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-<b>49-EDO</b>, or <b>49 equal division</b> divides the octave into 49 equal parts of 24.490 [[cent|cent]]s each. It is very much on the sharp side of things, with sharp tunings of 3 (it is the first square equal division with a "real" 3 of size coprime to its cardinality), 5, 7, and 11. It is the [[Optimal_patent_val|optimal patent val]] for [[Superpyth|superpyth temperament]] in the 7 and 11 limits, archytas ([[7-limit|7-limit]]) and [[Archytas_clan|ares]] ([[11-limit|11-limit]]) planar temperaments and almost identical to the e-based analog of [[LucyTuning|LucyTuning]]. It [[tempering_out|tempers out]] 64/63, 245/243 and 3125/3087 in the 7-limit, and 100/99 and 1375/1372 in the 11-limit.
+'''49-EDO''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.490 [[Cent|cents]] each.
+== Theory ==
+edo is very much on the sharp side of things, with sharp tunings of 3 (it is the first square equal division with a "real" 3 of size coprime to its cardinality), 5, 7, and 11. It is the [[Optimal_patent_val|optimal patent val]] for [[Superpyth|superpyth temperament]] in the 7 and 11 limits, archytas ([[7-limit]]) and [[Archytas_clan|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering_out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.
+== Intervals ==
+{| class="wikitable center-all right-2 left-3"
+! #
+! Cents
+! Approximate Ratios
+|-
+| 0
+| 0.000
+| [[1/1]]
+|-
+| 1
+| 24.490
+| [[50/49]]
+|-
+| 2
+| 48.980
+| [[81/80]], [[28/27]], [[36/35]], [[49/48]]
+|-
+| 3
+| 73.469
+| [[25/24]], [[22/21]], [[33/32]]
+|-
+| 4
+| 97.959
+| [[16/15]], [[21/20]]
+|-
+| 5
+| 122.449
+| [[15/14]]
+|-
+| 6
+| 146.939
+| [[12/11]]
+|-
+| 7
+| 171.429
+| [[10/9]], [[11/10]]
+|-
+| 8
+| 195.918
+|
+|-
+| 9
+| 220.408
+| [[9/8]], [[8/7]]
+|-
+| 10
+| 244.898
+|
+|-
+| 11
+| 269.388
+| [[7/6]]
+|-
+| 12
+| 293.878
+|
+|-
+| 13
+| 318.367
+| [[6/5]]
+|-
+| 14
+| 342.857
+| [[11/9]]
+|-
+| 15
+| 367.347
+| [[27/22]]
+|-
+| 16
+| 391.837
+| [[5/4]]
+|-
+| 17
+| 416.327
+| [[14/11]]
+|-
+| 18
+| 440.816
+| [[9/7]]
+|-
+| 19
+| 465.306
+|
+|-
+| 20
+| 489.796
+| [[4/3]], [[21/16]]
+|-
+| 21
+| 514.286
+|
+|-
+| 22
+| 538.776
+| [[27/20]], [[15/11]]
+|-
+| 23
+| 563.265
+| [[11/8]]
+|-
+| 24
+| 587.755
+| [[7/5]]
+|-
+| 25
+| 612.245
+| [[10/7]]
+|-
+| 26
+| 636.735
+| [[16/11]]
+|-
+| 27
+| 661.244
+| [[40/27]], [[22/15]]
+|-
+| 28
+| 685.714
+|
+|-
+| 29
+| 710.204
+| [[3/2]], [[32/21]]
+|-
+| 30
+| 734.694
+|
+|-
+| 31
+| 759.184
+| [[14/9]]
+|-
+| 32
+| 783.673
+| [[11/7]]
+|-
+| 33
+| 808.163
+| [[8/5]]
+|-
+| 34
+| 832.653
+| [[44/27]]
+|-
+| 35
+| 857.143
+| [[18/11]]
+|-
+| 36
+| 881.633
+| [[5/3]]
+|-
+| 37
+| 906.122
+|
+|-
+| 38
+| 930.612
+| [[12/7]]
+|-
+| 39
+| 955.102
+|
+|-
+| 40
+| 979.592
+| [[16/9]], [[7/4]]
+|-
+| 41
+| 1004.082
+|
+|-
+| 42
+| 1028.571
+| [[9/5]], [[20/11]]
+|-
+| 43
+| 1053.061
+| [[11/6]]
+|-
+| 44
+| 1077.551
+| [[28/15]]
+|-
+| 45
+| 1102.041
+| [[15/8]], [[40/21]]
+|-
+| 46
+| 1126.531
+| [[48/25]], [[21/11]], [[64/33]]
+|-
+| 47
+| 1151.020
+| [[160/81]], [[27/14]], [[35/18]], [[96/49]]
+|-
+| 48
+| 1175.510
+| [[49/25]]
+|-
+| 49
+| 1200.000
+| [[2/1]]
+|}
 [[Category:edo]]
 [[Category:superpyth]]

49edo: Difference between revisions