Xenharmonic Wiki

19edf: Difference between revisions

← Older edit
VisualWikitext
No edit summary
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
'''19EDF''' is the [[EDF|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of |-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.


==Intervals==
== Theory ==
{| class="wikitable"
19edf corresponds to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of {{monzo| -103/19 65/19 }} (1.425{{c}}) resulting from its inexact 4/1. It is not as similar to [[32edo]] as [[13edf]] and [[16edf]] are to [[22edo]] and [[27edo]].
 
== Harmonics ==
{{Harmonics in equal|19|3|2}}
{{Harmonics in equal|19|3|2|start=12|collapsed=1}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ style="font-size: 105%;" | Intervals of 19edf
|-
|-
! | degree
! Degree
! | cents value
! [[Cent]]s
! | corresponding <br>JI intervals
! Corresponding<br />JI intervals
! | comments
! comments
|-
|-
! colspan="2" | 0
! colspan="2" | 0
| | '''exact [[1/1]]'''
| '''exact [[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 36.945
| 36.945
| |  
|  
| |  
|  
|-
|-
| | 2
| 2
| | 73.89
| 73.89
| | [[24/23]]
| [[24/23]]
| |  
|  
|-
|-
| | 3
| 3
| | 110.835
| 110.835
| | [[16/15]]
| [[16/15]]
| |  
|  
|-
|-
| | 4
| 4
| | 147.78
| 147.78
| | [[12/11]]
| [[12/11]]
| |  
|  
|-
|-
| | 5
| 5
| | 184.725
| 184.725
| | [[10/9]]
| [[10/9]]
| |  
|  
|-
|-
| | 6
| 6
| | 221.67
| 221.67
| | [[25/22]]
| [[25/22]]
| |  
|  
|-
|-
| | 7
| 7
| | 258.615
| 258.615
| | 36/31
| 36/31
| |  
|  
|-
|-
| | 8
| 8
| | 295.56
| 295.56
| | [[19/16]]
| [[19/16]]
| |  
|  
|-
|-
| | 9
| 9
| | 332.505
| 332.505
| | 63/52, 40/33
| 63/52, 40/33
| |  
|  
|-
|-
| | 10
| 10
| | 369.45
| 369.45
| | [[26/21]]
| [[26/21]]
| |  
|  
|-
|-
| | 11
| 11
| | 406.395
| 406.395
| | [[24/19]], [[19/15]]
| [[24/19]], [[19/15]]
| |  
|  
|-
|-
| | 12
| 12
| | 443.34
| 443.34
| | 31/24
| 31/24
| |  
|  
|-
|-
| | 13
| 13
| | 480.285
| 480.285
| | 33/25
| 33/25
| |  
|  
|-
|-
| | 14
| 14
| | 517.23
| 517.23
| | [[27/20]]
| [[27/20]]
| |  
|  
|-
|-
| | 15
| 15
| | 554.175
| 554.175
| | [[11/8]]
| [[11/8]]
| |  
|  
|-
|-
| | 16
| 16
| | 591.12
| 591.12
| | [[45/32]]
| [[45/32]]
| |  
|  
|-
|-
| | 17
| 17
| | 628.065
| 628.065
| | [[23/16]]
| [[23/16]]
| |  
|  
|-
|-
| | 18
| 18
| | 665.01
| 665.01
| | [[22/15]]
| [[22/15]]
| |  
|  
|-
|-
| | 19
| 19
| | 701.955
| 701.955
| | '''exact [[3/2]]'''
| '''exact [[3/2]]'''
| | just perfect fifth
| just perfect fifth
|-
|-
| | 20
| 20
| | 738.9
| 738.9
| |  
|  
| |  
|  
|-
|-
| | 21
| 21
| | 775.845
| 775.845
| |  
|  
| |  
|  
|-
|-
| | 22
| 22
| | 812.79
| 812.79
| | [[8/5]]
| [[8/5]]
| |  
|  
|-
|-
| | 23
| 23
| | 849.735
| 849.735
| | [[18/11]]
| [[18/11]]
| |  
|  
|-
|-
| | 24
| 24
| | 886.68
| 886.68
| | [[5/3]]
| [[5/3]]
| |  
|  
|-
|-
| | 25
| 25
| | 923.625
| 923.625
| |  
|  
| |  
|  
|-
|-
| | 26
| 26
| | 960.57
| 960.57
| |  
|  
| |  
|  
|-
|-
| | 27
| 27
| | 997.515
| 997.515
| | [[16/9]]
| [[16/9]]
| |  
|  
|-
|-
| | 28
| 28
| | 1034.46
| 1034.46
| | [[20/11]]
| [[20/11]]
| |  
|  
|-
|-
| | 29
| 29
| | 1071.405
| 1071.405
| | [[13/7]]
| [[13/7]]
| |  
|  
|-
|-
| | 30
| 30
| | 1108.35
| 1108.35
| | [[36/19]]
| [[36/19]]
| |  
|  
|-
|-
| | 31
| 31
| | 1145.295
| 1145.295
| | 31/16
| 31/16
| |  
|  
|-
|-
| | 32
| 32
| | 1182.24
| 1182.24
| |  
|  
| |  
|  
|-
|-
| | 33
| 33
| | 1219.185
| 1219.185
| |  
|  
| |  
|  
|-
|-
|34
| 34
|1256.13
| 1256.13
|
|  
|
|  
|-
|-
|35
| 35
|1293.075
| 1293.075
|
|  
|
|  
|-
|-
|36
| 36
|1330.02
| 1330.02
|
|  
|
|  
|-
|-
|37
| 37
|1366.965
| 1366.965
|
|  
|
|  
|-
|-
|38
| 38
|1403.91
| 1403.91
|'''exact''' 9/4
| '''exact''' 9/4
|
|  
|}
|}
==Scale tree==
If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.


If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.
{{todo|expand}}
 
Generator range: 36.09023 cents (4\7/19 = 4\133) to 37.89474 cents (3\5/19 = 3\95)
{| class="wikitable center-all"
! colspan="7" | Fifth
!Cents
! Comments
|-
| 4\7|| || || || || || || 36.0902||
|-
| || || || || ||  ||27\47||36.2822||
|-
|  || || || || ||23\40||  ||36.3158 ||
|-
| || || || || || ||42\73 ||36.3374 ||
|-
| ||  || || || 19\33||  || ||36.{{Overline|36}}||
|-
| || || || || || ||53\92||36.3844||
|-
| || || ||  || ||34\59|| ||36.3961||
|-
| || ||  || || || ||49\85||36.4087 ||
|-
|  || || ||15\26|| ||  || ||36.43725||
|-
| || ||  || || || ||56\97||36.4633||
|-
| || ||  || || || 41\71|| ||36.4175||
|-
|  || || || || || ||67\116|| 36.4791||
|-
| || ||  || || 26\45||  || ||36.4912||[[Flattone]] is in this region
|-
| ||  || || || || ||63\109||36.5041||
|-
| || || ||  || ||37\64||  ||36.5132||
|-
| ||  || || || || ||48\83 || 36.52505||
|-
| ||  ||11\19|| || ||  || || 36.5651||
|-
| || || || || || || 51\88||36.6029||
|-
| || || ||  || ||40\69 || ||36.6133||
|-
|  || || || || || ||69\119|| 36.6210||
|-
|  || || || || 29\50|| ||  ||36.6316||
|-
| ||  || ||  || || || 76\131||36.6412||[[Golden meantone]] (696.2145¢)
|-
| || || || || ||47\81|| ||36.6472||
|-
| || || || || || ||65\112||36.6541||
|-
| || || ||18\31|| || || ||36.6723||[[Meantone]] is in this region
|-
| || || || || || ||61\105||36.6917||
|-
| || || || || ||43\74|| ||36.6999||
|-
| || || || || || ||68\117||36.70175||
|-
| || || || ||25\43|| || ||36.7197||
|-
| || || || || || ||57\98||36.7347||
|-
| || || || || ||32\55|| ||36.7464||
|-
| || || || || || ||39\67||36.76355||
|-
| ||7\12|| || || || || ||36.8421||
|-
| || || || || || ||38\65||36.9231||
|-
| || || || || ||31\53|| ||36.9414||The fifth closest to a just [[3/2]] for EDOs less than 200
|-
| || || || || || ||55\94||36.9541||[[Garibaldi]] / [[Cassandra]]
|-
| || || || ||24\41|| || ||36.9705||
|-
| || || || || || ||65\111||36.98435||
|-
| || || || || ||41\70|| ||36.9925||
|-
| || || || || || ||58\99||37.0016||
|-
| || || ||17\29|| || || ||37.0236||
|-
| || || || || || ||61\104||37.0445||
|-
| || || || || ||44\75|| ||37.0526||
|-
| || || || || || ||71\121||37.0596||Golden neogothic (704.0956¢)
|-
| || || || ||27\46|| || ||37.0709||[[Neogothic]] is in this region
|-
| || || || || || ||64\109||37.0835||
|-
| || || || || ||37\63|| ||37.0927||
|-
| || || || || || ||47\80||37.1053||
|-
| || ||10\17|| || || || ||37.1517||
|-
| || || || || || ||43\73||37.2026||
|-
| || || || || ||33\56|| ||37.21805||
|-
| || || || || || ||56\95||37.2299||
|-
| || || || ||23\39|| || ||37.2470||
|-
| || || || || || ||59\100||37.2632||
|-
| || || || || ||36\61|| ||37.2735||
|-
| || || || || || ||49\83||37.2388||
|-
| || || ||13\22|| || || ||37.3206||[[Archy]] is in this region
|-
| || || || || || ||42\71||37.3610||
|-
| || || || || ||29\49|| ||37.3792||
|-
| || || || || || ||45\76||37.3961||
|-
| || || || ||16\27|| || ||37.4269||
|-
| || || || || || ||35\59||37.46655||
|-
| || || || || ||19\32|| ||37.5000||
|-
| || || || || || ||22\37||37.5533||
|-
|3\5|| || || || || || ||37.8947||
|}Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.
[[Category:Edf]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/19edf"