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39-odd-limit: Difference between revisions

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{{Odd-limit navigation}}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 [[39-odd-limit|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.


* [[1/1]]
* [[1/1]]
* [[40/39]], [[39/20]]
* '''[[40/39]], [[39/20]]'''
* [[39/38]], [[76/39]]
* '''[[39/38]], [[76/39]]'''
* [[38/37]], [[37/19]]
* [[38/37]], [[37/19]]
* [[37/36]], [[72/37]]
* [[37/36]], [[72/37]]
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* [[21/20]], [[40/21]]
* [[21/20]], [[40/21]]
* [[20/19]], [[19/10]]
* [[20/19]], [[19/10]]
* [[39/37]], [[74/39]]
* '''[[39/37]], [[74/39]]'''
* [[19/18]], [[36/19]]
* [[19/18]], [[36/19]]
* [[37/35]], [[70/37]]
* [[37/35]], [[70/37]]
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* [[31/28]], [[56/31]]
* [[31/28]], [[56/31]]
* [[10/9]], [[9/5]]
* [[10/9]], [[9/5]]
* [[39/35]], [[70/39]]
* '''[[39/35]], [[70/39]]'''
* [[29/26]], [[52/29]]
* [[29/26]], [[52/29]]
* [[19/17]], [[34/19]]
* [[19/17]], [[34/19]]
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* [[37/33]], [[66/37]]
* [[37/33]], [[66/37]]
* [[9/8]], [[16/9]]
* [[9/8]], [[16/9]]
* [[44/39]], [[39/22]]
* '''[[44/39]], [[39/22]]'''
* [[35/31]], [[62/35]]
* [[35/31]], [[62/35]]
* [[26/23]], [[23/13]]
* [[26/23]], [[23/13]]
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* [[33/29]], [[58/33]]
* [[33/29]], [[58/33]]
* [[8/7]], [[7/4]]
* [[8/7]], [[7/4]]
* [[39/34]], [[68/39]]
* '''[[39/34]], [[68/39]]'''
* [[31/27]], [[54/31]]
* [[31/27]], [[54/31]]
* [[23/20]], [[40/23]]
* [[23/20]], [[40/23]]
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* [[20/17]], [[17/10]]
* [[20/17]], [[17/10]]
* [[33/28]], [[56/33]]
* [[33/28]], [[56/33]]
* [[46/39]], [[39/23]]
* '''[[46/39]], [[39/23]]'''
* [[13/11]], [[22/13]]
* [[13/11]], [[22/13]]
* [[32/27]], [[27/16]]
* [[32/27]], [[27/16]]
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* [[17/14]], [[28/17]]
* [[17/14]], [[28/17]]
* [[28/23]], [[23/14]]
* [[28/23]], [[23/14]]
* [[39/32]], [[64/39]]
* '''[[39/32]], [[64/39]]'''
* [[11/9]], [[18/11]]
* [[11/9]], [[18/11]]
* [[38/31]], [[31/19]]
* [[38/31]], [[31/19]]
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* [[5/4]], [[8/5]]
* [[5/4]], [[8/5]]
* [[44/35]], [[35/22]]
* [[44/35]], [[35/22]]
* [[39/31]], [[62/39]]
* '''[[39/31]], [[62/39]]'''
* [[34/27]], [[27/17]]
* [[34/27]], [[27/17]]
* [[29/23]], [[46/29]]
* [[29/23]], [[46/29]]
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* [[23/18]], [[36/23]]
* [[23/18]], [[36/23]]
* [[32/25]], [[25/16]]
* [[32/25]], [[25/16]]
* [[50/39]], [[39/25]]
* '''[[50/39]], [[39/25]]'''
* [[9/7]], [[14/9]]
* [[9/7]], [[14/9]]
* [[40/31]], [[31/20]]
* [[40/31]], [[31/20]]
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* [[37/28]], [[56/37]]
* [[37/28]], [[56/37]]
* [[4/3]], [[3/2]]
* [[4/3]], [[3/2]]
* [[39/29]], [[58/39]]
* '''[[39/29]], [[58/39]]'''
* [[35/26]], [[52/35]]
* [[35/26]], [[52/35]]
* [[31/23]], [[46/31]]
* [[31/23]], [[46/31]]
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* [[25/18]], [[36/25]]
* [[25/18]], [[36/25]]
* [[32/23]], [[23/16]]
* [[32/23]], [[23/16]]
* [[39/28]], [[56/39]]
* '''[[39/28]], [[56/39]]'''
* [[46/33]], [[33/23]]
* [[46/33]], [[33/23]]
* [[7/5]], [[10/7]]
* [[7/5]], [[10/7]]
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{| class="wikitable"
{| class="wikitable"
|'''Ratio'''
! Ratio
|'''Size ('''[[Cents|¢]]''')'''
! Size ([[cents|¢]])
|Color name
! Color name
|Name
! Name
|-
| 40/39
| 43.831
| tridecimal minor diesis
| thuyo 2nd
|-
| 39/38
| 44.97
| undevicesimal diesis
| nutho 2nd
|-
|-
|40/39
| 39/37
|43.831
| 91.139
|
| trigesimoseptimal limma
|
| thisutho 2nd
|-
|-
|39/38
| 39/35
|44.97
| 187.343
|
| animist major second
|
| thorugu 2nd
|-
|-
|39/37
| 44/39
|91.139
| 208.835
|
| major minthic tone
|
| thulo 2nd
|-
|-
|39/35
| 39/34
|187.343
| 237.527
|
| septendecimal supermajor second
|
| sutho 2nd
|-
|-
|44/39
| 46/39
|208.835
| 285.792
|
| laodicismic minor third
|
| twethothu 3rd
|-
|-
|39/34
| 39/32
|237.527
| 342.483
|
| lesser tridecimal neutral third
|
| tho 3rd
|-
|-
|46/39
| 39/31
|285.792
| 397.447
|
| trigesimoprimal major third
|
| thiwutho 4th
|-
|-
|39/31
| 50/39
|397.447
| 430.145
|
| major minthmic supermajor third
|
| thuyoyo 3rd
|-
|-
|50/39
| 39/29
|430.145
| 512.905
|
| vigesimononal acute fourth
|
| twenutho 4th
|-
|-
|39/29
| 39/28
|512.905
| 573.657
|
| mynucumic lesser tritone
|
| thoru 4th
|-
|-
|39/28
| 56/39
|573.657
| 626.343
|
| mynucumic greater tritone
|
| thuzo 5th
|-
|-
|56/39
| 58/39
|626.343
| 687.095
|
| vigesimononal grave fifth
|
| twenothu 5th
|-
|-
|58/39
| 39/25
|687.095
| 769.855
|
| major minthmic subminor sixth
|
| thogugu 6th
|-
|-
|39/25
| 62/39
|769.855
| 802.553
|
| trigesimoprimal minor sixth
|
| thiwothu 5th
|-
|-
|62/39
| 64/39
|802.553
| 857.517
|
| greater tridecimal neutral sixth
|
| thu 6th
|-
|-
|39/23
| 39/23
|914.208
| 914.208
|
| laodicismic major sixth
|
| twethutho 6th
|-
|-
|68/39
| 68/39
|962.473
| 962.473
|
| septendecimal subminor seventh
|
| sothu 7th
|-
|-
|39/22
| 39/22
|991.165
| 991.165
|
| major minthic minor seventh
|
| tholu 7th
|-
|-
|70/39
| 70/39
|1012.657
| 1012.657
|
| animist minor seventh
|
| thuzoyo 7th
|-
|-
|74/39
| 74/39
|1108.861
| 1108.861
|
| trigesimoseptimal major seventh
|
| thisothu octave
|-
|-
|76/39
| 76/39
|1155.03
| 1155.03
|
| vigesimononal suboctave
|
| nothu octave
|-
|-
|39/20
| 39/20
|1156.169
| 1156.169
|
| tridecimal suboctave
|
| 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 [[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 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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