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.

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