71edt

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71edt

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Prime factorization	71 (prime)
Step size	26.7881¢
Octave	45\71edt (1205.46¢)
Consistency limit	7
Distinct consistency limit	7

71EDT is the equal division of the third harmonic into 71 parts of 26.7881 cents each, corresponding to 44.7960 edo (45edo with 5.4644 cents octave stretch). It is related to the 13-limit temperament which tempers out 540/539, 1575/1573, 2200/2197, and 4375/4374, which is supported by 45edo (45ef val), 179edo (179ef val), 224edo, 269edo (269ce val), and 403edo (403def val).

71EDT is the 13th no-twos zeta peak EDT.

Harmonics

Approximation of prime harmonics in 71edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+5.5	+0.0	-0.4	+6.5	+0.8	+6.3	-2.7	-7.8	+9.7	+10.2	+1.9
	Relative (%)	+20.4	+0.0	-1.3	+24.2	+3.1	+23.5	-10.2	-29.0	+36.2	+38.2	+7.2
Steps (reduced)		45 (45)	71 (0)	104 (33)	126 (55)	155 (13)	166 (24)	183 (41)	190 (48)	203 (61)	218 (5)	222 (9)

Approximation of prime harmonics in 71edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-9.7	+0.1	-2.0	+4.7	+11.0	+12.9	+8.7	+7.1	-13.0	-7.5	-10.3
	Relative (%)	-36.3	+0.3	-7.5	+17.7	+41.2	+48.1	+32.7	+26.3	-48.4	-27.9	-38.4
Steps (reduced)		233 (20)	240 (27)	243 (30)	249 (36)	257 (44)	264 (51)	266 (53)	272 (59)	275 (62)	277 (64)	282 (69)

Intervals

degree	cents value	hekts	corresponding JI intervals	comments
0			exact 1/1
1	26.7881	18.3099	66/65
2	53.5762	36.6197	65/63
3	80.3643	54.9296	22/21
4	107.1524	73.2394	117/110
5	133.9405	91.5493	27/25
6	160.7286	109.85915	169/154
7	187.5167	128.169	39/35
8	214.3048	146.4789	147/130, 198/175
9	241.0929	164.7887	169/147
10	267.8810	183.0986	7/6
11	294.6691	201.40845	77/65
12	321.4572	219.7183	65/54
13	348.2453	238.0282	11/9
14	375.0334	256.338	273/220
15	401.8215	274.6479	63/50
16	428.6096	292.95775	169/132
17	455.3977	311.2676	13/10
18	482.1858	329.5775	33/25
19	508.9739	347.8873	169/126
20	535.7620	366.1972	15/11
21	562.5501	384.507	18/13
22	589.3382	402.8169	(45/32)
23	616.1263	421.1268	10/7
24	642.9144	439.4366	132/91
25	669.7025	457.7465	22/15
26	696.4906	476.0563	486/325, 220/147	pseudo-3/2
27	723.2787	494.3662	50/33
28	750.0668	512.6761	54/35
29	776.8549	530.9859	264/169
30	803.643	549.2958	35/22
31	830.4311	567.6056	21/13
32	857.2192	585.9155	18/11
33	884.0073	604.22535	5/3
34	910.7954	622.5352	22/13
35	937.5835	640.8451	12/7
36	964.3715	659.1549	7/4
37	991.1596	677.4648	39/22
38	1017.9477	695.77465	9/5
39	1044.7358	714.0845	11/6
40	1071.5239	732.3944	13/7
41	1098.312	750.7042	66/35
42	1125.1001	769.0141	21/11
43	1151.8882	787.3239	35/18
44	1178.6763	805.6338	22/13
45	1205.4644	823.9437	441/220, 325/162	pseudo-octave
46	1232.2525	842.2535	45/22
47	1259.0406	860.5634	91/44
48	1285.8287	878.8732	21/10
49	1312.6168	897.1831	(32/15)
50	1339.4049	915.493	13/6
51	1366.193	933.8028	11/5
52	1392.9811	952.1127	378/169
53	1419.7692	970.4225	25/11
54	1446.5573	988.7324	30/13
55	1473.3454	1007.04225	396/169
56	1500.1335	1025.3521	50/21
57	1526.9216	1043.662	220/91
58	1553.7097	1061.9718	27/11
59	1580.4978	1080.2817	162/65
60	1607.2859	1098.59155	195/77
61	1634.0740	1161.9014	18/7
62	1660.8621	1135.2113	441/169
63	1687.6502	1153.5211	175/66, 130/49
64	1714.4383	1171.831	35/13, 132/49
65	1741.2264	1190.14085	462/169
66	1768.0145	1208.4507	25/9
67	1794.8026	1226.7606	110/39
68	1821.5907	1245.0704	63/22
69	1848.3788	1263.3803	189/65
70	1875.1669	1281.6901	65/22
71	1901.9550	1300	exact 3/1	just perfect fifth plus an octave