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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 ==
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}}
|-
{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}}
! rowspan="2" |degree
 
! rowspan="2" |''ed233\420-5¢''
=== Subsets and supersets ===
! rowspan="2" |ed31\54
Since 10 factors into primes as {{nowrap| 2 × 5 }}, 10edf contains [[2edf]] and [[5edf]] as subset edfs.
! rowspan="2" |ed121/81 (~ed11\19)
 
! rowspan="2" |ed3/2
== Intervals ==
! colspan="2" |Pyrite
{| class="wikitable center-all right-2"
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57
! rowspan="2" |''ed37\60+5¢''
|-
|-
!(~ed17\29)
! #
!(~ed10\17)
! Cents
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 8\10edf
! [[Ed9/4|Neapolitan]] notation<br>using 3/10edf
|-
|-
| colspan="10" |0
| 0
| 0.0
| C
| F
|-
|-
|1
| 1
|''66.0714-66.5714''
| 70.2
|68.8889
| ^C, vDb
|69.4816
| F^, Gb
|70.1955
|70.3636
|70.58555
|70.9065
|71.57895
|''74-74.5''
|-
|-
|2
| 2
|''132.1429-133.1429''
| 140.4
|137.7778
| C#, Db
|138.9632
| F#, Gd
|140.391
|140.7272
|141.1711
|141.813
|143.1579
|''148-149''
|-
|-
|3
| 3
|''198.2143-199.7143''
| 210.6
|206.6667
| vD
|208.4448
| G
|210.5865
|211.0908
|211.7566
|212.7194
|214.7368
|''222-223.5''
|-
|-
|4
| 4
|''264.2857-266.2857''
| 280.8
|275.5556
| D
|277.92635
| G^, Ab
|280.782
|281.4544
|282.3422
|283.6259
|286.3158
|''296-298''
|-
|-
|5
| 5
|''330.3571-332.8571''
| 351.0
|344.4444
| ^D, vE
|347.4079
| G#, Ad
|350.9775
|351.818
|352.9277
|354.5324
|357.8947
|''370-372.5''
|-
|-
|6
| 6
|''396.4286-399.4286''
| 421.2
|413.3333
| E
|416.8895
| A
|421.173
|422.1816
|423.5133
|425.4389
|429.4737
|''444-447''
|-
|-
|7
| 7
|''462.5-466''
| 491.4
|482.2222
| ^E, vF
|486.3711
| A^, Hb
|491.3685
|492.5452
|494.0988
|496.3454
|501.0526
|''518-521.5''
|-
|-
|8
| 8
|''528.5714-532.5714''
| 561.6
|551.1111
| F
|555.8527
| A#, Hd
|561.564
|562.9088
|564.6843
|567.2518
|572.6316
|''592-596''
|-
|-
|9
| 9
|''594.6429-599.1429''
| 631.8
|620
| ^F, vC
|625.3343
| H
|631.7595
|633.2724
|635.2699
|638.1583
|644.2105
|''666-670.5''
|-
|-
|10
| 10
|''660.7143-665.714''3
| 702.0
|688.8889
| C
|694.8159
| B
|701.955
|703.636
|705.8555
|709.0648
|715.7895
|''740-745''
|-
|-
|11
| 11
|''726.7857-732.2857''
| 772.2
|757.7778
| ^C, vDb
|764.2974
| B^, Cb
|772.1505
|773.9996
|776.441
|779.9713
|787.3684
|''814-819.5''
|-
|-
|12
| 12
|''792.8571-798.8571''
| 842.3
|826.6667
| C#, Db
|833.7791
| B#, Cd
|842.346
|844.3632
|847.0265
|850.8778
|858.9474
|''888-894''
|-
|-
|13
| 13
|''858.9286-865.4286''
| 912.5
|895.5556
| vD
|903.26065
| C
|912.5415
|914.7268
|917.6121
|921.7842
|930.5263
|''962-968.5''
|-
|-
|14
| 14
|''925-932''
| 982.7
|964.4444
| D
|972.7422
| C^, Db
|982.737
|985.0904
|988.1976
|992.6907
|1002.1053
|''1036-1043''
|-
|-
|15
| 15
|''991.0714-998.5714''
| 1052.9
|1033.3333
| ^D, vE
|1042.2238
| C#, Dd
|1052.9325
|1055.45405
|1058.7832
|1063.5972
|1073.6842
|''1110-1117.5''
|-
|-
|16
| 16
|''1057.1429-1065.1429''
| 1123.1
|1102.2222
| E
|1111.7054
| D
|1123.128
|1125.81765
|1129.3688
|1134.5037
|1145.2632
|''1184-1192''
|-
|-
|17
| 17
|''1123.2143-1131.7143''
| 1193.3
|1171.1111
| ^E, vF
|1181.187
| D^, Eb
|1193.3235
|1196.18125
|1199.9543
|1205.4102
|1216.8451
|''1258-1268.5''
|-
|-
|18
| 18
|''1189.2857-1198.2857''
| 1263.5
|1240
| F
|1250.6686
| D#, Eb
|1263.519
|1266.5449
|1270.5398
|1276.3166
|1288.42105
|''1332-1341''
|-
|-
|19
| 19
|''1255.3571-1263.8571''
| 1333.7
|1308.8889
| ^F, vC
|1320.1502
| E
|1333.7145
|1336.9085
|1341.1254
|1347.2231
|1360
|''1406-1415.5''
|-
|-
|20
| 20
|''1321.4286-1331.4286''
| 1403.9
|1377.7778
| C
|1389.6318
| F
|1403.91
|1407.272
|1411.7109
|1418.1296
|1431.57895
|''1480-1490''
|}
|}
== 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"