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{{Infobox ET}}
{{Infobox ET}}
'''[[Ed5|Division of the 5th harmonic]] into 19 equal parts''' (19ED5) is related to the [[13edt|Bohlen-Pierce scale]], but with the 5/1 rather than the 3/1 being just. The step size is about 146.6481 cents, corresponding to 8.1829 [[EDO]]. It provides 5, 7, 13, and 15-odd-limit minimax generator for the [[bohpier]] temperament.
{{ED intro}}
 
19ED5 is related to the [[13edt|Bohlen–Pierce scale]], but with the 5/1 rather than the 3/1 being just. The step size is about 146.6481{{c}}, corresponding to 8.1829[[EDO]]. It provides 5, 7, 13, and 15-odd-limit minimax generator for the [[bohpier]] temperament.


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | degree
! Degree
! | cents value
! Cents
! | corresponding <br>JI intervals
! Corresponding<br />JI intervals
! | comments
! Comments
|-
|-
| | 0
| 0
| | 0.0000
| 0.0000
| | '''exact [[1/1]]'''
| '''exact [[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 146.6481
| 146.6481
| | [[49/45]]
| [[49/45]]
| |  
|  
|-
|-
| | 2
| 2
| | 293.2962
| 293.2962
| | [[13/11]]
| [[13/11]]
| |  
|  
|-
|-
| | 3
| 3
| | 439.9443
| 439.9443
| | [[9/7]]
| [[9/7]]
| |  
|  
|-
|-
| | 4
| 4
| | 586.5924
| 586.5924
| | [[7/5]]
| [[7/5]]
| |  
|  
|-
|-
| | 5
| 5
| | 733.2405
| 733.2405
| | [[49/32]]
| [[49/32]]
| |  
|  
|-
|-
| | 6
| 6
| | 879.8885
| 879.8885
| | [[5/3]]
| [[5/3]]
| |  
|  
|-
|-
| | 7
| 7
| | 1026.5366
| 1026.5366
| | [[9/5]]
| [[9/5]]
| |  
|  
|-
|-
| | 8
| 8
| | 1173.1847
| 1173.1847
| | 63/32
| 63/32
| |  
|  
|-
|-
| | 9
| 9
| | 1319.8328
| 1319.8328
| | [[15/7]]
| [[15/7]]
| |  
|  
|-
|-
| | 10
| 10
| | 1466.4809
| 1466.4809
| | [[7/3]]
| [[7/3]]
| |  
|  
|-
|-
| | 11
| 11
| | 1613.1290
| 1613.1290
| | [[14/11|28/11]]
| [[14/11|28/11]]
| |  
|  
|-
|-
| | 12
| 12
| | 1759.7771
| 1759.7771
| | [[11/4]]
| [[11/4]]
| |  
|  
|-
|-
| | 13
| 13
| | 1906.4252
| 1906.4252
| | [[3/1]]
| [[3/1]]
| |  
|  
|-
|-
| | 14
| 14
| | 2053.0733
| 2053.0733
| | 49/15
| 49/15
| |  
|  
|-
|-
| | 15
| 15
| | 2199.7214
| 2199.7214
| | 32/9
| 32/9
| |  
|  
|-
|-
| | 16
| 16
| | 2346.3694
| 2346.3694
| | 35/9
| 35/9
| |  
|  
|-
|-
| | 17
| 17
| | 2493.0175
| 2493.0175
| | [[21/20|21/5]]
| [[21/20|21/5]]
| |  
|  
|-
|-
| | 18
| 18
| | 2639.6656
| 2639.6656
| | [[8/7|32/7]]
| [[8/7|32/7]]
| |  
|  
|-
|-
| | 19
| 19
| | 2786.3137
| 2786.3137
| | '''exact [[5/1]]'''
| '''exact [[5/1]]'''
| | just major third plus two octaves
| just major third plus two octaves
|}
|}


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== See also ==
== See also ==
* [[13edt|13ED3]]: relative ED3 (Bohlen-Pierce scale)
* [[13edt|13ED3]]: relative ED3 (Bohlen–Pierce scale)
* [[23ed7|23ED7]]: relative ED7
* [[23ed7|23ED7]]: relative ED7


[[Category:Ed5]]
[[Category:Bohlen–Pierce]]
[[Category:Edonoi]]
[[Category:Bohlen-Pierce]]
[[Category:Bohpier]]
[[Category:Bohpier]]
Retrieved from "https://en.xen.wiki/w/19ed5"