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'''16EDF''' is the [[EDF|equal division of the just perfect fifth]] into 16 parts of 43.8722 [[cent|cents]] each, corresponding to 27.3522 [[edo]] (similar to every third step of [[82edo]]).
{{Infobox ET}}
{{ED intro}}


Lookalikes: [[27edo]], [[43edt]]
== Theory ==
16edf corresponds to 27.3522…[[edo]]. It is similar to every third step of [[82edo]] but not quite similar to [[27edo]]; the octave is compressed by 15.45{{c}}, a small but significant deviation. It contains good approximations of the [[7/1|7th]] and [[13/1|13th]] [[harmonic]]s.


==Intervals==
It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.
{| class="wikitable"
 
=== Harmonics ===
{{Harmonics in equal|16|3|2}}
{{Harmonics in equal|16|3|2|start=12|columns=12|collapsed=true|title=Approximation of harmonics in 16edf (continued)}}
 
=== Subsets and supersets ===
Since 16 factors into primes as 2<sup>4</sup>, 16edf contains subset edfs {{EDs|equave=f| 2, 4, and 8 }}.
 
== Intervals ==
{| class="wikitable center-1 right-2 mw-collapsible"
|+ Intervals of 16edf
|-
|-
! | degree
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Approximate ratios
! | comments
! Halftone[6] notation<br>(using [[ups and downs notation|ups and downs]])
! Comments
|-
|-
| colspan="2"| 0
| 0
| | '''exact [[1/1]]'''
| 0.0
| |  
| [[1/1]]
| C
|  
|-
|-
| | 1
| 1
| | 43.8722
| 43.9
| | 40/39, 39/38
| 40/39, 39/38
| |  
| ^C
|  
|-
|-
| | 2
| 2
| | 87.7444
| 87.7
| | [[20/19]]
| [[20/19]]
| |  
| Db
|  
|-
|-
| | 3
| 3
| | 131.6166
| 131.6
| | 55/51, ([[27/25]])
| 55/51, ([[27/25]])
| |  
| vD
|  
|-
|-
| | 4
| 4
| | 175.4888
| 175.5
| | ([[21/19]])
| ([[21/19]])
| |  
| D
|  
|-
|-
| | 5
| 5
| | 219.3609
| 219.4
| |  
|  
| |  
| vE
|  
|-
|-
| | 6
| 6
| | 263.2331
| 263.2
| | ([[7/6]])
| ([[7/6]])
| |  
| E
|  
|-
|-
| | 7
| 7
| | 307.1053
| 307.1
| |  
|  
| |  
| Fb
|  
|-
|-
| | 8
| 8
| | 350.9775
| 351.0
| | 60/49, 49/40
| 60/49, 49/40
| |  
| vF
|  
|-
|-
| | 9
| 9
| | 394.8497
| 394.8
| | (44/35)
| (44/35)
| |  
| F
|  
|-
|-
| | 10
| 10
| | 438.7219
| 438.7
| | ([[9/7]])
| ([[9/7]])
| |  
| Ab
|  
|-
|-
| | 11
| 11
| | 482.5941
| 482.6
| |  
|  
| |  
| vA
|  
|-
|-
| | 12
| 12
| | 526.4663
| 526.5
| | ([[19/14]])
| ([[19/14]])
| |  
| A
|  
|-
|-
| | 13
| 13
| | 570.3384
| 570.3
| | ([[25/18]]), 153/110
| ([[25/18]]), 153/110, 112/81
| |  
| B
|  
|-
|-
| | 14
| 14
| | 614.2106
| 614.2
| | ([[10/7]])
| ([[10/7]])
| |  
| Cb
|  
|-
|-
| | 15
| 15
| | 658.0828
| 658.1
| | [[19/13]]
| [[19/13]]
| |  
| vC
|  
|-
|-
| | 16
| 16
| | 701.9550
| 702.0
| | '''exact [[3/2]]'''
| [[3/2]]
| | just perfect fifth
| C
| Just perfect fifth
|-
|-
| | 17
| 17
| | 745.8272
| 745.8
| | [[20/13]]
| [[20/13]]
| |  
|
|  
|-
|-
| | 18
| 18
| | 789.6994
| 789.7
| | [[30/19]]
| [[30/19]]
| |  
|
|  
|-
|-
| | 19
| 19
| | 833.5716
| 833.6
| | 55/34
| 55/34
| |  
|
|  
|-
|-
| | 20
| 20
| | 877.4438
| 877.4
| |  
|
| |  
|  
|  
|-
|-
| | 21
| 21
| | 921.3159
| 921.3
| |  
|
| |  
|  
|  
|-
|-
| | 22
| 22
| | 965.1881
| 965.2
| | [[7/4]]
| [[7/4]]
| |  
|  
|  
|-
|-
| | 23
| 23
| | 1009.0603
| 1009.0
| |  
|
| |  
|  
|  
|-
|-
| | 24
| 24
| | 1052.9325
| 1052.9
| | 90/49, ([[11/6]])
| 90/49, ([[11/6]])
| |  
|
|  
|-
|-
| | 25
| 25
| | 1096.8047
| 1096.8
| | (66/35)
| (66/35)
| |  
|
|  
|-
|-
| | 26
| 26
| | 1140.6769
| 1140.7
| |  
|  
| |  
|
|  
|-
|-
| | 27
| 27
| | 1184.5491
| 1184.5
| |  
|  
| |  
|
|  
|-
|-
| | 28
| 28
| | 1228.4213
| 1228.4
| | 128/63
| 128/63
| |  
|  
|
|-
|-
|29
| 29
|1272.2934
| 1272.3
|25/12
| 25/12
|
|
|
|-
|-
|30
| 30
|1316.1656
| 1316.2
|15/7
| 15/7
|
|
|
|-
|-
|31
| 31
|1360.0378
| 1360.0
|57/26
| 57/26
|
|
|
|-
|-
|32
| 32
|1403.91
| 1403.9
|'''exact''' 9/4
| [[9/4]]
|
|
| Pythagorean major ninth
|}
|}


==Compositions==
== Music ==
; [[Nae Ayy]]
* [https://www.youtube.com/watch?v=8YegsoiO1Co ''Neptune''] (2021)
 
; [[nationalsolipsism]]
* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue''] (2011)
 
== See also ==
* [[27edo]] – relative edo
* [[43edt]] – relative edt
* [[70ed6]] – relative ed6
* [[90ed10]] – relative ed10
* [[97ed12]] – relative ed12


[http://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue]
{{Todo|expand}}


[[Category:Edf]]
[[Category:27edo]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/16edf"