65edt

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65edt

66edt →

Prime factorization	5 × 13
Step size	29.2608¢
Octave	41\65edt (1199.69¢) (convergent)
Consistency limit	16
Distinct consistency limit	10

Division of the third harmonic into 65 equal parts (65EDT) is almost identical to 41 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed and the step size is about 29.2608 cents. It is consistent to the 16-integer-limit.

Intervals

Degree	Cent value	Hekts	Corresponding JI intervals	Comments
0			exact 1/1
1	29.2608	20	57/56, 56/55
2	58.5217	40	30/29
3	87.7825	60	21/20, 20/19
4	117.0434	80	15/14
5	146.3042	100	49/45, 12/11
6	175.5651	120	21/19, 87/80, 72/65	pseudo-10/9
7	204.8259	140	9/8
8	234.0868	160	8/7
9	263.3476	180	7/6
10	292.6085	200	45/38, 32/27
11	321.8693	220	65/54	pseudo-6/5
12	351.1302	240	11/9, 27/22
13	380.391	260	56/45, 81/65	pseudo-5/4
14	409.6518	280	19/15
15	438.9127	300	9/7
16	468.1735	320	21/16
17	497.4344	340	4/3
18	526.6952	360	19/14
19	555.9561	380	40/29
20	585.2169	400	7/5
21	614.4778	420	10/7
22	643.7386	440	29/20
23	672.9995	460	28/19
24	702.2603	480	3/2
25	731.5212	500	32/21
26	760.782	520	45/29
27	790.0428	540	30/19
28	819.3037	560	45/28	pseudo-8/5
29	848.5645	580	18/11
30	877.8254	600	108/65	pseudo-5/3
31	907.0862	620	27/16
32	936.3471	640	12/7
33	965.6079	660	7/4
34	994.8688	680	16/9
35	1024.1296	700	65/36	pseudo-9/5
36	1053.3905	720	11/6
37	1082.6513	740	28/15
38	1111.9122	760	19/10
39	1141.173	780	29/15
40	1170.4338	800	55/28
41	1199.6947	820	2/1
42	1228.9555	840	57/28
43	1258.2164	860	60/29
44	1287.4772	880	21/10
45	1316.7381	900	15/7
46	1345.9989	920	87/40
47	1375.2598	940	42/19
48	1404.5206	960	9/4
49	1433.7815	980	16/7
50	1463.0423	1000	7/3
51	1492.3032	1020	45/19
52	1521.564	1040	65/27	pseudo-12/5
53	1550.8248	1060	22/9, 27/11
54	1580.0857	1080	162/65	pseudo-5/2
55	1609.3465	1100	38/15
56	1638.6074	1120	18/7
57	1667.8682	1140	21/8
58	1697.1291	1160	8/3
59	1726.3899	1180	19/7
60	1755.6508	1200	11/4
61	1784.9116	1220	14/5
62	1814.1725	1240	20/7
63	1843.4333	1260	29/10
64	1872.6942	1280	56/19
65	1901.9550	1300	exact 3/1	just perfect fifth plus an octave

Harmonics

Approximation of harmonics in 65edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.3	+0.0	-0.6	-6.5	-0.3	-3.8	-0.9	+0.0	-6.8	+3.7	-0.6
	Relative (%)	-1.0	+0.0	-2.1	-22.3	-1.0	-13.1	-3.1	+0.0	-23.4	+12.7	-2.1
Steps (reduced)		41 (41)	65 (0)	82 (17)	95 (30)	106 (41)	115 (50)	123 (58)	130 (0)	136 (6)	142 (12)	147 (17)

Approximation of harmonics in 65edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.1	-4.1	-6.5	-1.2	+10.9	-0.3	-6.1	-7.1	-3.8	+3.4	+14.2
	Relative (%)	+24.3	-14.1	-22.3	-4.2	+37.1	-1.0	-20.9	-24.4	-13.1	+11.7	+48.7
Steps (reduced)		152 (22)	156 (26)	160 (30)	164 (34)	168 (38)	171 (41)	174 (44)	177 (47)	180 (50)	183 (53)	186 (56)