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41-odd-limit: Difference between revisions

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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'' ≤ 41 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.


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{| 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
|quadragesimoprimal inframinor second
| quadragesimoprimal inframinor second
|-
|-
|41/40
| 41/40
|42.749
| 42.749
|fowogu unison
| fowogu unison
|quadragesimoprimal quartertone
| quadragesimoprimal quartertone
|-
|-
|41/39
| 41/39
|86.58
| 86.58
|fowothu unison
| fowothu unison
|quadragesimoprimal ultraprime
| quadragesimoprimal ultraprime
|-
|-
|44/41
| 44/41
|122.256
| 122.256
|fowulo 2nd
| fowulo 2nd
|quadragesimoprimal lesser minor second
| quadragesimoprimal lesser minor second
|-
|-
|41/38
| 41/38
|131.549
| 131.549
|fowonu unison
| fowonu unison
|quadragesimoprimal hyperprime
| quadragesimoprimal hyperprime
|-
|-
|41/37
| 41/37
|177.718
| 177.718
|fowothisu unison
| fowothisu unison
|quadragesimoprimal neutral second
| quadragesimoprimal neutral second
|-
|-
|46/41
| 46/41
|199.212
| 199.212
|fowutwetho 3rd
| fowutwetho 3rd
|quadragesimoprimal minor tone
| quadragesimoprimal minor tone
|-
|-
|41/36
| 41/36
|225.152
| 225.152
|fowo 2nd
| fowo 2nd
|quadragesimoprimal major tone
| quadragesimoprimal major tone
|-
|-
|48/41
| 48/41
|272.893
| 272.893
|fowu 3rd
| fowu 3rd
|quadragesimoprimal subminor third
| quadragesimoprimal subminor third
|-
|-
|41/35
| 41/35
|273.923
| 273.923
|foworugu 2nd
| foworugu 2nd
|quadragesimoprimal ultramajor second
| quadragesimoprimal ultramajor second
|-
|-
|41/34
| 41/34
|324.107
| 324.107
|fowosu 2nd
| fowosu 2nd
|quadragesimoprimal minor third
| quadragesimoprimal minor third
|-
|-
|50/41
| 50/41
|343.565
| 343.565
|fowuyoyo 3rd
| fowuyoyo 3rd
|quadragesimoprimal neutral third
| quadragesimoprimal neutral third
|-
|-
|41/33
| 41/33
|375.789
| 375.789
|fowolu 3rd
| fowolu 3rd
|quadragesimoprimal submajor third
| quadragesimoprimal submajor third
|-
|-
|52/41
| 52/41
|411.465
| 411.465
|fowutho 4th
| fowutho 4th
|quadragesimoprimal lesser major third
| quadragesimoprimal lesser major third
|-
|-
|41/32
| 41/32
|429.062
| 429.062
|fowo 3rd
| fowo 3rd
|quadragesimoprimal greater major third
| quadragesimoprimal greater major third
|-
|-
|54/41
| 54/41
|476.803
| 476.803
|fowu 4th
| fowu 4th
|quadragesimoprimal lesser minor fourth
| quadragesimoprimal lesser minor fourth
|-
|-
|41/31
| 41/31
|484.027
| 484.027
|fowothiwu 4th
| fowothiwu 4th
|quadragesimoprimal greater minor fourth
| quadragesimoprimal greater minor fourth
|-
|-
|56/41
| 56/41
|539.764
| 539.764
|fowuzo 5th
| fowuzo 5th
|quadragesimoprimal subdiminished fifth
| quadragesimoprimal subdiminished fifth
|-
|-
|41/30
| 41/30
|540.794
| 540.794
|fowogu 4th
| fowogu 4th
|quadragesimoprimal major fourth
| quadragesimoprimal major fourth
|-
|-
|41/29
| 41/29
|599.485
| 599.485
|fowotwenu 4th
| fowotwenu 4th
|quadragesimoprimal lesser tritone
| quadragesimoprimal lesser tritone
|-
|-
|58/41
| 58/41
|600.515
| 600.515
|fowutweno 5th
| fowutweno 5th
|quadragesimoprimal greater tritone
| quadragesimoprimal greater tritone
|-
|-
|60/41
| 60/41
|659.206
| 659.206
|fowuyo 5th
| fowuyo 5th
|quadragesimoprimal lesser minor fifth
| quadragesimoprimal lesser minor fifth
|-
|-
|41/28
| 41/28
|660.236
| 660.236
|foworu 4th
| foworu 4th
|quadragesimoprimal superaugmented fourth
| quadragesimoprimal superaugmented fourth
|-
|-
|62/41
| 62/41
|715.973
| 715.973
|fowuthiwo 5th
| fowuthiwo 5th
|quadragesimoprimal lesser major fifth
| quadragesimoprimal lesser major fifth
|-
|-
|41/27
| 41/27
|723.197
| 723.197
|fowo 5th
| fowo 5th
|quadragesimoprimal greater major fifth
| quadragesimoprimal greater major fifth
|-
|-
|64/41
| 64/41
|770.938
| 770.938
|fowu 6th
| fowu 6th
|quadragesimoprimal lesser minor sixth
| quadragesimoprimal lesser minor sixth
|-
|-
|41/26
| 41/26
|788.535
| 788.535
|fowothu 5th
| fowothu 5th
|quadragesimoprimal augmented fifth
| quadragesimoprimal augmented fifth
|-
|-
|66/41
| 66/41
|824.211
| 824.211
|fowulo 6th
| fowulo 6th
|quadragesimoprimal greater minor sixth
| quadragesimoprimal greater minor sixth
|-
|-
|41/25
| 41/25
|856.435
| 856.435
|fowogugu 6th
| fowogugu 6th
|quadragesimoprimal neutral sixth
| quadragesimoprimal neutral sixth
|-
|-
|68/41
| 68/41
|875.893
| 875.893
|fowuso 7th
| fowuso 7th
|quadragesimoprimal submajor sixth
| quadragesimoprimal submajor sixth
|-
|-
|70/41
| 70/41
|926.077
| 926.077
|fowuzoyo 7th
| fowuzoyo 7th
|quadragesimoprimal lesser major sixth
| quadragesimoprimal lesser major sixth
|-
|-
|41/24
| 41/24
|927.107
| 927.107
|fowo 6th
| fowo 6th
|quadragesimoprimal greater major sixth
| quadragesimoprimal greater major sixth
|-
|-
|72/41
| 72/41
|974.848
| 974.848
|fowu 7th
| fowu 7th
|quadragesimoprimal lesser minor seventh
| quadragesimoprimal lesser minor seventh
|-
|-
|41/23
| 41/23
|1000.788
| 1000.788
|fowotwethu 6th
| fowotwethu 6th
|quadragesimoprimal hypermajor sixth
| quadragesimoprimal hypermajor sixth
|-
|-
|74/41
| 74/41
|1022.282
| 1022.282
|fowuthiso octave
| fowuthiso octave
|quadragesimoprimal greater minor seventh
| quadragesimoprimal greater minor seventh
|-
|-
|76/41
| 76/41
|1068.451
| 1068.451
|fowuno octave
| fowuno octave
|quadragesimoprimal infraoctave
| quadragesimoprimal infraoctave
|-
|-
|41/22
| 41/22
|1077.744
| 1077.744
|fowolu 7th
| fowolu 7th
|quadragesimoprimal lesser major seventh
| quadragesimoprimal lesser major seventh
|-
|-
|78/41
| 78/41
|1113.42
| 1113.42
|fowutho octave
| fowutho octave
|quadragesimoprimal greater major seventh
| quadragesimoprimal greater major seventh
|-
|-
|80/41
| 80/41
|1157.251
| 1157.251
|fowuyo octave
| fowuyo octave
|quadragesimoprimal ultramajor seventh
| quadragesimoprimal ultramajor seventh
|-
|-
|41/21
| 41/21
|1158.281
| 1158.281
|foworu 7th
| foworu 7th
|quadragesimoprimal ultramajor seventh
| quadragesimoprimal ultramajor seventh
|}
|}
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]].
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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