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18edf is related to the [[regular temperament]] which [[tempering out|tempers out]] 2401/2400 and 8589934592/8544921875 in the [[7-limit]]; with 5632/5625, 46656/46585, and 166698/166375 in the [[11-limit]], which is supported by [[31edo]], [[369edo]], [[400edo]], [[431edo]], and [[462edo]].
18edf is related to the [[regular temperament]] which [[tempering out|tempers out]] 2401/2400 and 8589934592/8544921875 in the [[7-limit]]; with 5632/5625, 46656/46585, and 166698/166375 in the [[11-limit]], which is supported by [[31edo]], [[369edo]], [[400edo]], [[431edo]], and [[462edo]].


Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[80ed6]]
Lookalikes: [[31edo]], [[39cET]], [[49edt]], [[72ed5]], [[80ed6]]


=== Harmonics ===
=== Harmonics ===
Line 13: Line 13:
== Intervals ==
== Intervals ==
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|+ Intervals of 18edf
|+ style="font-size: 105%;" | Intervals of 18edf
|-
|-
! | degree
! Degree
! | cents value
! Cents value
! | corresponding <br>JI intervals
! Corresponding<br />JI intervals
! | comments
! Comments
|-
|-
! colspan="2" | 0
! colspan="2" | 0
| | '''exact [[1/1]]'''
| '''exact [[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 38.9975
| 38.9975
| | 45/44
| 45/44
| |  
|  
|-
|-
| | 2
| 2
| | 77.995
| 77.995
| |  
|  
| |  
|  
|-
|-
| | 3
| 3
| | 116.9925
| 116.9925
| |16/15
| 16/15
| |  
|  
|-
|-
| | 4
| 4
| | 155.99
| 155.99
| | 128/117
| 128/117
| |  
|  
|-
|-
| | 5
| 5
| | 194.9875
| 194.9875
| | 28/25
| 28/25
| |  
|  
|-
|-
| | 6
| 6
| | 233.985
| 233.985
| |8/7
| 8/7
| |  
|  
|-
|-
| | 7
| 7
| | 272.9825
| 272.9825
| |7/6
| 7/6
| |  
|  
|-
|-
| | 8
| 8
| | 311.98
| 311.98
| |6/5
| 6/5
| |  
|  
|-
|-
| | 9
| 9
| | 350.9775
| 350.9775
| | 60/49, 49/40
| 60/49, 49/40
| |  
|  
|-
|-
| | 10
| 10
| | 389.975
| 389.975
| |5/4
| 5/4
| |  
|  
|-
|-
| | 11
| 11
| | 428.9725
| 428.9725
| |9/7
| 9/7
| |  
|  
|-
|-
| | 12
| 12
| | 467.97
| 467.97
| |  
|  
| |  
|  
|-
|-
| | 13
| 13
| | 506.9675
| 506.9675
| | 75/56
| 75/56
| |  
|  
|-
|-
| | 14
| 14
| | 545.965
| 545.965
| |  
|  
| |  
|  
|-
|-
| | 15
| 15
| | 584.9625
| 584.9625
| |  
|  
| |  
|  
|-
|-
| | 16
| 16
| | 623.96
| 623.96
| |  
|  
| |  
|  
|-
|-
| | 17
| 17
| | 662.9575
| 662.9575
| | [[22/15]]
| [[22/15]]
| |  
|  
|-
|-
| | 18
| 18
| | 701.955
| 701.955
| | '''exact [[3/2]]'''
| '''exact [[3/2]]'''
| | just perfect fifth
| just perfect fifth
|-
|-
|19
| 19
|740.9525
| 740.9525
|135/88
| 135/88
|
|  
|-
|-
|20
| 20
|779.95
| 779.95
|
|  
|
|  
|-
|-
|21
| 21
|818.9475
| 818.9475
|8/5
| 8/5
|
|  
|-
|-
|22
| 22
|857.945
| 857.945
|64/39
| 64/39
|
|  
|-
|-
|23
| 23
|896.9425
| 896.9425
|42/25
| 42/25
|
|  
|-
|-
|24
| 24
|935.94
| 935.94
|12/7
| 12/7
|
|  
|-
|-
|25
| 25
|974.9375
| 974.9375
|7/4
| 7/4
|
|  
|-
|-
|26
| 26
|1013.935
| 1013.935
|9/5
| 9/5
|
|  
|-
|-
|27
| 27
|1052.9325
| 1052.9325
|90/49, 147/80
| 90/49, 147/80
|
|  
|-
|-
|28
| 28
|1091.93
| 1091.93
|15/8
| 15/8
|
|  
|-
|-
|29
| 29
|1130.9275
| 1130.9275
|27/14
| 27/14
|
|  
|-
|-
|30
| 30
|1169.925
| 1169.925
|
|  
|
|  
|-
|-
|31
| 31
|1208.9225
| 1208.9225
|225/112
| 225/112
|
|  
|-
|-
|32
| 32
|1247.92
| 1247.92
|
|  
|
|  
|-
|-
|33
| 33
|1286.9175
| 1286.9175
|
|  
|
|  
|-
|-
|34
| 34
|1325.915
| 1325.915
|
|  
|
|  
|-
|-
|35
| 35
|1364.9125
| 1364.9125
|
|  
|
|  
|-
|-
|36
| 36
|1403.91
| 1403.91
|'''exact''' 9/4
| '''exact''' 9/4
|
|  
|}
|}


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


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


Mapping: [&lt;1 19 2 7|, &lt;0 -54 1 -13|]
Mapping: [{{map| 1 19 2 7 }}, {{map| 0 -54 1 -13 }}]


EDOs: {{EDOs|31, 369, 400, 431, 462}}
EDOs: {{EDOs|31, 369, 400, 431, 462}}


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


POTE generator: ~5/4 = 386.999
POTE generator: ~5/4 = 386.999


Mapping: [&lt;1 19 2 7 37|, &lt;0 -54 1 -13 -104|]
Mapping: [{{map| 1 19 2 7 37 }}, {{map| 0 -54 1 -13 -104 }}]


EDOs: 31, 369, 400, 431, 462
EDOs: 31, 369, 400, 431, 462


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


POTE generator: ~5/4 = 387.003
POTE generator: ~5/4 = 387.003


Mapping: [&lt;1 19 2 7 37 -35|, &lt;0 -54 1 -13 -104 120|]
Mapping: [{{map| 1 19 2 7 37 -35 }}, {{map| 0 -54 1 -13 -104 120 }}]


EDOs: 31, 369, 400, 431, 462
EDOs: 31, 369, 400, 431, 462


{{Todo|cleanup|expand|inline=1|comment=say what the temperaments are like and why one would want to use them, and for what}}
{{Todo|cleanup|expand|inline=1|comment=say what the temperaments are like and why one would want to use them, and for what}}
Retrieved from "https://en.xen.wiki/w/18edf"