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39-odd-limit: Difference between revisions

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{{Odd-limit navigation|39}}The 39'''-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'' ≤ 39 and ''k'' is an integer. To the [[37-odd-limit]], it adds 11 pairs of [[octave-reduced]] intervals involving 39.
{{Odd-limit navigation|39}}
 
{{Odd-limit intro|39}}
Below is a list of all octave-reduced intervals in the 39-odd-limit.


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{| class="wikitable"
{| class="wikitable"
|'''Ratio'''
! Ratio
|'''Size ('''[[Cents|¢]]''')'''
! Size ([[cents|¢]])
|Color name
! Color name
|Name
! Name
|-
|-
|40/39
| 40/39
|43.831
| 43.831
|tridecimal minor diesis
| tridecimal minor diesis
|thuyo 2nd
| thuyo 2nd
|-
|-
|39/38
| 39/38
|44.97
| 44.97
|undevicesimal diesis
| undevicesimal diesis
|nutho 2nd
| nutho 2nd
|-
|-
|39/37
| 39/37
|91.139
| 91.139
|trigesimoseptimal limma
| trigesimoseptimal limma
|thisutho 2nd
| thisutho 2nd
|-
|-
|39/35
| 39/35
|187.343
| 187.343
|animist major second
| animist major second
|thorugu 2nd
| thorugu 2nd
|-
|-
|44/39
| 44/39
|208.835
| 208.835
|major minthic tone
| major minthic tone
|thulo 2nd
| thulo 2nd
|-
|-
|39/34
| 39/34
|237.527
| 237.527
|septendecimal supermajor second
| septendecimal supermajor second
|sutho 2nd
| sutho 2nd
|-
|-
|46/39
| 46/39
|285.792
| 285.792
|laodicismic minor third
| laodicismic minor third
|twethothu 3rd
| twethothu 3rd
|-
|-
|39/32
| 39/32
|342.483
| 342.483
|lesser tridecimal neutral third
| lesser tridecimal neutral third
|tho 3rd
| tho 3rd
|-
|-
|39/31
| 39/31
|397.447
| 397.447
|trigesimoprimal major third
| trigesimoprimal major third
|thiwutho 4th
| thiwutho 4th
|-
|-
|50/39
| 50/39
|430.145
| 430.145
|major minthmic supermajor third
| major minthmic supermajor third
|thuyoyo 3rd
| thuyoyo 3rd
|-
|-
|39/29
| 39/29
|512.905
| 512.905
|vigesimononal acute fourth
| vigesimononal acute fourth
|twenutho 4th
| twenutho 4th
|-
|-
|39/28
| 39/28
|573.657
| 573.657
|mynucumic lesser tritone
| mynucumic lesser tritone
|thoru 4th
| thoru 4th
|-
|-
|56/39
| 56/39
|626.343
| 626.343
|mynucumic greater tritone
| mynucumic greater tritone
|thuzo 5th
| thuzo 5th
|-
|-
|58/39
| 58/39
|687.095
| 687.095
|vigesimononal grave fifth
| vigesimononal grave fifth
|twenothu 5th
| twenothu 5th
|-
|-
|39/25
| 39/25
|769.855
| 769.855
|major minthmic subminor sixth
| major minthmic subminor sixth
|thogugu 6th
| thogugu 6th
|-
|-
|62/39
| 62/39
|802.553
| 802.553
|trigesimoprimal minor sixth
| trigesimoprimal minor sixth
|thiwothu 5th
| thiwothu 5th
|-
|-
|64/39
| 64/39
|857.517
| 857.517
|greater tridecimal neutral sixth
| greater tridecimal neutral sixth
|thu 6th
| thu 6th
|-
|-
|39/23
| 39/23
|914.208
| 914.208
|laodicismic major sixth
| laodicismic major sixth
|twethutho 6th
| twethutho 6th
|-
|-
|68/39
| 68/39
|962.473
| 962.473
|septendecimal subminor seventh
| septendecimal subminor seventh
|sothu 7th
| sothu 7th
|-
|-
|39/22
| 39/22
|991.165
| 991.165
|major minthic minor seventh
| major minthic minor seventh
|tholu 7th
| tholu 7th
|-
|-
|70/39
| 70/39
|1012.657
| 1012.657
|animist minor seventh
| animist minor seventh
|thuzoyo 7th
| thuzoyo 7th
|-
|-
|74/39
| 74/39
|1108.861
| 1108.861
|trigesimoseptimal major seventh
| trigesimoseptimal major seventh
|thisothu octave
| thisothu octave
|-
|-
|76/39
| 76/39
|1155.03
| 1155.03
|vigesimononal suboctave
| vigesimononal suboctave
|nothu octave
| nothu octave
|-
|-
|39/20
| 39/20
|1156.169
| 1156.169
|tridecimal suboctave
| tridecimal suboctave
|thogu octave
| thogu octave
|}
|}
The smallest [[equal division of the octave]] which is consistent to the 39-odd-limit is [[311edo]] (by virtue of it being consistent in the [[41-odd-limit]]); that which is distinctly consistent to the same is [[2554edo]].
The smallest [[equal division of the octave]] which is consistent to the 39-odd-limit is [[311edo]] (by virtue of it being consistent in the [[41-odd-limit]]); that which is distinctly consistent to the same is [[2554edo]].
[[Category:39-odd-limit| ]] <!-- main article -->
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