39-odd-limit - Revision history

FloraC: + category

2025-09-23T15:37:04Z

+ category

← Older revision		Revision as of 15:37, 23 September 2025
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	\|}		\|}
	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 -->

FloraC at 15:36, 23 September 2025

2025-09-23T15:36:46Z

Show changes

Lériendil: fixes

2025-09-23T15:26:28Z

fixes

← Older revision		Revision as of 15:26, 23 September 2025
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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 [[37-odd-limit]], it adds 11 pairs of [[octave-reduced]] intervals involving 39.		{{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.

	Below is a list of all octave-reduced intervals in the 39-odd-limit.		Below is a list of all octave-reduced intervals in the 39-odd-limit.
Line 59:		Line 59:
	* [[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]]

Eufalesio: Proposed a name for all the 39-odd intervals (also thanks Overthink for discovering that distinct odd-limit EDO!)

2025-09-23T15:21:56Z

Proposed a name for all the 39-odd intervals (also thanks Overthink for discovering that distinct odd-limit EDO!)

← Older revision		Revision as of 15:21, 23 September 2025
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	\|40/39		\|40/39
	\|43.831		\|43.831
	\|		\|tridecimal minor diesis
	\|		\|thuyo 2nd
	\|-		\|-
	\|39/38		\|39/38
	\|44.97		\|44.97
	\|		\|undevicesimal diesis
	\|		\|nutho 2nd
	\|-		\|-
	\|39/37		\|39/37
	\|91.139		\|91.139
	\|		\|trigesimoseptimal limma
	\|		\|thisutho 2nd
	\|-		\|-
	\|39/35		\|39/35
	\|187.343		\|187.343
	\|		\|animist major second
	\|		\|thorugu 2nd
	\|-		\|-
	\|44/39		\|44/39
	\|208.835		\|208.835
	\|		\|major minthic tone
	\|		\|thulo 2nd
	\|-		\|-
	\|39/34		\|39/34
	\|237.527		\|237.527
	\|		\|septendecimal supermajor second
	\|		\|sutho 2nd
	\|-		\|-
	\|46/39		\|46/39
	\|285.792		\|285.792
	\|		\|laodicismic minor third
	\|		\|twethothu 3rd
			\|-
			\|39/32
			\|342.483
			\|lesser tridecimal neutral third
			\|tho 3rd
	\|-		\|-
	\|39/31		\|39/31
	\|397.447		\|397.447
	\|		\|trigesimoprimal major third
	\|		\|thiwutho 4th
	\|-		\|-
	\|50/39		\|50/39
	\|430.145		\|430.145
	\|		\|major minthmic supermajor third
	\|		\|thuyoyo 3rd
	\|-		\|-
	\|39/29		\|39/29
	\|512.905		\|512.905
	\|		\|vigesimononal acute fourth
	\|		\|twenutho 4th
	\|-		\|-
	\|39/28		\|39/28
	\|573.657		\|573.657
	\|		\|mynucumic lesser tritone
	\|		\|thoru 4th
	\|-		\|-
	\|56/39		\|56/39
	\|626.343		\|626.343
	\|		\|mynucumic greater tritone
	\|		\|thuzo 5th
	\|-		\|-
	\|58/39		\|58/39
	\|687.095		\|687.095
	\|		\|vigesimononal grave fifth
	\|		\|twenothu 5th
	\|-		\|-
	\|39/25		\|39/25
	\|769.855		\|769.855
	\|		\|major minthmic subminor sixth
	\|		\|thogugu 6th
	\|-		\|-
	\|62/39		\|62/39
	\|802.553		\|802.553
	\|		\|trigesimoprimal minor sixth
	\|		\|thiwothu 5th
			\|-
			\|64/39
			\|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]].

Eufalesio at 21:31, 18 September 2025

2025-09-18T21:31:07Z

← Older revision		Revision as of 21:31, 18 September 2025
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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}}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.

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

Eufalesio at 21:30, 18 September 2025

2025-09-18T21:30:37Z

← Older revision		Revision as of 21:30, 18 September 2025
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	* [[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]]
Line 25:		Line 25:
	* [[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]]'''
	* [[17/15]], [[30/17]]		* [[17/15]], [[30/17]]
	* [[42/37]], [[37/21]]		* [[42/37]], [[37/21]]
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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]]
Line 95:		Line 95:
	* [[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]]
Line 108:		Line 108:
	* [[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]]
Line 118:		Line 118:
	* [[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]]
Line 136:		Line 136:
	* [[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]]

Eufalesio: Birth (Intervals TBA)

2025-09-18T21:09:57Z

Birth (Intervals TBA)

New page

{{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.

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

* [[1/1]]
* [[40/39]], [[39/20]]
* [[39/38]], [[76/39]]
* [[38/37]], [[37/19]]
* [[37/36]], [[72/37]]
* [[36/35]], [[35/18]]
* [[35/34]], [[68/35]]
* [[34/33]], [[33/17]]
* [[33/32]], [[64/33]]
* [[32/31]], [[31/16]]
* [[31/30]], [[60/31]]
* [[30/29]], [[29/15]]
* [[29/28]], [[56/29]]
* [[28/27]], [[27/14]]
* [[27/26]], [[52/27]]
* [[26/25]], [[25/13]]
* [[25/24]], [[48/25]]
* [[24/23]], [[23/12]]
* [[23/22]], [[44/23]]
* [[22/21]], [[21/11]]
* [[21/20]], [[40/21]]
* [[20/19]], [[19/10]]
* [[39/37]], [[74/39]]
* [[19/18]], [[36/19]]
* [[37/35]], [[70/37]]
* [[18/17]], [[17/9]]
* [[35/33]], [[66/35]]
* [[17/16]], [[32/17]]
* [[33/31]], [[62/33]]
* [[16/15]], [[15/8]]
* [[31/29]], [[58/31]]
* [[15/14]], [[28/15]]
* [[29/27]], [[54/29]]
* [[14/13]], [[13/7]]
* [[27/25]], [[50/27]]
* [[40/37]], [[37/20]]
* [[13/12]], [[24/13]]
* [[38/35]], [[35/19]]
* [[25/23]], [[46/25]]
* [[37/34]], [[68/37]]
* [[12/11]], [[11/6]]
* [[35/32]], [[64/35]]
* [[23/21]], [[42/23]]
* [[34/31]], [[31/17]]
* [[11/10]], [[20/11]]
* [[32/29]], [[29/16]]
* [[21/19]], [[38/21]]
* [[31/28]], [[56/31]]
* [[10/9]], [[9/5]]
* [[39/35]], [[70/39]]
* [[29/26]], [[52/29]]
* [[19/17]], [[34/19]]
* [[28/25]], [[25/14]]
* [[37/33]], [[66/37]]
* [[9/8]], [[16/9]]
* [[44/39]], [[39/22]]
* [[35/31]], [[62/35]]
* [[26/23]], [[23/13]]
* [[17/15]], [[30/17]]
* [[42/37]], [[37/21]]
* [[25/22]], [[44/25]]
* [[33/29]], [[58/33]]
* [[8/7]], [[7/4]]
* [[39/34]], [[68/39]]
* [[31/27]], [[54/31]]
* [[23/20]], [[40/23]]
* [[38/33]], [[33/19]]
* [[15/13]], [[26/15]]
* [[37/32]], [[64/37]]
* [[22/19]], [[19/11]]
* [[29/25]], [[50/29]]
* [[36/31]], [[31/18]]
* [[7/6]], [[12/7]]
* [[34/29]], [[29/17]]
* [[27/23]], [[46/27]]
* [[20/17]], [[17/10]]
* [[33/28]], [[56/33]]
* [[46/39]], [[39/23]]
* [[13/11]], [[22/13]]
* [[32/27]], [[27/16]]
* [[19/16]], [[32/19]]
* [[44/37]], [[37/22]]
* [[25/21]], [[42/25]]
* [[31/26]], [[52/31]]
* [[37/31]], [[62/37]]
* [[6/5]], [[5/3]]
* [[35/29]], [[58/35]]
* [[29/24]], [[48/29]]
* [[23/19]], [[38/23]]
* [[40/33]], [[33/20]]
* [[17/14]], [[28/17]]
* [[28/23]], [[23/14]]
* [[39/32]], [[64/39]]
* [[11/9]], [[18/11]]
* [[38/31]], [[31/19]]
* [[27/22]], [[44/27]]
* [[16/13]], [[13/8]]
* [[37/30]], [[60/37]]
* [[21/17]], [[34/21]]
* [[26/21]], [[21/13]]
* [[31/25]], [[50/31]]
* [[36/29]], [[29/18]]
* [[46/37]], [[37/23]]
* [[5/4]], [[8/5]]
* [[44/35]], [[35/22]]
* [[39/31]], [[62/39]]
* [[34/27]], [[27/17]]
* [[29/23]], [[46/29]]
* [[24/19]], [[19/12]]
* [[19/15]], [[30/19]]
* [[33/26]], [[52/33]]
* [[14/11]], [[11/7]]
* [[37/29]], [[58/37]]
* [[23/18]], [[36/23]]
* [[32/25]], [[25/16]]
* [[50/39]], [[39/25]]
* [[9/7]], [[14/9]]
* [[40/31]], [[31/20]]
* [[31/24]], [[48/31]]
* [[22/17]], [[17/11]]
* [[35/27]], [[54/35]]
* [[48/37]], [[37/24]]
* [[13/10]], [[20/13]]
* [[30/23]], [[23/15]]
* [[17/13]], [[26/17]]
* [[38/29]], [[29/19]]
* [[21/16]], [[32/21]]
* [[46/35]], [[35/23]]
* [[25/19]], [[38/25]]
* [[29/22]], [[44/29]]
* [[33/25]], [[50/33]]
* [[37/28]], [[56/37]]
* [[4/3]], [[3/2]]
* [[39/29]], [[58/39]]
* [[35/26]], [[52/35]]
* [[31/23]], [[46/31]]
* [[27/20]], [[40/27]]
* [[50/37]], [[37/25]]
* [[23/17]], [[34/23]]
* [[42/31]], [[31/21]]
* [[19/14]], [[28/19]]
* [[34/25]], [[25/17]]
* [[15/11]], [[22/15]]
* [[26/19]], [[19/13]]
* [[37/27]], [[54/37]]
* [[48/35]], [[35/24]]
* [[11/8]], [[16/11]]
* [[40/29]], [[29/20]]
* [[29/21]], [[42/29]]
* [[18/13]], [[13/9]]
* [[25/18]], [[36/25]]
* [[32/23]], [[23/16]]
* [[39/28]], [[56/39]]
* [[46/33]], [[33/23]]
* [[7/5]], [[10/7]]
* [[52/37]], [[37/26]]
* [[38/27]], [[27/19]]
* [[31/22]], [[44/31]]
* [[24/17]], [[17/12]]

{| class="wikitable"
|'''Ratio'''
|'''Size ('''[[Cents|¢]]''')'''
|Color name
|Name
|-
|40/39
|43.831
|
|
|-
|39/38
|44.97
|
|
|-
|39/37
|91.139
|
|
|-
|39/35
|187.343
|
|
|-
|44/39
|208.835
|
|
|-
|39/34
|237.527
|
|
|-
|46/39
|285.792
|
|
|-
|39/31
|397.447
|
|
|-
|50/39
|430.145
|
|
|-
|39/29
|512.905
|
|
|-
|39/28
|573.657
|
|
|-
|56/39
|626.343
|
|
|-
|58/39
|687.095
|
|
|-
|39/25
|769.855
|
|
|-
|62/39
|802.553
|
|
|-
|39/23
|914.208
|
|
|-
|68/39
|962.473
|
|
|-
|39/22
|991.165
|
|
|-
|70/39
|1012.657
|
|
|-
|74/39
|1108.861
|
|
|-
|76/39
|1155.03
|
|
|-
|39/20
|1156.169
|
|
|}
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).