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{{Odd-limit navigation}}The '''41-odd-limit''' is the set of all [[Rational interval|rational intervals]] which can be written as 2<sup>''k''</sup>(''a''/''b'') where ''a'', ''b'' ≤ 31 and ''k'' is an integer. To the [[39-odd-limit]], it adds 20 pairs of [[octave-reduced]] intervals involving 41.
{{Odd-limit navigation|41}}
{{Odd-limit intro|41}}


Below is a list of all octave-reduced intervals in the 41-odd-limit.
* [[1/1]]
 
* '''[[42/41]], [[41/21]]'''
* 1/1
* '''[[41/40]], [[80/41]]'''
* '''42/41, 41/21'''
* [[40/39]], [[39/20]]
* '''41/40, 80/41'''
* [[39/38]], [[76/39]]
* 40/39, 39/20
* [[38/37]], [[37/19]]
* 39/38, 76/39
* [[37/36]], [[72/37]]
* 38/37, 37/19
* [[36/35]], [[35/18]]
* 37/36, 72/37
* [[35/34]], [[68/35]]
* 36/35, 35/18
* [[34/33]], [[33/17]]
* 35/34, 68/35
* [[33/32]], [[64/33]]
* 34/33, 33/17
* [[32/31]], [[31/16]]
* 33/32, 64/33
* [[31/30]], [[60/31]]
* 32/31, 31/16
* [[30/29]], [[29/15]]
* 31/30, 60/31
* [[29/28]], [[56/29]]
* 30/29, 29/15
* [[28/27]], [[27/14]]
* 29/28, 56/29
* [[27/26]], [[52/27]]
* 28/27, 27/14
* [[26/25]], [[25/13]]
* 27/26, 52/27
* [[25/24]], [[48/25]]
* 26/25, 25/13
* [[24/23]], [[23/12]]
* 25/24, 48/25
* [[23/22]], [[44/23]]
* 24/23, 23/12
* [[22/21]], [[21/11]]
* 23/22, 44/23
* [[21/20]], [[40/21]]
* 22/21, 21/11
* '''[[41/39]], [[78/41]]'''
* 21/20, 40/21
* [[20/19]], [[19/10]]
* '''41/39, 78/41'''
* [[39/37]], [[74/39]]
* 20/19, 19/10
* [[19/18]], [[36/19]]
* 39/37, 74/39
* [[37/35]], [[70/37]]
* 19/18, 36/19
* [[18/17]], [[17/9]]
* 37/35, 70/37
* [[35/33]], [[66/35]]
* 18/17, 17/9
* [[17/16]], [[32/17]]
* 35/33, 66/35
* [[33/31]], [[62/33]]
* 17/16, 32/17
* [[16/15]], [[15/8]]
* 33/31, 62/33
* [[31/29]], [[58/31]]
* 16/15, 15/8
* [[15/14]], [[28/15]]
* 31/29, 58/31
* '''[[44/41]], [[41/22]]'''
* 15/14, 28/15
* [[29/27]], [[54/29]]
* '''44/41, 41/22'''
* [[14/13]], [[13/7]]
* 29/27, 54/29
* '''[[41/38]], [[76/41]]'''
* 14/13, 13/7
* [[27/25]], [[50/27]]
* '''41/38, 76/41'''
* [[40/37]], [[37/20]]
* 27/25, 50/27
* [[13/12]], [[24/13]]
* 40/37, 37/20
* [[38/35]], [[35/19]]
* 13/12, 24/13
* [[25/23]], [[46/25]]
* 38/35, 35/19
* [[37/34]], [[68/37]]
* 25/23, 46/25
* [[12/11]], [[11/6]]
* 37/34, 68/37
* [[35/32]], [[64/35]]
* 12/11, 11/6
* [[23/21]], [[42/23]]
* 35/32, 64/35
* [[34/31]], [[31/17]]
* 23/21, 42/23
* [[11/10]], [[20/11]]
* 34/31, 31/17
* [[32/29]], [[29/16]]
* 11/10, 20/11
* [[21/19]], [[38/21]]
* 32/29, 29/16
* [[31/28]], [[56/31]]
* 21/19, 38/21
* '''[[41/37]], [[74/41]]'''
* 31/28, 56/31
* [[10/9]], [[9/5]]
* '''41/37, 74/41'''
* [[39/35]], [[70/39]]
* 10/9, 9/5
* [[29/26]], [[52/29]]
* 39/35, 70/39
* [[19/17]], [[34/19]]
* 29/26, 52/29
* [[28/25]], [[25/14]]
* 19/17, 34/19
* [[37/33]], [[66/37]]
* 28/25, 25/14
* '''[[46/41]], [[41/23]]'''
* 37/33, 66/37
* [[9/8]], [[16/9]]
* '''46/41, 41/23'''
* [[44/39]], [[39/22]]
* 9/8, 16/9
* [[35/31]], [[62/35]]
* 44/39, 39/22
* [[26/23]], [[23/13]]
* 35/31, 62/35
* [[17/15]], [[30/17]]
* 26/23, 23/13
* [[42/37]], [[37/21]]
* 17/15, 30/17
* [[25/22]], [[44/25]]
* 42/37, 37/21
* [[33/29]], [[58/33]]
* 25/22, 44/25
* '''[[41/36]], [[72/41]]'''
* 33/29, 58/33
* [[8/7]], [[7/4]]
* '''41/36, 72/41'''
* [[39/34]], [[68/39]]
* 8/7, 7/4
* [[31/27]], [[54/31]]
* 39/34, 68/39
* [[23/20]], [[40/23]]
* 31/27, 54/31
* [[38/33]], [[33/19]]
* 23/20, 40/23
* [[15/13]], [[26/15]]
* 38/33, 33/19
* [[37/32]], [[64/37]]
* 15/13, 26/15
* [[22/19]], [[19/11]]
* 37/32, 64/37
* [[29/25]], [[50/29]]
* 22/19, 19/11
* [[36/31]], [[31/18]]
* 29/25, 50/29
* [[7/6]], [[12/7]]
* 36/31, 31/18
* '''[[48/41]], [[41/24]]'''
* 7/6, 12/7
* '''[[41/35]], [[70/41]]'''
* '''48/41, 41/24'''
* [[34/29]], [[29/17]]
* '''41/35, 70/41'''
* [[27/23]], [[46/27]]
* 34/29, 29/17
* [[20/17]], [[17/10]]
* 27/23, 46/27
* [[33/28]], [[56/33]]
* 20/17, 17/10
* [[46/39]], [[39/23]]
* 33/28, 56/33
* [[13/11]], [[22/13]]
* 46/39, 39/23
* [[32/27]], [[27/16]]
* 13/11, 22/13
* [[19/16]], [[32/19]]
* 32/27, 27/16
* [[44/37]], [[37/22]]
* 19/16, 32/19
* [[25/21]], [[42/25]]
* 44/37, 37/22
* [[31/26]], [[52/31]]
* 25/21, 42/25
* [[37/31]], [[62/37]]
* 31/26, 52/31
* [[6/5]], [[5/3]]
* 37/31, 62/37
* '''[[41/34]], [[68/41]]'''
* 6/5, 5/3
* [[35/29]], [[58/35]]
* '''41/34, 68/41'''
* [[29/24]], [[48/29]]
* 35/29, 58/35
* [[23/19]], [[38/23]]
* 29/24, 48/29
* [[40/33]], [[33/20]]
* 23/19, 38/23
* [[17/14]], [[28/17]]
* 40/33, 33/20
* [[28/23]], [[23/14]]
* 17/14, 28/17
* [[39/32]], [[64/39]]
* 28/23, 23/14
* '''[[50/41]], [[41/25]]'''
* 39/32, 64/39
* [[11/9]], [[18/11]]
* '''50/41, 41/25'''
* [[38/31]], [[31/19]]
* 11/9, 18/11
* [[27/22]], [[44/27]]
* 38/31, 31/19
* [[16/13]], [[13/8]]
* 27/22, 44/27
* [[37/30]], [[60/37]]
* 16/13, 13/8
* [[21/17]], [[34/21]]
* 37/30, 60/37
* [[26/21]], [[21/13]]
* 21/17, 34/21
* [[31/25]], [[50/31]]
* 26/21, 21/13
* [[36/29]], [[29/18]]
* 31/25, 50/31
* '''[[41/33]], [[66/41]]'''
* 36/29, 29/18
* [[46/37]], [[37/23]]
* '''41/33, 66/41'''
* [[5/4]], [[8/5]]
* 46/37, 37/23
* [[44/35]], [[35/22]]
* 5/4, 8/5
* [[39/31]], [[62/39]]
* 44/35, 35/22
* [[34/27]], [[27/17]]
* 39/31, 62/39
* [[29/23]], [[46/29]]
* 34/27, 27/17
* [[24/19]], [[19/12]]
* 29/23, 46/29
* [[19/15]], [[30/19]]
* 24/19, 19/12
* '''[[52/41]], [[41/26]]'''
* 19/15, 30/19
* [[33/26]], [[52/33]]
* '''52/41, 41/26'''
* [[14/11]], [[11/7]]
* 33/26, 52/33
* [[37/29]], [[58/37]]
* 14/11, 11/7
* [[23/18]], [[36/23]]
* 37/29, 58/37
* [[32/25]], [[25/16]]
* 23/18, 36/23
* '''[[41/32]], [[64/41]]'''
* 32/25, 25/16
* [[50/39]], [[39/25]]
* '''41/32, 64/41'''
* [[9/7]], [[14/9]]
* 50/39, 39/25
* [[40/31]], [[31/20]]
* 9/7, 14/9
* [[31/24]], [[48/31]]
* 40/31, 31/20
* [[22/17]], [[17/11]]
* 31/24, 48/31
* [[35/27]], [[54/35]]
* 22/17, 17/11
* [[48/37]], [[37/24]]
* 35/27, 54/35
* [[13/10]], [[20/13]]
* 48/37, 37/24
* [[30/23]], [[23/15]]
* 13/10, 20/13
* [[17/13]], [[26/17]]
* 30/23, 23/15
* [[38/29]], [[29/19]]
* 17/13, 26/17
* [[21/16]], [[32/21]]
* 38/29, 29/19
* [[46/35]], [[35/23]]
* 21/16, 32/21
* [[25/19]], [[38/25]]
* 46/35, 35/23
* '''[[54/41]], [[41/27]]'''
* 25/19, 38/25
* [[29/22]], [[44/29]]
* '''54/41, 41/27'''
* [[33/25]], [[50/33]]
* 29/22, 44/29
* [[37/28]], [[56/37]]
* 33/25, 50/33
* '''[[41/31]], [[62/41]]'''
* 37/28, 56/37
* [[4/3]], [[3/2]]
* '''41/31, 62/41'''
* [[39/29]], [[58/39]]
* 4/3, 3/2
* [[35/26]], [[52/35]]
* 39/29, 58/39
* [[31/23]], [[46/31]]
* 35/26, 52/35
* [[27/20]], [[40/27]]
* 31/23, 46/31
* [[50/37]], [[37/25]]
* 27/20, 40/27
* [[23/17]], [[34/23]]
* 50/37, 37/25
* [[42/31]], [[31/21]]
* 23/17, 34/23
* [[19/14]], [[28/19]]
* 42/31, 31/21
* [[34/25]], [[25/17]]
* 19/14, 28/19
* [[15/11]], [[22/15]]
* 34/25, 25/17
* '''[[56/41]], [[41/28]]'''
* 15/11, 22/15
* '''[[41/30]], [[60/41]]'''
* '''56/41, 41/28'''
* [[26/19]], [[19/13]]
* '''41/30, 60/41'''
* [[37/27]], [[54/37]]
* 26/19, 19/13
* [[48/35]], [[35/24]]
* 37/27, 54/37
* [[11/8]], [[16/11]]
* 48/35, 35/24
* [[40/29]], [[29/20]]
* 11/8, 16/11
* [[29/21]], [[42/29]]
* 40/29, 29/20
* [[18/13]], [[13/9]]
* 29/21, 42/29
* [[25/18]], [[36/25]]
* 18/13, 13/9
* [[32/23]], [[23/16]]
* 25/18, 36/25
* [[39/28]], [[56/39]]
* 32/23, 23/16
* [[46/33]], [[33/23]]
* 39/28, 56/39
* [[7/5]], [[10/7]]
* 46/33, 33/23
* [[52/37]], [[37/26]]
* 7/5, 10/7
* [[38/27]], [[27/19]]
* 52/37, 37/26
* [[31/22]], [[44/31]]
* 38/27, 27/19
* [[24/17]], [[17/12]]
* 31/22, 44/31
* '''[[41/29]], [[58/41]]'''
* 24/17, 17/12
* '''41/29, 58/41'''


{| class="wikitable"
{| class="wikitable"
|'''Ratio'''
! Ratio
|'''Size ('''[[Cents|¢]]''')'''
! Size ([[cents|¢]])
|Color name
! Color name
|Name
! Name
|-
|-
|42/41
| 42/41
|41.719
| 41.719
|fowuzo 2nd
| fowuzo 2nd
|quadragintaunimal inframinor second
| quadragesimoprimal inframinor second
|-
|-
|41/40
| 41/40
|42.749
| 42.749
|fowogu unison
| fowogu unison
|quadragintaunimal quartertone
| quadragesimoprimal quartertone
|-
|-
|41/39
| 41/39
|86.58
| 86.58
|fowothu unison
| fowothu unison
|quadragintaunimal ultraprime
| quadragesimoprimal ultraprime
|-
|-
|44/41
| 44/41
|122.256
| 122.256
|fowulo 2nd
| fowulo 2nd
|quadragintaunimal lesser minor second
| quadragesimoprimal lesser minor second
|-
|-
|41/38
| 41/38
|131.549
| 131.549
|fowonu unison
| fowonu unison
|quadragintaunimal hyperprime
| quadragesimoprimal hyperprime
|-
|-
|41/37
| 41/37
|177.718
| 177.718
|fowothisu unison
| fowothisu unison
|quadragintaunimal neutral second
| quadragesimoprimal neutral second
|-
|-
|46/41
| 46/41
|199.212
| 199.212
|fowutwetho 3rd
| fowutwetho 3rd
|quadragintaunimal minor tone
| quadragesimoprimal minor tone
|-
|-
|41/36
| 41/36
|225.152
| 225.152
|fowo 2nd
| fowo 2nd
|quadragintaunimal major tone
| quadragesimoprimal major tone
|-
|-
|48/41
| 48/41
|272.893
| 272.893
|fowu 3rd
| fowu 3rd
|quadragintaunimal subminor third
| quadragesimoprimal subminor third
|-
|-
|41/35
| 41/35
|273.923
| 273.923
|foworugu 2nd
| foworugu 2nd
|quadragintaunimal ultramajor second
| quadragesimoprimal ultramajor second
|-
|-
|41/34
| 41/34
|324.107
| 324.107
|fowosu 2nd
| fowosu 2nd
|quadragintaunimal minor third
| quadragesimoprimal minor third
|-
|-
|50/41
| 50/41
|343.565
| 343.565
|fowuyoyo 3rd
| fowuyoyo 3rd
|quadragintaunimal neutral third
| quadragesimoprimal neutral third
|-
|-
|41/33
| 41/33
|375.789
| 375.789
|fowolu 3rd
| fowolu 3rd
|quadragintaunimal submajor third
| quadragesimoprimal submajor third
|-
|-
|52/41
| 52/41
|411.465
| 411.465
|fowutho 4th
| fowutho 4th
|quadragintaunimal lesser major third
| quadragesimoprimal lesser major third
|-
|-
|41/32
| 41/32
|429.062
| 429.062
|fowo 3rd
| fowo 3rd
|quadragintaunimal greater major third
| quadragesimoprimal greater major third
|-
|-
|54/41
| 54/41
|476.803
| 476.803
|fowu 4th
| fowu 4th
|quadragintaunimal lesser minor fourth
| quadragesimoprimal lesser minor fourth
|-
|-
|41/31
| 41/31
|484.027
| 484.027
|fowothiwu 4th
| fowothiwu 4th
|quadragintaunimal greater minor fourth
| quadragesimoprimal greater minor fourth
|-
|-
|56/41
| 56/41
|539.764
| 539.764
|fowuzo 5th
| fowuzo 5th
|quadragintaunimal subdiminished fifth
| quadragesimoprimal subdiminished fifth
|-
|-
|41/30
| 41/30
|540.794
| 540.794
|fowogu 4th
| fowogu 4th
|quadragintaunimal major fourth
| quadragesimoprimal major fourth
|-
|-
|41/29
| 41/29
|599.485
| 599.485
|fowotwenu 4th
| fowotwenu 4th
|quadragintaunimal lesser tritone
| quadragesimoprimal lesser tritone
|-
|-
|58/41
| 58/41
|600.515
| 600.515
|fowutweno 5th
| fowutweno 5th
|quadragintaunimal greater tritone
| quadragesimoprimal greater tritone
|-
|-
|60/41
| 60/41
|659.206
| 659.206
|fowuyo 5th
| fowuyo 5th
|quadragintaunimal lesser minor fifth
| quadragesimoprimal lesser minor fifth
|-
|-
|41/28
| 41/28
|660.236
| 660.236
|foworu 4th
| foworu 4th
|quadragintaunimal superaugmented fourth
| quadragesimoprimal superaugmented fourth
|-
|-
|62/41
| 62/41
|715.973
| 715.973
|fowuthiwo 5th
| fowuthiwo 5th
|quadragintaunimal lesser major fifth
| quadragesimoprimal lesser major fifth
|-
|-
|41/27
| 41/27
|723.197
| 723.197
|fowo 5th
| fowo 5th
|quadragintaunimal greater major fifth
| quadragesimoprimal greater major fifth
|-
|-
|64/41
| 64/41
|770.938
| 770.938
|fowu 6th
| fowu 6th
|quadragintaunimal lesser minor sixth
| quadragesimoprimal lesser minor sixth
|-
|-
|41/26
| 41/26
|788.535
| 788.535
|fowothu 5th
| fowothu 5th
|quadragintaunimal augmented fifth
| quadragesimoprimal augmented fifth
|-
|-
|66/41
| 66/41
|824.211
| 824.211
|fowulo 6th
| fowulo 6th
|quadragintaunimal greater minor sixth
| quadragesimoprimal greater minor sixth
|-
|-
|41/25
| 41/25
|856.435
| 856.435
|fowogugu 6th
| fowogugu 6th
|quadragintaunimal neutral sixth
| quadragesimoprimal neutral sixth
|-
|-
|68/41
| 68/41
|875.893
| 875.893
|fowuso 7th
| fowuso 7th
|quadragintaunimal submajor sixth
| quadragesimoprimal submajor sixth
|-
|-
|70/41
| 70/41
|926.077
| 926.077
|fowuzoyo 7th
| fowuzoyo 7th
|quadragintaunimal lesser major sixth
| quadragesimoprimal lesser major sixth
|-
|-
|41/24
| 41/24
|927.107
| 927.107
|fowo 6th
| fowo 6th
|quadragintaunimal greater major sixth
| quadragesimoprimal greater major sixth
|-
|-
|72/41
| 72/41
|974.848
| 974.848
|fowu 7th
| fowu 7th
|quadragintaunimal lesser minor seventh
| quadragesimoprimal lesser minor seventh
|-
|-
|41/23
| 41/23
|1000.788
| 1000.788
|fowotwethu 6th
| fowotwethu 6th
|quadragintaunimal hypermajor sixth
| quadragesimoprimal hypermajor sixth
|-
|-
|74/41
| 74/41
|1022.282
| 1022.282
|fowuthiso octave
| fowuthiso octave
|quadragintaunimal greater minor seventh
| quadragesimoprimal greater minor seventh
|-
|-
|76/41
| 76/41
|1068.451
| 1068.451
|fowuno octave
| fowuno octave
|quadragintaunimal infraoctave
| quadragesimoprimal infraoctave
|-
|-
|41/22
| 41/22
|1077.744
| 1077.744
|fowolu 7th
| fowolu 7th
|quadragintaunimal lesser major seventh
| quadragesimoprimal lesser major seventh
|-
|-
|78/41
| 78/41
|1113.42
| 1113.42
|fowutho octave
| fowutho octave
|quadragintaunimal greater major seventh
| quadragesimoprimal greater major seventh
|-
|-
|80/41
| 80/41
|1157.251
| 1157.251
|fowuyo octave
| fowuyo octave
|quadragintaunimal ultramajor seventh
| quadragesimoprimal ultramajor seventh
|-
|-
|41/21
| 41/21
|1158.281
| 1158.281
|foworu 7th
| foworu 7th
|quadragintaunimal ultramajor seventh
| quadragesimoprimal ultramajor seventh
|}
|}
The smallest [[equal division of the octave]] which is consistent to the 41-odd-limit is [[311edo]]; that which is distinctly consistent to the same is [[20567edo]] (by virtue of it being distinctly consistent through the 57-odd-limit).
The smallest [[equal division of the octave]] which is consistent to the 41-odd-limit is [[311edo]]; The smallest edo that comes closest to being distinct in the 41-odd-limit is [[1600edo]] (misses 50/39, 39/25). that which is truly distinctly consistent to the same is [[2554edo]].
 
[[Category:41-odd-limit| ]] <!-- main article -->
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