309edo - Revision history

FloraC: Support of 7-limit rank-3 is trivial information on top of the commas

2026-06-07T06:56:08Z

Support of 7-limit rank-3 is trivial information on top of the commas

← Older revision		Revision as of 06:56, 7 June 2026
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	* {{val\| 309 490 '''718''' '''868''' }} (309cd)		* {{val\| 309 490 '''718''' '''868''' }} (309cd)

	Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit~~, supporting the [[hemifamity]] temperament~~. Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880 in the 7-limit~~, supporting [[mitonic]] and [[ragismic]]~~. Using the 309d val, it tempers out [[2109375/2097152]] in the 5-limit; [[4000/3969]], [[420175/419904]], 829440/823543, 1071875/1062882 and 9765625/9633792 in the 7-limit~~. It supports the [[octagar]] temperament~~. Using the 309cd val, it tempers out [[67108864/66430125]] in the 5-limit; [[3136/3125]], [[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in the 7-limit. It supports [[misty~~]], [[hemifamity]] and [[landscape~~]]. Note that the 309b val {{val\| 309 '''489''' 717 867 }} (309b) is [[enfactoring\|enfactored]] [[103edo]].		Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit. Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880 in the 7-limit. Using the 309d val, it tempers out [[2109375/2097152]] in the 5-limit; [[4000/3969]], [[420175/419904]], 829440/823543, 1071875/1062882 and 9765625/9633792 in the 7-limit. Using the 309cd val, it tempers out [[67108864/66430125]] in the 5-limit; [[3136/3125]], [[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in the 7-limit. It supports [[misty]]. Note that the 309b val {{val\| 309 '''489''' 717 867 }} (309b) is [[enfactoring\|enfactored]] [[103edo]].

	This system is quite accurate in the 2.81.45.63.11.117.17 (or alternatively 2.81.5/9.7/9.11.13/9.17) subgroup, with the same tuning and commas as [[1236edo]].		This system is quite accurate in the 2.81.45.63.11.117.17 (or alternatively 2.81.5/9.7/9.11.13/9.17) subgroup, with the same tuning and commas as [[1236edo]].
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	309 factors into 3 × 103, ~~with~~ [[3edo]] and [[103edo]] as its subset edos. [[1236edo]], which quadruples it, gives a good correction to the harmonics 3, 5, 7, and 13.		309 factors into prime as {{nowrap\| 3 × 103 }}, so 309edo has [[3edo]] and [[103edo]] as its subset edos. [[1236edo]], which quadruples it, gives a good correction to the harmonics 3, 5, 7, and 13.

Overthink at 17:38, 14 October 2025

2025-10-14T17:38:22Z

← Older revision		Revision as of 17:38, 14 October 2025
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	{{ED intro}}		{{ED intro}}

			== Theory ==
	309edo is in[[consistent]] to the [[5-odd-limit]], with four possible mappings in the [[7-limit]]:		309edo is in[[consistent]] to the [[5-odd-limit]], with four possible mappings in the [[7-limit]]:
	* {{val\| 309 490 717 867 }} ([[patent val]])		* {{val\| 309 490 717 867 }} ([[patent val]])
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	* {{val\| 309 490 '''718''' '''868''' }} (309cd)		* {{val\| 309 490 '''718''' '''868''' }} (309cd)

	Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit, supporting the [[hemifamity]] temperament.		Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit, supporting the [[hemifamity]] temperament. Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880 in the 7-limit, supporting [[mitonic]] and [[ragismic]]. Using the 309d val, it tempers out [[2109375/2097152]] in the 5-limit; [[4000/3969]], [[420175/419904]], 829440/823543, 1071875/1062882 and 9765625/9633792 in the 7-limit. It supports the [[octagar]] temperament. Using the 309cd val, it tempers out [[67108864/66430125]] in the 5-limit; [[3136/3125]], [[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in the 7-limit. It supports [[misty]], [[hemifamity]] and [[landscape]]. Note that the 309b val {{val\| 309 '''489''' 717 867 }} (309b) is [[enfactoring\|enfactored]] [[103edo]].

	~~Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880~~ in the ~~7-limit, supporting [[mitonic]] and [[ragismic]]~~.		This system is quite accurate in the 2.81.45.63.11.117.17 (or alternatively 2.81.5/9.7/9.11.13/9.17) subgroup, with the same tuning and commas as [[1236edo]].

	~~Using the 309d val, it tempers out [[2109375/2097152]] in the~~ 5~~-limit; [[4000~~/~~3969]], [[420175/419904]], 829440/823543, 1071875/1062882 and 9765625~~/~~9633792 in the 7-limit~~. ~~It supports the [[octagari]] temperament~~.

	~~Using the 309cd val, it tempers out [[67108864~~/~~66430125]] in the 5-limit; [[3136/3125]]~~, ~~[[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in~~ the ~~7-limit. It supports [[misty]], [[hemifamity]]~~ and [[~~landscape]].~~

	~~Additionally, the 309b val {{val\| 309 '''489''' 717 867 }} (309b) is [[enfactoring\|enfactored]] [[103edo~~]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	309 factors into 3 × 103, with [[3edo]] and [[103edo]] as its subset edos. [[~~927edo~~]], which ~~triples~~ it, gives a good correction to the ~~harmonic~~ 5.		309 factors into 3 × 103, with [[3edo]] and [[103edo]] as its subset edos. [[1236edo]], which quadruples it, gives a good correction to the harmonics 3, 5, 7, and 13.

Francium: changed EDO intro to ED intro

2025-02-21T06:08:47Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:08, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|309~~}}		{{ED intro}}

	309edo is in[[consistent]] to the [[5-odd-limit]], with four possible mappings in the [[7-limit]]:		309edo is in[[consistent]] to the [[5-odd-limit]], with four possible mappings in the [[7-limit]]:

FloraC: Review

2024-02-21T10:49:01Z

Review

← Older revision		Revision as of 10:49, 21 February 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|309}}		{{EDO intro\|309}}
	~~== Theory ==~~
	309edo is ~~only~~ consistent to the 3-limit, with ~~five~~ possible mappings in the 7-limit:		309edo is in[[consistent]] to the [[5-odd-limit]], with four possible mappings in the [[7-limit]]:
	* {{val\|309 490 717 867}} (patent val)		* {{val\| 309 490 717 867 }} ([[patent val]])
	* {{val\|309 '''489''' 717 867}} (309b)		* {{val\| 309 490 '''718''' 867 }} (309c)
	* {{val\|309 490 '''718''' 867}} (309c)		* {{val\| 309 490 717 '''868''' }} (309d)
	* {{val\|309 490 717 '''868'''}} (309d)		* {{val\| 309 490 '''718''' '''868''' }} (309cd)
	* {{val\|309 490 '''718''' '''868'''}} (309cd)

	Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit, supporting the [[hemifamity]] temperament.		Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit, supporting the [[hemifamity]] temperament.

	~~Using the 309b val, it tempers out [[78732/78125]] in the 5-limit; [[225/224]], [[1029/1024]], [[2401/2400]], [[16875/16807]] and 33075/32768 in the 7-limit.~~

	Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880 in the 7-limit, supporting [[mitonic]] and [[ragismic]].		Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880 in the 7-limit, supporting [[mitonic]] and [[ragismic]].

	Using the 309d val, it tempers out [[2109375/2097152]] in the 5-limit; [[4000/3969]], 420175/419904, 829440/823543, 1071875/1062882 and 9765625/9633792 in the 7-limit. It supports the [[octagari]] temperament.		Using the 309d val, it tempers out [[2109375/2097152]] in the 5-limit; [[4000/3969]], [[420175/419904]], 829440/823543, 1071875/1062882 and 9765625/9633792 in the 7-limit. It supports the [[octagari]] temperament.

	Using the 309cd val, it tempers out [[67108864/66430125]] in the 5-limit; [[3136/3125]], [[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in the 7-limit. It supports [[misty]], [[hemifamity]] and [[landscape]].		Using the 309cd val, it tempers out [[67108864/66430125]] in the 5-limit; [[3136/3125]], [[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in the 7-limit. It supports [[misty]], [[hemifamity]] and [[landscape]].

			Additionally, the 309b val {{val\| 309 '''489''' 717 867 }} (309b) is [[enfactoring\|enfactored]] [[103edo]].

	=== Prime harmonics ===		=== Prime harmonics ===

Francium: Created page with "{{Infobox ET}} {{EDO intro|309}} == Theory == 309edo is only consistent to the 3-limit, with five possible mappings in the 7-limit: * {{val|309 490 717 867}} (patent val) * {{..."

2023-11-04T16:47:07Z

Created page with "{{Infobox ET}} {{EDO intro|309}} == Theory == 309edo is only consistent to the 3-limit, with five possible mappings in the 7-limit: * {{val|309 490 717 867}} (patent val) * {{..."

New page

{{Infobox ET}}
{{EDO intro|309}}
== Theory ==
309edo is only consistent to the 3-limit, with five possible mappings in the 7-limit:
* {{val|309 490 717 867}} (patent val)
* {{val|309 '''489''' 717 867}} (309b)
* {{val|309 490 '''718''' 867}} (309c)
* {{val|309 490 717 '''868'''}} (309d)
* {{val|309 490 '''718''' '''868'''}} (309cd)

Using the patent val, it tempers out [[5120/5103]], 117649/116640, 390625/387072, 537824/531441, [[823543/819200]] and 1953125/1928934 in the 7-limit, supporting the [[hemifamity]] temperament.

Using the 309b val, it tempers out [[78732/78125]] in the 5-limit; [[225/224]], [[1029/1024]], [[2401/2400]], [[16875/16807]] and 33075/32768 in the 7-limit.

Using the 309c val, it tempers out [[4375/4374]], 153664/151875, 395136/390625, 537824/531441, [[2100875/2097152]] and 5250987/5242880 in the 7-limit, supporting [[mitonic]] and [[ragismic]].

Using the 309d val, it tempers out [[2109375/2097152]] in the 5-limit; [[4000/3969]], 420175/419904, 829440/823543, 1071875/1062882 and 9765625/9633792 in the 7-limit. It supports the [[octagari]] temperament.

Using the 309cd val, it tempers out [[67108864/66430125]] in the 5-limit; [[3136/3125]], [[5120/5103]], [[250047/250000]], 458752/455625, 49009212/48828125 and 725594112/720600125 in the 7-limit. It supports [[misty]], [[hemifamity]] and [[landscape]].

=== Prime harmonics ===
{{Harmonics in equal|309}}

=== Subsets and supersets ===
309 factors into 3 × 103, with [[3edo]] and [[103edo]] as its subset edos. [[927edo]], which triples it, gives a good correction to the harmonic 5.