53ed7/3

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53ed7/3

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Prime factorization	53 (prime)
Step size	27.6768¢
Octave	43\53ed7/3 (1190.1¢)
Twelfth	69\53ed7/3 (1909.7¢)
Consistency limit	2
Distinct consistency limit	2

53 equal divisions of 7/3 (abbreviated 53ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 53 equal parts of about 27.7 ¢ each. Each step represents a frequency ratio of (7/3)^1/53, or the 53rd root of 7/3.

Intervals

Degrees	Enneatonic			Pentadecatonic		Enneadecatonic	ed11\9~ed7/3
1	8x	Ex		W\\	Wb	Q#	27.673	27.6768
2	2b	Jb	Ab	Qp	Q#	Wb	55.3459	55.3536
3	9#	F#		W			83.0189	83.0304
4	3bb	Abb	Bbb	Ex	Ebb	W#	110.6918	110.7073
5	1#	G#		Wp	W#	Eb	138.3648	138.38405
6	8*/4bbb	E*		E\\	Eb	E	166.0377	166.0609
		Bbbb	Cbbb
7	2	J	A	Wpp	Wx	E#/Rb	193.7107	193.7377
8	9x	Fx		E		R	221.38365	221.4145
9	3b	Ab	Bb	R\\	Rb	R#	249.0566	249.0913
10	1x	Gx		Ep	E#	Tb	276.7296	276.7681
11	4bb	Bbb	Cbb	R		T	304.4025	304.4449
12	2#	J#	A#	T\\	Tb	T#	332.0755	332.1217
13	9*/5bb	F*		Rp	R#	Yb	359.7484	359.7985
		Cbb	Qbb
14	3	A	B	T		Y	387.4214	387.4753
15	1*/6bbb	G*		A\\	Ab	Y#	415.0943	415.1521
		Qbbb	Dbbb
16	4b	Bb	Cb	Tp	T#	Ab	442.7673	442.82895
17	2x	Jx	Ax	A		U	470.44025	470.8058
18	5b	Cb	Qb	Sx	Sbb	U#	498.1132	498.1826
19	3#	A#	B#	Ap	A#	Ab	525.7862	525.8594
20	6bb	Qbb	Dbb	S\\	Sb	A	553.4591	553.5362
21	4	B	C	App	Ax	A#/Sb	581.1321	581.213
22	2*/7bbb	J*/Dbbb	A*/Sbb	S			608.805	608.889
23	5	C	Q	D\\	Db	S#	636.478	636.5666
24	3x	Ax	Bx	Sp	S#	Db	664.1509	664.2434
25	6b	Qb	Db	D			691.8239	691.9202
26	4#	B#	C#	F\\	Fb	D#	719.4969	719.59705
27	7bb	Dbb	Sbb	Dp	D#	Fb	747.1698	747.2739
28	5#	C#	Q#	F			774.8428	774.9507
29	3*/8bbb	A*	Bx	G\\	Gb	F#	802.6275	802.6275
		Ebbb
30	6	Q	D	Fp	F#	Gb	830.1887	830.3043
31	4x	Bx	Cx	G			857.8616	857.9811
32	7b	Db	Sb	Zx	Zbb	G#	885.5346	885.6579
33	5x	Cx	Qx	Gp	G#	Hb	913.20755	913.3347
34	8bb	Ebb		Z\\	Zb	H	940.8805	941.0115
35	6#	Q#	D#	Gpp	Gx	H#	968.5535	968.6883
36	4*/9bbb	B*	C*	Z		Jb	996.2264	996.3651
		Fbbb
37	7	D	S	X\\	Z#	J	1023.8994	1024.04195
38	5*/1bbb	C*	Q*	Zp	Xb	J#	1051.5723	1051.7188
		Gbbb
39	8b	Eb		X		Zb	1079.2453	1079.3956
40	6x	Qx	Dx	C\\	X#	Z	1106.9182	1107.0724
41	9bb	Fbb		Xp	Cb	Z#/Xb	1134.5912	1134.7492
42	7#	D#	S#	C		X	1162.26415	1162.426
43	1bb	Gbb		V\\	C#	X#	1189.9371	1190.1028
44	8	E		Cp	Vb	Cb	1217.6101	1217.7796
45	6*/2bbb	Q*/Jbbb	D*/Abbb	V		C	1245.253	1245.4564
46	9b	Fb		Bx	Bbb	C#/Vb	1272.956	1273.1332
47	7x	Dx	Sx	Vp	V#	V	1300.6289	1300.81005
48	1b	Gb		B\\	Bb	V#	1328.3019	1328.4869
49	8#	E#		Vpp	Vx	Bb	1355.9748	1356.1164
50	2bb	Jbb	Abb	B			1383.6478	1383.8405
51	9	F		Q\\	Qb	B#	1411.3208	1411.5173
52	7*/3bbb	D*/Abbb	S*/Bbbb	Bp	B#	Qb	1438.9937	1439.1941
53	1	G		Q			1466.6	1466.8709

Harmonics

Approximation of harmonics in 53ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-9.9	+7.7	+7.9	+9.0	-2.2	+7.7	-2.0	-12.2	-0.9	+0.2	-12.0
	Relative (%)	-35.8	+28.0	+28.5	+32.7	-7.8	+28.0	-7.3	-44.0	-3.1	+0.7	-43.5
Steps (reduced)		43 (43)	69 (16)	87 (34)	101 (48)	112 (6)	122 (16)	130 (24)	137 (31)	144 (38)	150 (44)	155 (49)

Approximation of harmonics in 53ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-12.2	-2.2	-10.9	-11.9	-6.2	+5.6	-5.0	-10.8	-12.2	-9.7	-3.6
	Relative (%)	-44.2	-7.8	-39.3	-43.0	-22.3	+20.2	-18.0	-38.8	-44.0	-35.0	-13.1
Steps (reduced)		160 (1)	165 (6)	169 (10)	173 (14)	177 (18)	181 (22)	184 (25)	187 (28)	190 (31)	193 (34)	196 (37)