309edo: Difference between revisions

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* {{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]].

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=== 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.

@@ Line 9: / Line 9: @@
 * {{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]].
@@ Line 17: / Line 17: @@
 === Subsets and supersets ===
-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.
+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.