18edf: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 1: / Line 1: @@
-=18edf=
+'''18EDF''' is the [[EDF|equal division of the just perfect fifth]] into 18 parts of 38.9975 [[cent|cents]] each, corresponding to 30.7712 [[edo]]. It is related to the regular temperament which tempers out 2401/2400 and 8589934592/8544921875 in the 7-limit; 5632/5625, 46656/46585, and 166698/166375 in the 11-limit, which is supported by [[31edo]], [[369edo]], [[400edo]], 431edo, and 462edo.
-: 1/1 0.000 unison, perfect prime
+Lookalikes: [[31edo]], [[49edt]]
-: 38.998 cents 38.998
+==Intervals==
+{| class="wikitable"
+|-
+! | degree
+! | cents value
+! | corresponding <br>JI intervals
+! | comments
+|-
+| | 0
+| | 0.0000
+| | '''exact [[1/1]]'''
+| |
+|-
+| | 1
+| | 38.9975
+| | 45/44
+| |
+|-
+| | 2
+| | 77.9950
+| |
+| |
+|-
+| | 3
+| | 116.9925
+| |
+| |
+|-
+| | 4
+| | 155.9900
+| | 128/117
+| |
+|-
+| | 5
+| | 194.9875
+| | 28/25
+| |
+|-
+| | 6
+| | 233.9850
+| |
+| |
+|-
+| | 7
+| | 272.9825
+| |
+| |
+|-
+| | 8
+| | 311.9800
+| |
+| |
+|-
+| | 9
+| | 350.9775
+| | 60/49, 49/40
+| |
+|-
+| | 10
+| | 389.9750
+| |
+| |
+|-
+| | 11
+| | 428.9725
+| |
+| |
+|-
+| | 12
+| | 467.9700
+| |
+| |
+|-
+| | 13
+| | 506.9675
+| | 75/56
+| |
+|-
+| | 14
+| | 545.9650
+| |
+| |
+|-
+| | 15
+| | 584.9625
+| |
+| |
+|-
+| | 16
+| | 623.9600
+| |
+| |
+|-
+| | 17
+| | 662.9575
+| | [[22/15]]
+| |
+|-
+| | 18
+| | 701.9550
+| | '''exact [[3/2]]'''
+| | just perfect fifth
+|}
-: 77.995 cents 77.995
+==Related regular temperaments==
+The rank-two regular temperament supported by 31edo and 369edo has three equal divisions of the interval which equals an octave minus the step interval of 18EDF as a generator.
-: 116.993 cents 116.993
+===7-limit 31&amp;369===
+Commas: 2401/2400, 8589934592/8544921875
-: 155.990 cents 155.990
+POTE generator: ~5/4 = 386.997
-: 194.988 cents 194.988
+Map: [&lt;1 19 2 7|, &lt;0 -54 1 -13|]
-: 233.985 cents 233.985
+EDOs: 31, 369, 400, 431, 462
-: 272.983 cents 272.983
+===11-limit 31&amp;369===
+Commas: 2401/2400, 5632/5625, 46656/46585
-: 311.980 cents 311.980
+POTE generator: ~5/4 = 386.999
-: 350.978 cents 350.978
+Map: [&lt;1 19 2 7 37|, &lt;0 -54 1 -13 -104|]
-: 389.975 cents 389.975
+EDOs: 31, 369, 400, 431, 462
-: 428.973 cents 428.973
+===13-limit 31&amp;369===
+Commas: 1001/1000, 1716/1715, 4096/4095, 46656/46585
-: 467.970 cents 467.970
+POTE generator: ~5/4 = 387.003
-: 506.968 cents 506.968
+Map: [&lt;1 19 2 7 37 -35|, &lt;0 -54 1 -13 -104 120|]
-: 545.965 cents 545.965
+EDOs: 31, 369, 400, 431, 462
-: 584.963 cents 584.963
+[[Category:Edf]]
+[[Category:Edonoi]]
-: 623.960 cents 623.960
-: 662.958 cents 662.958
-: 3/2 701.955 perfect fifth
-Lookalikes: [[31edo|31edo]]