39-odd-limit: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Eufalesio (talk | contribs)
autopatrolled
634 edits
mNo edit summary
m + category
 
(4 intermediate revisions by 3 users not shown)
Line 1: Line 1:
{{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]]
Line 59: Line 58:
* [[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]]
* [[17/15]], [[30/17]]
* [[17/15]], [[30/17]]
* [[42/37]], [[37/21]]
* [[42/37]], [[37/21]]
Line 164: Line 163:


{| 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 -->

Latest revision as of 15:37, 23 September 2025

← 37-odd-limit  39-odd-limit  41-odd-limit →

The 39-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 39 and k is an integer. To the 37-odd-limit, it adds 12 pairs of octave-reduced intervals involving 39.

Below is a list of all octave-reduced intervals in the 39-odd-limit.

Ratio Size (¢) Color name Name
40/39 43.831 tridecimal minor diesis thuyo 2nd
39/38 44.97 undevicesimal diesis nutho 2nd
39/37 91.139 trigesimoseptimal limma thisutho 2nd
39/35 187.343 animist major second thorugu 2nd
44/39 208.835 major minthic tone thulo 2nd
39/34 237.527 septendecimal supermajor second sutho 2nd
46/39 285.792 laodicismic minor third twethothu 3rd
39/32 342.483 lesser tridecimal neutral third tho 3rd
39/31 397.447 trigesimoprimal major third thiwutho 4th
50/39 430.145 major minthmic supermajor third thuyoyo 3rd
39/29 512.905 vigesimononal acute fourth twenutho 4th
39/28 573.657 mynucumic lesser tritone thoru 4th
56/39 626.343 mynucumic greater tritone thuzo 5th
58/39 687.095 vigesimononal grave fifth twenothu 5th
39/25 769.855 major minthmic subminor sixth thogugu 6th
62/39 802.553 trigesimoprimal minor sixth thiwothu 5th
64/39 857.517 greater tridecimal neutral sixth thu 6th
39/23 914.208 laodicismic major sixth twethutho 6th
68/39 962.473 septendecimal subminor seventh sothu 7th
39/22 991.165 major minthic minor seventh tholu 7th
70/39 1012.657 animist minor seventh thuzoyo 7th
74/39 1108.861 trigesimoseptimal major seventh thisothu octave
76/39 1155.03 vigesimononal suboctave nothu octave
39/20 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 2554edo.

Retrieved from "https://en.xen.wiki/index.php?title=39-odd-limit&oldid=210582"