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'''[[Edt|Division of the third harmonic]] into 41 equal parts''' (41edt) is related to [[26edo|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 [[9-odd-limit|10-integer-limit]], with discrepancy for the 11th harmonic.
{{Infobox ET}}
{{ED intro}}


41edt is related to the regular  temperament which tempers out 823543/820125 and 2199023255552/2197176384375 in the 7-limit, which is supported by [[181edo|181]], [[207edo|207]], [[388edo|388]], 569, and 595 EDOs.
41edt is related to [[26edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 6.12 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.


=Related regular temperaments=
41edt is related to the regular temperament which tempers out 823543/820125 and 2199023255552/2197176384375 in the 7-limit, which is supported by {{EDOs| 181, 207, 388, 569, and 595 }} EDOs.
==181&207 temperament==
===5-limit===
Comma: |287 -121 -41>


POTE generator: ~|140 -59 -20> = 46.3927
== Intervals ==
{{Interval table}}


Map: [<1 0 7|, <0 41 -121|]
== Harmonics ==
{{Harmonics in equal
| steps = 41
| num = 3
| denom = 1
| intervals = prime
}}
{{Harmonics in equal
| steps = 41
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = prime
}}


EDOs: 181, 207, 388, 569, 595, 957, 1345
= Related regular temperaments =
== 181 & 207 temperament ==
=== 5-limit ===
Comma: {{monzo| 287 -121 -41 }}


===7-limit===
POTE generator: ~{{monzo| 140 -59 -20 }} = 46.3927
 
Mapping: [{{map| 1 0 7 }}, {{map| 0 41 -121 }}]
 
EDOs: {{EDOs|181, 207, 388, 569, 595, 957, 1345}}
 
Badness: 17.5651
 
=== 7-limit ===
Commas: 823543/820125, 2199023255552/2197176384375
Commas: 823543/820125, 2199023255552/2197176384375


POTE generator: ~131072/127575 = 46.3932
POTE generator: ~131072/127575 = 46.3932


Map: [<1 0 7 3|, <0 41 -121 -5|]
Mapping: [{{map| 1 0 7 3 }}, {{map| 0 41 -121 -5}}]


EDOs: 181, 207, 388, 569, 595
EDOs: {{EDOs|181, 207, 388, 569, 595}}


===11-limit===
Badness: 0.6461
 
=== 11-limit ===
Commas: 42592/42525, 43923/43904, 184877/184320
Commas: 42592/42525, 43923/43904, 184877/184320


POTE generator: ~352/343 = 46.3934
POTE generator: ~352/343 = 46.3934


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


EDOs: 181, 207, 388, 569, 595
EDOs: {{EDOs|181, 207, 388, 569, 595}}


===13-limit===
Badness: 0.1362
 
=== 13-limit ===
Commas: 847/845, 4096/4095, 4459/4455, 17303/17280
Commas: 847/845, 4096/4095, 4459/4455, 17303/17280


POTE generator: ~352/343 = 46.3921
POTE generator: ~352/343 = 46.3921


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


EDOs: 181, 207, 388, 569, 595
EDOs: {{EDOs|181, 207, 388, 569, 595}}


===17-limit===
Badness: 0.0707
 
=== 17-limit ===
Commas: 833/832, 847/845, 1089/1088, 2058/2057, 2431/2430
Commas: 833/832, 847/845, 1089/1088, 2058/2057, 2431/2430


POTE generator: ~187/182 = 46.3918
POTE generator: ~187/182 = 46.3918


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


EDOs: 181, 207, 388, 569, 595
EDOs: {{EDOs|181, 207, 388, 569, 595}}


==26&388 temperament==
Badness: 0.0411
===5-limit===
Comma: |-41 146 -82>


POTE generator: ~|-16 57 -32> = 46.3883
== 26 & 388 temperament ==
=== 5-limit ===
Comma: {{monzo| -41 146 -82 }}


Map: [<2 0 -1|, <0 41 73|]
POTE generator: ~{{monzo| -16 57 -32 }} = 46.3883


EDOs: 26, 388, 414, 802, 1190, 1578, 1966, 2354
Mapping: [{{map| 2 0 -1 }}, {{map| 0 41 73 }}]


===7-limit===
EDOs: {{EDOs|26, 388, 414, 802, 1190, 1578, 1966, 2354}}
Commas: 4375/4374, |-62 -1 2 21>
 
Badness: 3.9285
 
=== 7-limit ===
Commas: 4375/4374, {{monzo| -62 -1 2 21 }}


POTE generator: ~17294403/16777216 = 46.3835
POTE generator: ~17294403/16777216 = 46.3835


Map: [<2 0 -1 6|, <0 41 73 -5|]
Mapping: [{{map| 2 0 -1 6 }}, {{map| 0 41 73 -5 }}]
 
EDOs: {{EDOs|26, 362, 388, 414, 802}}


EDOs: 26, 362, 388, 414, 802
Badness: 0.4543


===11-limit===
=== 11-limit ===
Commas: 3025/3024, 4375/4374, 5931980229/5905580032
Commas: 3025/3024, 4375/4374, 5931980229/5905580032


POTE generator: ~352/343 = 46.3827
POTE generator: ~352/343 = 46.3827


Map: [<2 0 -1 6 8|, <0 41 73 -5 -14|]
Mapping: [{{map| 2 0 -1 6 8 }}, {{map| 0 41 73 -5 -14 }}]
 
EDOs: {{EDOs|26, 362, 388, 414, 802}}


EDOs: 26, 362, 388, 414, 802
Badness: 0.1020


===13-limit===
=== 13-limit ===
Commas: 2200/2197, 3025/3024, 4375/4374, 50421/50336
Commas: 2200/2197, 3025/3024, 4375/4374, 50421/50336


POTE generator: ~352/343 = 46.3825
POTE generator: ~352/343 = 46.3825


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


EDOs: 26, 362, 388, 414, 802
EDOs: {{EDOs|26, 362, 388, 414, 802}}


===17-limit===
Badness: 0.0595
 
=== 17-limit ===
Commas: 833/832, 1089/1088, 1225/1224, 1701/1700, 2200/2197
Commas: 833/832, 1089/1088, 1225/1224, 1701/1700, 2200/2197


POTE generator: ~187/182 = 46.3824
POTE generator: ~187/182 = 46.3824


Map: [<2 0 -1 6 8 4 4|, <0 41 73 -5 -14 44 54|]
Mapping: [{{map| 2 0 -1 6 8 4 4 }}, {{map| 0 41 73 -5 -14 44 54 }}]
 
EDOs: {{EDOs|26, 362, 388, 414, 802}}


EDOs: 26, 362, 388, 414, 802
Badness: 0.0326


[[Category:Edt]]
{{todo|expand}}
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/41edt"