41edt

← 40edt

41edt

42edt →

Prime factorization	41 (prime)
Step size	46.3891¢
Octave	26\41edt (1206.12¢)
Consistency limit	10
Distinct consistency limit	8

Division of the third harmonic into 41 equal parts (41edt) is related to 26 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 6.1178 cents stretched and the step size is about 46.3891 cents. Unlike 26edo, it is only consistent up to the 10-integer-limit, with discrepancy for the 11th harmonic.

41edt is related to the regular temperament which tempers out 823543/820125 and 2199023255552/2197176384375 in the 7-limit, which is supported by 181, 207, 388, 569, and 595 EDOs.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	46.389
2	92.778	18/17, 19/18, 20/19
3	139.167	13/12, 25/23, 27/25
4	185.557	10/9, 19/17, 29/26
5	231.946	8/7
6	278.335	20/17, 27/23
7	324.724	23/19, 29/24
8	371.113	21/17, 26/21
9	417.502	23/18
10	463.891	17/13, 21/16, 30/23
11	510.281
12	556.67	18/13, 29/21
13	603.059	17/12, 24/17, 27/19
14	649.448	29/20
15	695.837	3/2
16	742.226	20/13, 23/15, 26/17
17	788.615	19/12, 30/19
18	835.005	13/8, 21/13
19	881.394	5/3
20	927.783	12/7, 29/17
21	974.172	7/4
22	1020.561	9/5
23	1066.95	13/7, 24/13
24	1113.34	19/10
25	1159.729
26	1206.118	2/1
27	1252.507
28	1298.896	17/8, 19/9
29	1345.285	13/6
30	1391.674	29/13
31	1438.064	16/7, 23/10
32	1484.453
33	1530.842	17/7, 29/12
34	1577.231
35	1623.62	23/9
36	1670.009	21/8
37	1716.398	27/10
38	1762.788	25/9
39	1809.177	17/6
40	1855.566
41	1901.955	3/1

Harmonics

Approximation of harmonics in 41edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.1	+0.0	+12.2	-3.0	+6.1	+17.6	+18.4	+0.0	+3.2	-22.7	+12.2
	Relative (%)	+13.2	+0.0	+26.4	-6.4	+13.2	+37.9	+39.6	+0.0	+6.8	-48.9	+26.4
Steps (reduced)		26 (26)	41 (0)	52 (11)	60 (19)	67 (26)	73 (32)	78 (37)	82 (0)	86 (4)	89 (7)	93 (11)

Approximation of harmonics in 41edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+12.8	-22.7	-3.0	-21.9	+12.3	+6.1	+5.3	+9.3	+17.6	-16.6	-0.7
	Relative (%)	+27.7	-48.9	-6.4	-47.2	+26.5	+13.2	+11.4	+20.0	+37.9	-35.7	-1.6
Steps (reduced)		96 (14)	98 (16)	101 (19)	103 (21)	106 (24)	108 (26)	110 (28)	112 (30)	114 (32)	115 (33)	117 (35)

Related regular temperaments

181&207 temperament

5-limit

Comma: |287 -121 -41>

POTE generator: ~|140 -59 -20> = 46.3927

Mapping: [<1 0 7|, <0 41 -121|]

EDOs: 181, 207, 388, 569, 595, 957, 1345

Badness: 17.5651

7-limit

Commas: 823543/820125, 2199023255552/2197176384375

POTE generator: ~131072/127575 = 46.3932

Mapping: [<1 0 7 3|, <0 41 -121 -5|]

EDOs: 181, 207, 388, 569, 595

Badness: 0.6461

11-limit

Commas: 42592/42525, 43923/43904, 184877/184320

POTE generator: ~352/343 = 46.3934

Mapping: [<1 0 7 3 4|, <0 41 -121 -5 -14|]

EDOs: 181, 207, 388, 569, 595

Badness: 0.1362

13-limit

Commas: 847/845, 4096/4095, 4459/4455, 17303/17280

POTE generator: ~352/343 = 46.3921

Mapping: [<1 0 7 3 4 2|, <0 41 -121 -5 -14 44|]

EDOs: 181, 207, 388, 569, 595

Badness: 0.0707

17-limit

Commas: 833/832, 847/845, 1089/1088, 2058/2057, 2431/2430

POTE generator: ~187/182 = 46.3918

Mapping: [<1 0 7 3 4 2 2|, <0 41 -121 -5 -14 44 54|]

EDOs: 181, 207, 388, 569, 595

Badness: 0.0411

26&388 temperament

5-limit

Comma: |-41 146 -82>

POTE generator: ~|-16 57 -32> = 46.3883

Mapping: [<2 0 -1|, <0 41 73|]

EDOs: 26, 388, 414, 802, 1190, 1578, 1966, 2354

Badness: 3.9285

7-limit

Commas: 4375/4374, |-62 -1 2 21>

POTE generator: ~17294403/16777216 = 46.3835

Mapping: [<2 0 -1 6|, <0 41 73 -5|]

EDOs: 26, 362, 388, 414, 802

Badness: 0.4543

11-limit

Commas: 3025/3024, 4375/4374, 5931980229/5905580032

POTE generator: ~352/343 = 46.3827

Mapping: [<2 0 -1 6 8|, <0 41 73 -5 -14|]

EDOs: 26, 362, 388, 414, 802

Badness: 0.1020

13-limit

Commas: 2200/2197, 3025/3024, 4375/4374, 50421/50336

POTE generator: ~352/343 = 46.3825

Mapping: [<2 0 -1 6 8 4|, <0 41 73 -5 -14 44|]

EDOs: 26, 362, 388, 414, 802

Badness: 0.0595

17-limit

Commas: 833/832, 1089/1088, 1225/1224, 1701/1700, 2200/2197

POTE generator: ~187/182 = 46.3824

Mapping: [<2 0 -1 6 8 4 4|, <0 41 73 -5 -14 44 54|]

EDOs: 26, 362, 388, 414, 802

Badness: 0.0326