10edf: Difference between revisions

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-'''[[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]].
+{{Infobox ET}}
+{{ED intro}}
-Lookalikes: [[17edo]], [[27edt]]
+== Theory ==
+edf 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}}
+{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}}
+=== 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"
+|-
+! #
+! 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
+| 70.2
+| ^C, vDb
+| F^, Gb
 |-
-!degree
+| 2
-!cents value
+| 140.4
+| C#, Db
+| F#, Gd
 |-
-|0
+| 3
-|0
+| 210.6
+| vD
+| G
 |-
-|1
+| 4
-|70.1955
+| 280.8
+| D
+| G^, Ab
 |-
-|2
+| 5
-|140.391
+| 351.0
+| ^D, vE
+| G#, Ad
 |-
-|3
+| 6
-|210.5865
+| 421.2
+| E
+| A
 |-
-|4
+| 7
-|280.782
+| 491.4
+| ^E, vF
+| A^, Hb
 |-
-|5
+| 8
-|350.9775
+| 561.6
+| F
+| A#, Hd
 |-
-|6
+| 9
-|421.173
+| 631.8
+| ^F, vC
+| H
 |-
-|7
+| 10
-|491.3685
+| 702.0
+| C
+| B
 |-
-|8
+| 11
-|561.564
+| 772.2
+| ^C, vDb
+| B^, Cb
 |-
-|9
+| 12
-|631.7595
+| 842.3
+| C#, Db
+| B#, Cd
 |-
-|10
+| 13
-|701.955
+| 912.5
+| vD
+| C
 |-
-|11
+| 14
-|772.1505
+| 982.7
+| D
+| C^, Db
 |-
-|12
+| 15
-|842.346
+| 1052.9
+| ^D, vE
+| C#, Dd
 |-
-|13
+| 16
-|912.5415
+| 1123.1
+| E
+| D
 |-
-|14
+| 17
-|982.737
+| 1193.3
+| ^E, vF
+| D^, Eb
 |-
-|15
+| 18
-|1052.9325
+| 1263.5
+| F
+| D#, Eb
 |-
-|16
+| 19
-|1123.128
+| 1333.7
+| ^F, vC
+| E
 |-
-|17
+| 20
-|1193.3235
+| 1403.9
+| C
+| F
 |}
 == 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:todo:expand]]
-[[Category:todo:improve synopsis]]