
7	693.6	3/2	G	vG
8	792.7	19/12	G#/Ab	^Ab
9	891.7	5/3	A	vvA
10	990.8	16/9, 23/13	A#/Bb	Bb
11	1089.9	15/8	B	vvvB
12	1189		C	vC
13	1288.1	19/9, 21/10	C#/Db	^Db
14	1387.2	20/9	D	vvD
15	1486.2	26/11	D#/Eb	Eb
16	1585.3	5/2	E	vvvE
17	1684.4		F	vF
18	1783.5	14/5	F#/Gb	^Gb
19	1882.6		G	vvG
20	1981.7	22/7	G#/Ab	Ab
21	2080.7	10/3	A	vvvA
22	2179.8		A#/Bb	vBb
23	2278.9	26/7	B	vvvvB
24	2378		C	vvC
25	2477.1	21/5, 25/6	C#/Db	Db
26	2576.2		D	vvvD
27	2675.2	14/3	D#/Eb	vEb
28	2774.3		E	vvvvE
29	2873.4	21/4	F	vvF
30	2972.5		F#/Gb	Gb
31	3071.6		G	vvvG
32	3170.7	25/4	G#/Ab	vAb
33	3269.7		A	vvvvA
34	3368.8	7/1	A#/Bb	vvBb

Approximation of harmonics in 34ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.0	-19.4	-22.0	-12.0	-30.4	+0.0	-33.0	-38.8	-23.0	+10.2	-41.4
	Relative (%)	-11.1	-19.6	-22.2	-12.1	-30.7	+0.0	-33.3	-39.1	-23.2	+10.3	-41.8
Steps (reduced)		12 (12)	19 (19)	24 (24)	28 (28)	31 (31)	34 (0)	36 (2)	38 (4)	40 (6)	42 (8)	43 (9)