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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}}
|-
{{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" |ed32\55
== Intervals ==
! rowspan="2" |ed700¢=''r¢''
{| class="wikitable center-all right-2"
! rowspan="2" |ed3/2
! colspan="2" |Pyrite
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57
! rowspan="2" |''ed37\60+5¢''
! rowspan="2" | [[1L 3s (fifth-equivalent)|Neptunian]] notation using 8\10edf
|-
|-
!(~ed17\29)
! #
!(~ed10\17)
! Cents
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 8\10edf
! [[Ed9/4|Neapolitan]] notation<br>using 3/10edf
|-
|-
! colspan="12" |0
| 0
|C
| 0.0
| C
| F
|-
|-
|1
| 1
|''66.0714-66.5714''
| 70.2
|68.8889
| ^C, vDb
|69.4816
| F^, Gb
|69.82
|''70''
|70.1955
|70.3636
|70.58555
|70.9065
|71.57895
|''74-74.5''
|^C, vDb
|-
|-
|2
| 2
|''132.1429-133.1429''
| 140.4
|[[Tel:137.7778|137.7778]]
| C#, Db
|[[Tel:138.9632|138.9632]]
| F#, Gd
|139.64
|''140''
|140.391
|[[Tel:140.7272|140.7272]]
|[[Tel:141.1711|141.1711]]
|141.813
|[[Tel:143.1579|143.1579]]
|''148-149''
|C#, Db
|-
|-
|3
| 3
|''198.2143-199.7143''
| 210.6
|[[Tel:206.6667|206.6667]]
| vD
|[[Tel:208.4448|208.4448]]
| G
|209.455
|''210''
|[[Tel:210.5865|210.5865]]
|[[Tel:211.0908|211.0908]]
|[[Tel:211.7566|211.7566]]
|[[Tel:212.7194|212.7194]]
|[[Tel:214.7368|214.7368]]
|''222-223.5''
|vD
|-
|-
|4
| 4
|''264.2857-266.2857''
| 280.8
|[[Tel:275.5556|275.5556]]
| D
|277.92635
| G^, Ab
|279.27
|''280''
|280.782
|[[Tel:281.4544|281.4544]]
|[[Tel:282.3422|282.3422]]
|[[Tel:283.6259|283.6259]]
|[[Tel:286.3158|286.3158]]
|''296-298''
|D
|-
|-
|5
| 5
|''330.3571-332.8571''
| 351.0
|[[Tel:344.4444|344.4444]]
| ^D, vE
|[[Tel:347.4079|347.4079]]
| G#, Ad
|349.09
|''350''
|[[Tel:350.9775|350.9775]]
|351.818
|[[Tel:352.9277|352.9277]]
|[[Tel:354.5324|354.5324]]
|[[Tel:357.8947|357.8947]]
|''370-372.5''
|^D, vE
|-
|-
|6
| 6
|''396.4286-399.4286''
| 421.2
|[[Tel:413.3333|413.3333]]
| E
|[[Tel:416.8895|416.8895]]
| A
|418.91
|''420''
|421.173
|[[Tel:422.1816|422.1816]]
|[[Tel:423.5133|423.5133]]
|[[Tel:425.4389|425.4389]]
|[[Tel:429.4737|429.4737]]
|''444-447''
|E
|-
|-
|7
| 7
|''462.5-466''
| 491.4
|[[Tel:482.2222|482.2222]]
| ^E, vF
|[[Tel:486.3711|486.3711]]
| A^, Hb
|488.73
|''490''
|[[Tel:491.3685|491.3685]]
|[[Tel:492.5452|492.5452]]
|[[Tel:494.0988|494.0988]]
|[[Tel:496.3454|496.3454]]
|[[Tel:501.0526|501.0526]]
|''518-521.5''
|^E, vF
|-
|-
|8
| 8
|''528.5714-532.5714''
| 561.6
|[[Tel:551.1111|551.1111]]
| F
|[[Tel:555.8527|555.8527]]
| A#, Hd
|558.545
|''560''
|561.564
|[[Tel:562.9088|562.9088]]
|[[Tel:564.6843|564.6843]]
|[[Tel:567.2518|567.2518]]
|[[Tel:572.6316|572.6316]]
|''592-596''
|F
|-
|-
|9
| 9
|''594.6429-599.1429''
| 631.8
|620
| ^F, vC
|[[Tel:625.3343|625.3343]]
| H
|628.36
|''630''
|[[Tel:631.7595|631.7595]]
|[[Tel:633.2724|633.2724]]
|[[Tel:635.2699|635.2699]]
|[[Tel:638.1583|638.1583]]
|[[Tel:644.2105|644.2105]]
|''666-670.5''
|^F, vC
|-
|-
|10
| 10
|''660.7143-665.714''3
| 702.0
|[[Tel:688.8889|688.8889]]
| C
|[[Tel:694.8159|694.8159]]
| B
|698.18
|''700''
|701.955
|703.636
|[[Tel:705.8555|705.8555]]
|[[Tel:709.0648|709.0648]]
|[[Tel:715.7895|715.7895]]
|''740-745''
|C
|-
|-
|11
| 11
|''726.7857-732.2857''
| 772.2
|[[Tel:757.7778|757.7778]]
| ^C, vDb
|[[Tel:764.2974|764.2974]]
| B^, Cb
|768
|''770''
|[[Tel:772.1505|772.1505]]
|[[Tel:773.9996|773.9996]]
|776.441
|[[Tel:779.9713|779.9713]]
|[[Tel:787.3684|787.3684]]
|''814-819.5''
|^C, vDb
|-
|-
|12
| 12
|''792.8571-798.8571''
| 842.3
|[[Tel:826.6667|826.6667]]
| C#, Db
|[[Tel:833.7791|833.7791]]
| B#, Cd
|837.82
|''840''
|842.346
|[[Tel:844.3632|844.3632]]
|[[Tel:847.0265|847.0265]]
|[[Tel:850.8778|850.8778]]
|[[Tel:858.9474|858.9474]]
|''888-894''
|C#, Db
|-
|-
|13
| 13
|''858.9286-865.4286''
| 912.5
|[[Tel:895.5556|895.5556]]
| vD
|903.26065
| C
|907.64
|''910''
|[[Tel:912.5415|912.5415]]
|[[Tel:914.7268|914.7268]]
|[[Tel:917.6121|917.6121]]
|[[Tel:921.7842|921.7842]]
|[[Tel:930.5263|930.5263]]
|''962-968.5''
|vD
|-
|-
|14
| 14
|''925-932''
| 982.7
|[[Tel:964.4444|964.4444]]
| D
|[[Tel:972.7422|972.7422]]
| C^, Db
|977.455
|''980''
|982.737
|[[Tel:985.0904|985.0904]]
|[[Tel:988.1976|988.1976]]
|[[Tel:992.6907|992.6907]]
|1002.1053
|''1036-1043''
|D
|-
|-
|15
| 15
|''991.0714-998.5714''
| 1052.9
|1033.3333
| ^D, vE
|1042.2238
| C#, Dd
|1047.27
|''1050''
|1052.9325
|1055.45405
|1058.7832
|1063.5972
|1073.6842
|''1110-1117.5''
|^D, vE
|-
|-
|16
| 16
|''1057.1429-1065.1429''
| 1123.1
|1102.2222
| E
|1111.7054
| D
|1117.09
|''1120''
|1123.128
|1125.81765
|1129.3688
|1134.5037
|1145.2632
|''1184-1192''
|E
|-
|-
|17
| 17
|''1123.2143-1131.7143''
| 1193.3
|1171.1111
| ^E, vF
|1181.187
| D^, Eb
|1186.91
|''1190''
|1193.3235
|1196.18125
|1199.9543
|1205.4102
|1216.8451
|''1258-1268.5''
|^E, vF
|-
|-
|18
| 18
|''1189.2857-1198.2857''
| 1263.5
|1240
| F
|1250.6686
| D#, Eb
|1256.73
|''1260''
|1263.519
|1266.5449
|1270.5398
|1276.3166
|1288.42105
|''1332-1341''
|F
|-
|-
|19
| 19
|''1255.3571-1263.8571''
| 1333.7
|1308.8889
| ^F, vC
|1320.1502
| E
|1326.545
|''1330''
|1333.7145
|1336.9085
|1341.1254
|1347.2231
|1360
|''1406-1415.5''
|^F, vC
|-
|-
|20
| 20
|''1321.4286-1331.4286''
| 1403.9
|1377.7778
| C
|1389.6318
| F
|1396.36
|''1400''
|1403.91
|1407.272
|1411.7109
|1418.1296
|1431.57895
|''1480-1490''
|C
|}
|}
== 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"