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{{Infobox ET}}
{{Infobox ET}}
'''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]]). 16edf contains good approximations of the 7th and 13th harmonics.
{{ED intro}}


It serves as a good approximation to [[halftone]] temperament, containing the ~[[7/5]] generator at 13 steps.
== Theory ==
16edf corresponds to 27.3522…[[edo]]. It is not quite similar to [[27edo]], but it is similar to every third step of [[82edo]]. It contains good approximations of the [[7/1|7th]] and [[13/1|13th]] [[harmonics]].


Lookalikes: [[27edo]], [[43edt]]
It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.


== Harmonics ==
=== Harmonics ===
{{Harmonics in equal|16|3|2}}
{{Harmonics in equal|16|3|2}}
{{Harmonics in equal|16|3|2|start=12|collapsed=1}}
{{Harmonics in equal|16|3|2|start=12|columns=12|collapsed=true|title=Approximation of harmonics in 16edf (continued)}}


== Intervals ==
== Intervals ==
{| class="wikitable right-2 mw-collapsible"
{| class="wikitable center-1 right-2 mw-collapsible"
|+ Intervals of 16edf
|+ Intervals of 16edf
|-
|-
! degree
! #
! cents value
! Cents
! corresponding <br>JI intervals
! Approximate ratios
! Halftone[6] notation (using [[ups and downs notation|ups and downs]])
! Halftone[6] notation<br>(using [[ups and downs notation|ups and downs]])
! comments
! Comments
|-
|-
| 0
| 0
| 0.0000
| 0.0
| [[1/1]]
| [[1/1]]
| C
| C
Line 27: Line 28:
|-
|-
| 1
| 1
| 43.8722
| 43.9
| 40/39, 39/38
| 40/39, 39/38
| ^C
| ^C
Line 33: Line 34:
|-
|-
| 2
| 2
| 87.7444
| 87.7
| [[20/19]]
| [[20/19]]
| Db
| Db
Line 39: Line 40:
|-
|-
| 3
| 3
| 131.6166
| 131.6
| 55/51, ([[27/25]])
| 55/51, ([[27/25]])
| vD
| vD
Line 45: Line 46:
|-
|-
| 4
| 4
| 175.4888
| 175.5
| ([[21/19]])
| ([[21/19]])
| D
| D
Line 51: Line 52:
|-
|-
| 5
| 5
| 219.3609
| 219.4
|  
|  
| vE
| vE
Line 57: Line 58:
|-
|-
| 6
| 6
| 263.2331
| 263.2
| ([[7/6]])
| ([[7/6]])
| E
| E
Line 63: Line 64:
|-
|-
| 7
| 7
| 307.1053
| 307.1
|  
|  
| Fb
| Fb
Line 69: Line 70:
|-
|-
| 8
| 8
| 350.9775
| 351.0
| 60/49, 49/40
| 60/49, 49/40
| vF
| vF
Line 75: Line 76:
|-
|-
| 9
| 9
| 394.8497
| 394.8
| (44/35)
| (44/35)
| F
| F
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|-
|-
| 10
| 10
| 438.7219
| 438.7
| ([[9/7]])
| ([[9/7]])
| Ab
| Ab
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|-
|-
| 11
| 11
| 482.5941
| 482.6
|  
|  
| vA
| vA
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|-
|-
| 12
| 12
| 526.4663
| 526.5
| ([[19/14]])
| ([[19/14]])
| A
| A
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|-
|-
| 13
| 13
| 570.3384
| 570.3
| ([[25/18]]), 153/110, 112/81
| ([[25/18]]), 153/110, 112/81
| B
| B
Line 105: Line 106:
|-
|-
| 14
| 14
| 614.2106
| 614.2
| ([[10/7]])
| ([[10/7]])
| Cb
| Cb
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|-
|-
| 15
| 15
| 658.0828
| 658.1
| [[19/13]]
| [[19/13]]
| vC
| vC
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|-
|-
| 16
| 16
| 701.9550
| 702.0
| [[3/2]] (exact)
| [[3/2]]
| C
| C
| just perfect fifth
| Just perfect fifth
|-
|-
| 17
| 17
| 745.8272
| 745.8
| [[20/13]]
| [[20/13]]
|
|
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|-
|-
| 18
| 18
| 789.6994
| 789.7
| [[30/19]]
| [[30/19]]
|
|
Line 135: Line 136:
|-
|-
| 19
| 19
| 833.5716
| 833.6
| 55/34
| 55/34
|
|
Line 141: Line 142:
|-
|-
| 20
| 20
| 877.4438
| 877.4
|
|
|  
|  
Line 147: Line 148:
|-
|-
| 21
| 21
| 921.3159
| 921.3
|
|
|  
|  
Line 153: Line 154:
|-
|-
| 22
| 22
| 965.1881
| 965.2
|
|
| [[7/4]]
| [[7/4]]
Line 159: Line 160:
|-
|-
| 23
| 23
| 1009.0603
| 1009.0
|
|
|  
|  
Line 165: Line 166:
|-
|-
| 24
| 24
| 1052.9325
| 1052.9
| 90/49, ([[11/6]])
| 90/49, ([[11/6]])
|
|
Line 171: Line 172:
|-
|-
| 25
| 25
| 1096.8047
| 1096.8
| (66/35)
| (66/35)
|
|
Line 177: Line 178:
|-
|-
| 26
| 26
| 1140.6769
| 1140.7
|  
|  
|
|
Line 183: Line 184:
|-
|-
| 27
| 27
| 1184.5491
| 1184.5
|  
|  
|
|
Line 189: Line 190:
|-
|-
| 28
| 28
| 1228.4213
| 1228.4
| 128/63
| 128/63
|  
|  
Line 195: Line 196:
|-
|-
| 29
| 29
| 1272.2934
| 1272.3
| 25/12
| 25/12
|
|
Line 201: Line 202:
|-
|-
| 30
| 30
| 1316.1656
| 1316.2
| 15/7
| 15/7
|
|
Line 207: Line 208:
|-
|-
| 31
| 31
| 1360.0378
| 1360.0
| 57/26
| 57/26
|
|
Line 213: Line 214:
|-
|-
| 32
| 32
| 1403.9100
| 1403.9
| [[9/4]] (exact)
| [[9/4]]
|
|
| pythagorean ninth
| Pythagorean major ninth
|}
|}


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue] by [[nationalsolipsism]]
; [[Nae Ayy]]
* [https://www.youtube.com/watch?v=8YegsoiO1Co Neptune] by [[Nae Ayy]]
* [https://www.youtube.com/watch?v=8YegsoiO1Co ''Neptune'']


[[Category:Edf]]
; [[nationalsolipsism]]
[[Category:Edonoi]]
* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue'']
{{todo|expand}}
 
{{Todo|expand}}
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