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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.
 
It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.
 
=== 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 ==
== Intervals ==
 
{| class="wikitable center-1 right-2 mw-collapsible"
{| class="wikitable right-2"
|+ 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
|-
|-
| 0
| 0
| 0.0000
| 0.0
| [[1/1]]
| [[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
| [[3/2]] (exact)
| [[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
| 1403.9100
| 1403.9
| [[9/4]] (exact)
| [[9/4]]
| pythagorean ninth
|
| 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"