34ed7/3

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34ed7/3

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Prime factorization	2 × 17
Step size	43.1433 ¢
Octave	28\34ed7/3 (1208.01 ¢) (→ 14\17ed7/3)
Twelfth	44\34ed7/3 (1898.3 ¢) (→ 22\17ed7/3)
Consistency limit	4
Distinct consistency limit	4

34 equal divisions of 7/3 (abbreviated 34ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 34 equal parts of about 43.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/34, or the 34th root of 7/3.

Intervals

Degrees	Enneatonic							Pentadecatonic		Enneadecatonic	ed11\9~ed7/3
1	1#	G#		G^				Qp/W\\	Q#/Wb		43.13725	43.1433
				Jv	Av	Jbv	Abv
2	1x/2bb	Gx		J	A	Jb	Ab	W			86.2745	86.2865
		Jbb	Abb
3	2b	Jb	Ab	J^/A\\v	A^/B\\v	Jb^	Ab^	Wp	W#	W#/Eb	129.4118	129.4298
						G#v
4	2	J	A	A\\	B\\	G#		E(\\/b)			172.549	172.57305
5	2#	J#	A#	A\\^/Jpv	B\\^/Apv	G#v		E		R	215.6863	215.7163
						Jv	Av
6	2x/3bb	Jx/Abb	Ax/Bbb	Jp	Ap	J	A	Ep/R\\	E#/Rb	R#/Tb	258.8235	258.8596
7	3b	Ab	Bb	Jp^/Av	Ap^/Bv	J^/Av	A^/Bv	R		T	301.9608	302.0028
8	3	A	B	A	B	A	B	Rp/T\\	R#/Tb	T#/Yb	345.098	345.1461
9	3#	A#	B#	A^/Bv	B^/Cv	A^/Bbv	B^/Cbv	T		Y	388.2353	388.2894
10	3x/4b	Ax/Bbb	Bx/Cbb	B	C	Bb	Cb	Tp\A\\	T#/Ab	Y#/Ub	431.37255	431.4326
11	4b	Bb	Cb	B^/C\\v	C^/Q\\v	Bb^/A#v	Cb^/B#v	A		U	474.5098	474.5759
12	4	B	C	C\\	Q\\	A#	B#	Ap	A#	U#/Ab	517.6471	517.7191
13	4#	B#	C#	C\\^/Bpv	Q\\^/Cpv	A#^/Bv	B#^/Cv	S\\	Sb	A	560.7843	560.8624
14	5b	Cb	Qb	Bp	Cp	B	C	S			603.9216	604.0057
15	5	C	Q	Bp^/Cv	Cp^/Qv	B^/Cv	C^/Qv	Sp/D\\	S#/Db	S#/Db	647.0588	647.1489
16	5#	C#	Q#	C	Q	C	Q	D			690.1961	690.2922
17	5x/6bb	Cx/Qbb	Qx/Dbb	C^/Qv	Q^/Dv	C^/Qbv	Q^/Dbv	Dp/F\\	D#/Fb	D#/Fb	733.3	733.43545
18	6b	Qb	Db	Q	D	Qb	Db	F			776.4706	776.5787
19	6	Q	D	Q^/D\\v	D^/E\\v	Qb^/C#v	Db^/Q#v	Fp/G\\	F#/Gb	F#/Gb	819.6078	819.722
20	6#	Q#	D#	D\\	E\\	C#	Q#	G			862.7451	862.8982
21	6x/7bb	Qx/Dbb	Dx/Sbb	D\\^/Qpv	E\\^/Dpv	C#^/Qv	Q#^/Dv	Gp	G#	H	905.88235	906.0085
22	7b	Db	Sb	Qp	Dp	Q	D	Z\\	Zb	H#	949.0196	949.1518
23	7	D	S	Qp^/Dv	Dp^/Ev	Q^/Dv	D^/Sv	Z		Jb	992.1569	922.295
24	7#	D#	S#	D	E	D	S	Zp/X\\	Z#/Xb	J	1035.2941	1035.4383
25	7x/8bb	Dx/Ebb	Sx/Ebb	D^/Ev	E^/Sv	D^	S^	X		J#/Zb	1078.4314	1078.58155
						Ebv
26	8b	Eb		E	S	Eb		Xp/C\\	X#/Cb	Z	1121.5686	1121.7248
27	8	E		E^	S^	Eb^		C		X	1164.7059	1164.8681
				Fv		D#v	S#v
28	8#	E#		F		D#	S#	Cp/V\\	C#/Vb	X#/Cb	1207.8731	1208.0113
29	8x/9bb	Ex/Fbb		F^/G\\v		D#v	S#v	V		C	1250.9804	1251.1546
						Eb
30	9b	Fb		G\\		E		V(p/#)			1294.11765	1294.2979
31	9	F		G\\^Fpv		E^/Fv		B//	Bb	V#/Bb	1337.2549	1337.4411
32	9#	F#		Fp		F		B			1380.3922	1380.5844
33	1#	G#		Fp^		F^		Bp/Q\\	B#/Qb		1423.5297	1423.7276
				Gv
34	1	G						Q			1466.6	1466.8709

Harmonics

Approximation of harmonics in 34ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.0	-3.7	+16.0	+18.0	+4.4	-3.7	-19.1	-7.3	-17.1	-9.6	+12.4
	Relative (%)	+18.6	-8.5	+37.1	+41.7	+10.1	-8.5	-44.3	-16.9	-39.7	-22.2	+28.7
Steps (reduced)		28 (28)	44 (10)	56 (22)	65 (31)	72 (4)	78 (10)	83 (15)	88 (20)	92 (24)	96 (28)	100 (32)

Approximation of harmonics in 34ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.2	+4.4	+14.3	-11.1	+13.4	+0.7	-6.6	-9.1	-7.3	-1.6	+7.8
	Relative (%)	+7.5	+10.1	+33.3	-25.7	+31.0	+1.6	-15.3	-21.1	-16.9	-3.6	+18.0
Steps (reduced)		103 (1)	106 (4)	109 (7)	111 (9)	114 (12)	116 (14)	118 (16)	120 (18)	122 (20)	124 (22)	126 (24)