43edt: Difference between revisions

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+'''[[Edt|Division of the third harmonic]] into 43 equal parts''' (43EDT) is related to [[27edo|27 EDO]], but with the 3/1 rather than the 2/1 being just. The octave is about 5.7492 cents compressed and the step size is about 44.2315 cents. It is consistent to the [[9-odd-limit|10-integer-limit]].
 =43 EDT=
-This tuning is related to [[27edo|27edo]] having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).
+This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).
-However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt|13edt]] is not. The 4L+5s MOS has L=7 s=3.
+However, in addition to its rich octave-based harmony, the 43EDT is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt|13EDT]] is not. The 4L+5s MOS has L=7 s=3.
 {| class="wikitable"
 |-
-! | Degrees
+! | degrees
-! | Cents
+! | cents value
+! | corresponding <br>JI intervals
 |-
 | | 1
 | | 44.232
+| | 40/39, 39/38
 |-
 | | 2
 | | 88.463
+| | [[20/19]]
 |-
 | | 3
 | | 132.695
+| | [[27/25]]
 |-
 | | 4
 | | 176.926
+| |
 |-
 | | 5
 | | 221.158
+| | [[25/22]]
 |-
 | | 6
 | | 265.389
+| | ([[7/6]])
 |-
 | | 7
 | | 309.621
+| |
 |-
 | | 8
 | | 353.852
+| | [[27/22]]
 |-
 | | 9
 | | 398.084
+| |
 |-
 | | 10
 | | 442.315
+| |
 |-
 | | 11
 | | 486.547
+| | (45/34)
 |-
 | | 12
 | | 530.778
+| | (34/25)
 |-
 | | 13
 | | 575.010
+| | (39/28)
 |-
 | | 14
 | | 619.241
+| | ([[10/7]])
 |-
 | | 15
 | | 663.473
+| | [[22/15]]
 |-
 | | 16
 | | 707.704
+| |
 |-
 | | 17
 | | 751.936
+| |
 |-
 | | 18
 | | 796.167
+| | [[19/12]]
 |-
 | | 19
 | | 840.399
+| | [[13/8]]
 |-
 | | 20
 | | 884.630
+| | [[5/3]]
 |-
 | | 21
 | | 928.862
+| |
 |-
 | | 22
 | | 973.093
+| |
 |-
 | | 23
 | | 1017.325
+| | [[9/5]]
 |-
 | | 24
 | | 1061.556
+| | [[24/13]]
 |-
 | | 25
 | | 1105.788
+| | [[36/19]]
 |-
 | | 26
 | | 1150.019
+| | 68/35
 |-
 | | 27
 | | 1194.251
+| |
 |-
 | | 28
 | | 1238.482
+| | [[45/44|45/22]]
 |-
 | | 29
 | | 1282.713
+| | ([[21/20|21/10]])
 |-
 | | 30
 | | 1326.946
+| | ([[14/13|28/13]])
 |-
 | | 31
 | | 1371.177
+| |
 |-
 | | 32
 | | 1415.408
+| | ([[17/15|34/15]])
 |-
 | | 33
 | | 1459.640
+| |
 |-
 | | 34
 | | 1503.871
+| |
 |-
 | | 35
 | | 1548.193
+| | [[11/9|22/9]]
 |-
 | | 36
 | | 1592.334
+| |
 |-
 | | 37
 | | 1636.566
+| | ([[9/7|18/7]])
 |-
 | | 38
 | | 1680.797
+| | [[33/25|66/25]]
 |-
 | | 39
 | | 1725.029
+| |
 |-
 | | 40
 | | 1769.261
+| | [[25/9]]
 |-
 | | 41
 | | 1813.492
+| | 57/20
 |-
 | | 42
 | | 1857.724
+| | [[19/13|38/13]]
 |-
 | | 43
 | | 1901.955
+| | '''exact [[3/1]]'''
 |}
-[[Category:edt]]
+[[Category:Edt]]
-[[Category:tritave]]
+[[Category:Edonoi]]