@@ Line 1: / Line 1: @@
-The '''division of the 10th harmonic into 40 equal parts''' is related to [[12edo]], but with 10/1 instead of 2/1 being just. The step size (99.657843 [[cent]]s) of this [[equal-step tuning]] is very close to 1\12 (one step of 12 EDO).
+The '''division of the 10th harmonic into 40 equal parts''' (40ED10) is related to [[12edo|12EDO]], but with 10/1 instead of 2/1 being just. The step size (99.657843 [[cent]]s) of this [[equal-step tuning]] is very close to 1\12 (one step of 12 EDO).
 It is possible to call this division a form of '''decibel tuning''' or '''kilobyte tuning''', as
@@ Line 12: / Line 12: @@
 == Theory ==
-Since 40ed10 has relations to the proximity of 1024 to 1000, just like 12edo it tempers out the lesser diesis of [[128/125]]. However in this situation the tempering has a different interpretation, namely that "in favor of 1000".
+Since 40ED10 has relations to the proximity of 1024 to 1000, just like 12EDO it tempers out the lesser diesis of [[128/125]]. However in this situation the tempering has a different interpretation, namely that "in favor of 1000".
+=== Interval ===
+{| class="wikitable"
+|-
+! | degree
+! | cents value
+! | corresponding <br>JI intervals
+! | comments
+|-
+| | 0
+| | 0.0000
+| | '''exact [[1/1]]'''
+| |
+|-
+| | 1
+| | 99.6578
+| | [[18/17]]
+| |
+|-
+| | 2
+| | 199.3157
+| |
+| |
+|-
+| | 3
+| | 298.9735
+| | [[19/16]]
+| |
+|-
+| | 4
+| | 398.6314
+| |
+| |
+|-
+| | 5
+| | 498.2892
+| | [[4/3]]
+| |
+|-
+| | 6
+| | 597.9471
+| | [[24/17]]
+| |
+|-
+| | 7
+| | 697.6049
+| |
+| |
+|-
+| | 8
+| | 797.2627
+| |
+| |
+|-
+| | 9
+| | 896.9206
+| |
+| |
+|-
+| | 10
+| | 996.5784
+| | [[16/9]]
+| |
+|-
+| | 11
+| | 1096.2363
+| | [[32/17]]
+| |
+|-
+| | 12
+| | 1195.8941
+| |
+| | compressed [[octave]]
+|-
+| | 13
+| | 1295.5520
+| |
+| |
+|-
+| | 14
+| | 1395.2098
+| | [[28/25|56/25]]
+| |
+|-
+| | 15
+| | 1494.8676
+| |
+| |
+|-
+| | 16
+| | 1594.5255
+| |
+| |
+|-
+| | 17
+| | 1694.1833
+| |
+| |
+|-
+| | 18
+| | 1793.8412
+| |
+| |
+|-
+| | 19
+| | 1893.4990
+| | [[112/75|224/75]]
+| |
+|-
+| | 20
+| | 1993.1569
+| |
+| |
+|-
+| | 21
+| | 2092.8147
+| | 375/112
+| |
+|-
+| | 22
+| | 2192.4725
+| |
+| |
+|-
+| | 23
+| | 2292.1304
+| |
+| |
+|-
+| | 24
+| | 2391.7882
+| |
+| |
+|-
+| | 25
+| | 2491.4461
+| |
+| |
+|-
+| | 26
+| | 2591.1039
+| | 125/28
+| |
+|-
+| | 27
+| | 2690.7618
+| |
+| |
+|-
+| | 28
+| | 2790.4196
+| |
+| |
+|-
+| | 29
+| | 2890.0774
+| | 85/16
+| |
+|-
+| | 30
+| | 2989.7353
+| | [[45/32|45/8]]
+| |
+|-
+| | 31
+| | 3089.3931
+| |
+| |
+|-
+| | 32
+| | 3189.0510
+| |
+| |
+|-
+| | 33
+| | 3288.7088
+| |
+| |
+|-
+| | 34
+| | 3388.3667
+| | 85/12
+| |
+|-
+| | 35
+| | 3488.0245
+| | [[15/2]]
+| |
+|-
+| | 36
+| | 3587.6823
+| |
+| |
+|-
+| | 37
+| | 3687.3402
+| |
+| |
+|-
+| | 38
+| | 3786.9980
+| |
+| |
+|-
+| | 39
+| | 3886.6559
+| | 85/9
+| |
+|-
+| | 40
+| | 3986.3137
+| | '''exact [[10/1]]'''
+| |
+|}
 [[Category:Equal-step tuning]]
+[[Category:Ed10]]

40ed10: Difference between revisions