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=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.


0: 1/1 0.000 unison, perfect prime
Lookalikes: [[31edo]], [[49edt]]


1: 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
|}


2: 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.


3: 116.993 cents 116.993
===7-limit 31&amp;369===
Commas: 2401/2400, 8589934592/8544921875


4: 155.990 cents 155.990
POTE generator: ~5/4 = 386.997


5: 194.988 cents 194.988
Map: [&lt;1 19 2 7|, &lt;0 -54 1 -13|]


6: 233.985 cents 233.985
EDOs: 31, 369, 400, 431, 462


7: 272.983 cents 272.983
===11-limit 31&amp;369===
Commas: 2401/2400, 5632/5625, 46656/46585


8: 311.980 cents 311.980
POTE generator: ~5/4 = 386.999


9: 350.978 cents 350.978
Map: [&lt;1 19 2 7 37|, &lt;0 -54 1 -13 -104|]


10: 389.975 cents 389.975
EDOs: 31, 369, 400, 431, 462


11: 428.973 cents 428.973
===13-limit 31&amp;369===
Commas: 1001/1000, 1716/1715, 4096/4095, 46656/46585


12: 467.970 cents 467.970
POTE generator: ~5/4 = 387.003


13: 506.968 cents 506.968
Map: [&lt;1 19 2 7 37 -35|, &lt;0 -54 1 -13 -104 120|]


14: 545.965 cents 545.965
EDOs: 31, 369, 400, 431, 462


15: 584.963 cents 584.963
[[Category:Edf]]
 
[[Category:Edonoi]]
16: 623.960 cents 623.960
 
17: 662.958 cents 662.958
 
18: 3/2 701.955 perfect fifth
 
Lookalikes: [[31edo|31edo]]

Revision as of 10:58, 6 February 2019

18EDF is the equal division of the just perfect fifth into 18 parts of 38.9975 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.

Lookalikes: 31edo, 49edt

Intervals

degree cents value corresponding
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

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.

7-limit 31&369

Commas: 2401/2400, 8589934592/8544921875

POTE generator: ~5/4 = 386.997

Map: [<1 19 2 7|, <0 -54 1 -13|]

EDOs: 31, 369, 400, 431, 462

11-limit 31&369

Commas: 2401/2400, 5632/5625, 46656/46585

POTE generator: ~5/4 = 386.999

Map: [<1 19 2 7 37|, <0 -54 1 -13 -104|]

EDOs: 31, 369, 400, 431, 462

13-limit 31&369

Commas: 1001/1000, 1716/1715, 4096/4095, 46656/46585

POTE generator: ~5/4 = 387.003

Map: [<1 19 2 7 37 -35|, <0 -54 1 -13 -104 120|]

EDOs: 31, 369, 400, 431, 462

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