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{{Infobox ET}}
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 10 equal parts''' (10EDF) is related to [[17edo|17 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 6.6765 cents compressed and the step size is about 70.1955 cents. It is consistent to the [[7-odd-limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the [[3-odd-limit|4-integer-limit]].
{{ED intro}}


Lookalikes: [[17edo]], [[27edt]]
== Theory ==
10edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.


==Intervals==
=== Harmonics ===
{| class="wikitable"
{{Harmonics in equal|10|3|2|intervals=integer|columns=11}}
!degree
{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}}
!
 
![[1L 3s (fifth-equivalent)|Neptunian]] notation using 8\10edf
=== Subsets and supersets ===
Since 10 factors into primes as {{nowrap| 2 × 5 }}, 10edf contains [[2edf]] and [[5edf]] as subset edfs.
 
== Intervals ==
{| class="wikitable center-all right-2"
|-
|-
! colspan="2" |0
! #
|C
! Cents
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 8\10edf
! [[Ed9/4|Neapolitan]] notation<br>using 3/10edf
|-
| 0
| 0.0
| C
| F
|-
|-
| 1
| 1
|70.1955
| 70.2
|^C, vDb
| ^C, vDb
| F^, Gb
|-
|-
|2
| 2
|140.391
| 140.4
|C#, Db
| C#, Db
| F#, Gd
|-
|-
|3
| 3
|210.5865
| 210.6
|vD
| vD
| G
|-
|-
|4
| 4
|280.782
| 280.8
|D
| D
| G^, Ab
|-
|-
|5
| 5
|350.9775
| 351.0
|^D, vE
| ^D, vE
| G#, Ad
|-
|-
|6
| 6
|421.173
| 421.2
|E
| E
| A
|-
|-
|7
| 7
|491.3685
| 491.4
|^E, vF
| ^E, vF
| A^, Hb
|-
|-
| 8
| 8
|561.564
| 561.6
|F
| F
| A#, Hd
|-
|-
|9
| 9
|631.7595
| 631.8
|^F, vC
| ^F, vC
| H
|-
|-
|10
| 10
|701.955
| 702.0
|C
| C
| B
|-
|-
|11
| 11
|772.1505
| 772.2
|^C, vDb
| ^C, vDb
| B^, Cb
|-
|-
|12
| 12
|842.346
| 842.3
|C#, Db
| C#, Db
| B#, Cd
|-
|-
|13
| 13
|912.5415
| 912.5
|vD
| vD
| C
|-
|-
|14
| 14
|982.737
| 982.7
|D
| D
| C^, Db
|-
|-
|15
| 15
|1052.9325
| 1052.9
|^D, vE
| ^D, vE
| C#, Dd
|-
|-
|16
| 16
|1123.128
| 1123.1
|E
| E
| D
|-
|-
|17
| 17
|1193.3235
| 1193.3
|^E, vF
| ^E, vF
| D^, Eb
|-
|-
|18
| 18
|1263.519
| 1263.5
|F
| F
| D#, Eb
|-
|-
|19
| 19
|1333.7145
| 1333.7
|^F, vC
| ^F, vC
| E
|-
|-
|20
| 20
|1403.91
| 1403.9
|C
| C
| F
|}
|}


==Music==
== Music ==
*http://www.archive.org/details/10Edf by [[Peter Kosmorsky]]
; [[Peter Kosmorsky]]
* [https://www.archive.org/details/10Edf ''10 edf''] (archived 2011)
 
== See also ==
* [[17edo]] – relative edo
* [[27edt]] – relative edt
* [[44ed6]] – relative ed6


[[Category:Edf]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:todo:expand]]
[[Category:todo:improve synopsis]]
Retrieved from "https://en.xen.wiki/w/10edf"