10edf: Difference between revisions

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Line 42: Line 42:
|2
|2
|''132.1429-133.1429''
|''132.1429-133.1429''
|137.7778
|[[Tel:137.7778|137.7778]]
|138.9632
|[[Tel:138.9632|138.9632]]
|139.64
|139.64
|''140''
|''140''
|140.391
|140.391
|140.7272
|[[Tel:140.7272|140.7272]]
|141.1711
|[[Tel:141.1711|141.1711]]
|141.813
|141.813
|143.1579
|[[Tel:143.1579|143.1579]]
|''148-149''
|''148-149''
|C#, Db
|C#, Db
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|3
|3
|''198.2143-199.7143''
|''198.2143-199.7143''
|206.6667
|[[Tel:206.6667|206.6667]]
|208.4448
|[[Tel:208.4448|208.4448]]
|209.455
|209.455
|''210''
|''210''
|210.5865
|[[Tel:210.5865|210.5865]]
|211.0908
|[[Tel:211.0908|211.0908]]
|211.7566
|[[Tel:211.7566|211.7566]]
|212.7194
|[[Tel:212.7194|212.7194]]
|214.7368
|[[Tel:214.7368|214.7368]]
|''222-223.5''
|''222-223.5''
|vD
|vD
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|4
|4
|''264.2857-266.2857''
|''264.2857-266.2857''
|275.5556
|[[Tel:275.5556|275.5556]]
|277.92635
|277.92635
|279.27
|279.27
|''280''
|''280''
|280.782
|280.782
|281.4544
|[[Tel:281.4544|281.4544]]
|282.3422
|[[Tel:282.3422|282.3422]]
|283.6259
|[[Tel:283.6259|283.6259]]
|286.3158
|[[Tel:286.3158|286.3158]]
|''296-298''
|''296-298''
|D
|D
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|5
|5
|''330.3571-332.8571''
|''330.3571-332.8571''
|344.4444
|[[Tel:344.4444|344.4444]]
|347.4079
|[[Tel:347.4079|347.4079]]
|349.09
|349.09
|''350''
|''350''
|350.9775
|[[Tel:350.9775|350.9775]]
|351.818
|351.818
|352.9277
|[[Tel:352.9277|352.9277]]
|354.5324
|[[Tel:354.5324|354.5324]]
|357.8947
|[[Tel:357.8947|357.8947]]
|''370-372.5''
|''370-372.5''
|^D, vE
|^D, vE
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|6
|6
|''396.4286-399.4286''
|''396.4286-399.4286''
|413.3333
|[[Tel:413.3333|413.3333]]
|416.8895
|[[Tel:416.8895|416.8895]]
|418.91
|418.91
|''420''
|''420''
|421.173
|421.173
|422.1816
|[[Tel:422.1816|422.1816]]
|423.5133
|[[Tel:423.5133|423.5133]]
|425.4389
|[[Tel:425.4389|425.4389]]
|429.4737
|[[Tel:429.4737|429.4737]]
|''444-447''
|''444-447''
|E
|E
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|7
|7
|''462.5-466''
|''462.5-466''
|482.2222
|[[Tel:482.2222|482.2222]]
|486.3711
|[[Tel:486.3711|486.3711]]
|488.73
|488.73
|''490''
|''490''
|491.3685
|[[Tel:491.3685|491.3685]]
|492.5452
|[[Tel:492.5452|492.5452]]
|494.0988
|[[Tel:494.0988|494.0988]]
|496.3454
|[[Tel:496.3454|496.3454]]
|501.0526
|[[Tel:501.0526|501.0526]]
|''518-521.5''
|''518-521.5''
|^E, vF
|^E, vF
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|8
|8
|''528.5714-532.5714''
|''528.5714-532.5714''
|551.1111
|[[Tel:551.1111|551.1111]]
|555.8527
|[[Tel:555.8527|555.8527]]
|558.545
|558.545
|''560''
|''560''
|561.564
|561.564
|562.9088
|[[Tel:562.9088|562.9088]]
|564.6843
|[[Tel:564.6843|564.6843]]
|567.2518
|[[Tel:567.2518|567.2518]]
|572.6316
|[[Tel:572.6316|572.6316]]
|''592-596''
|''592-596''
|F
|F
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|''594.6429-599.1429''
|''594.6429-599.1429''
|620
|620
|625.3343
|[[Tel:625.3343|625.3343]]
|628.36
|628.36
|''630''
|''630''
|631.7595
|[[Tel:631.7595|631.7595]]
|633.2724
|[[Tel:633.2724|633.2724]]
|635.2699
|[[Tel:635.2699|635.2699]]
|638.1583
|[[Tel:638.1583|638.1583]]
|644.2105
|[[Tel:644.2105|644.2105]]
|''666-670.5''
|''666-670.5''
|^F, vC
|^F, vC
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|10
|10
|''660.7143-665.714''3
|''660.7143-665.714''3
|688.8889
|[[Tel:688.8889|688.8889]]
|694.8159
|[[Tel:694.8159|694.8159]]
|698.18
|698.18
|''700''
|''700''
|701.955
|701.955
|703.636
|703.636
|705.8555
|[[Tel:705.8555|705.8555]]
|709.0648
|[[Tel:709.0648|709.0648]]
|715.7895
|[[Tel:715.7895|715.7895]]
|''740-745''
|''740-745''
|C
|C
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|11
|11
|''726.7857-732.2857''
|''726.7857-732.2857''
|757.7778
|[[Tel:757.7778|757.7778]]
|764.2974
|[[Tel:764.2974|764.2974]]
|768
|768
|''770''
|''770''
|772.1505
|[[Tel:772.1505|772.1505]]
|773.9996
|[[Tel:773.9996|773.9996]]
|776.441
|776.441
|779.9713
|[[Tel:779.9713|779.9713]]
|787.3684
|[[Tel:787.3684|787.3684]]
|''814-819.5''
|''814-819.5''
|^C, vDb
|^C, vDb
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|12
|12
|''792.8571-798.8571''
|''792.8571-798.8571''
|826.6667
|[[Tel:826.6667|826.6667]]
|833.7791
|[[Tel:833.7791|833.7791]]
|837.82
|837.82
|''840''
|''840''
|842.346
|842.346
|844.3632
|[[Tel:844.3632|844.3632]]
|847.0265
|[[Tel:847.0265|847.0265]]
|850.8778
|[[Tel:850.8778|850.8778]]
|858.9474
|[[Tel:858.9474|858.9474]]
|''888-894''
|''888-894''
|C#, Db
|C#, Db
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|13
|13
|''858.9286-865.4286''
|''858.9286-865.4286''
|895.5556
|[[Tel:895.5556|895.5556]]
|903.26065
|903.26065
|907.64
|907.64
|''910''
|''910''
|912.5415
|[[Tel:912.5415|912.5415]]
|914.7268
|[[Tel:914.7268|914.7268]]
|917.6121
|[[Tel:917.6121|917.6121]]
|921.7842
|[[Tel:921.7842|921.7842]]
|930.5263
|[[Tel:930.5263|930.5263]]
|''962-968.5''
|''962-968.5''
|vD
|vD
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|14
|14
|''925-932''
|''925-932''
|964.4444
|[[Tel:964.4444|964.4444]]
|972.7422
|[[Tel:972.7422|972.7422]]
|977.455
|977.455
|''980''
|''980''
|982.737
|982.737
|985.0904
|[[Tel:985.0904|985.0904]]
|988.1976
|[[Tel:988.1976|988.1976]]
|992.6907
|[[Tel:992.6907|992.6907]]
|1002.1053
|1002.1053
|''1036-1043''
|''1036-1043''
|
|D
|-
|-
|15
|15
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|1073.6842
|1073.6842
|''1110-1117.5''
|''1110-1117.5''
|
|^D, vE
|-
|-
|16
|16
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|1145.2632
|1145.2632
|''1184-1192''
|''1184-1192''
|
|E
|-
|-
|17
|17
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|1216.8451
|1216.8451
|''1258-1268.5''
|''1258-1268.5''
|
|^E, vF
|-
|-
|18
|18
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|1288.42105
|1288.42105
|''1332-1341''
|''1332-1341''
|
|F
|-
|-
|19
|19
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|1360
|1360
|''1406-1415.5''
|''1406-1415.5''
|
|^F, vC
|-
|-
|20
|20
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|1431.57895
|1431.57895
|''1480-1490''
|''1480-1490''
|
|C
|}
|}
== Music ==
== Music ==

Revision as of 07:25, 7 March 2023

← 9edf 10edf 11edf →
Prime factorization 2 × 5
Step size 70.1955 ¢ 
Octave 17\10edf (1193.32 ¢)
(semiconvergent)
Twelfth 27\10edf (1895.28 ¢)
(semiconvergent)
Consistency limit 7
Distinct consistency limit 6

Division of the just perfect fifth into 10 equal parts (10EDF) is related to 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-integer-limit, but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.

Lookalikes: 17edo, 27edt

Intervals

degree ed233\420-5¢ ed31\54 ed121/81 (~ed11\19) ed32\55 ed700¢=r¢ ed3/2 Pyrite ed122/81 (~ed13\22) ed34\57 ed37\60+5¢ Neptunian notation using 8\10edf
(~ed17\29) (~ed10\17)
0 C
1 66.0714-66.5714 68.8889 69.4816 69.82 70 70.1955 70.3636 70.58555 70.9065 71.57895 74-74.5 ^C, vDb
2 132.1429-133.1429 [[1]] [[2]] 139.64 140 140.391 [[3]] [[4]] 141.813 [[5]] 148-149 C#, Db
3 198.2143-199.7143 [[6]] [[7]] 209.455 210 [[8]] [[9]] [[10]] [[11]] [[12]] 222-223.5 vD
4 264.2857-266.2857 [[13]] 277.92635 279.27 280 280.782 [[14]] [[15]] [[16]] [[17]] 296-298 D
5 330.3571-332.8571 [[18]] [[19]] 349.09 350 [[20]] 351.818 [[21]] [[22]] [[23]] 370-372.5 ^D, vE
6 396.4286-399.4286 [[24]] [[25]] 418.91 420 421.173 [[26]] [[27]] [[28]] [[29]] 444-447 E
7 462.5-466 [[30]] [[31]] 488.73 490 [[32]] [[33]] [[34]] [[35]] [[36]] 518-521.5 ^E, vF
8 528.5714-532.5714 [[37]] [[38]] 558.545 560 561.564 [[39]] [[40]] [[41]] [[42]] 592-596 F
9 594.6429-599.1429 620 [[43]] 628.36 630 [[44]] [[45]] [[46]] [[47]] [[48]] 666-670.5 ^F, vC
10 660.7143-665.7143 [[49]] [[50]] 698.18 700 701.955 703.636 [[51]] [[52]] [[53]] 740-745 C
11 726.7857-732.2857 [[54]] [[55]] 768 770 [[56]] [[57]] 776.441 [[58]] [[59]] 814-819.5 ^C, vDb
12 792.8571-798.8571 [[60]] [[61]] 837.82 840 842.346 [[62]] [[63]] [[64]] [[65]] 888-894 C#, Db
13 858.9286-865.4286 [[66]] 903.26065 907.64 910 [[67]] [[68]] [[69]] [[70]] [[71]] 962-968.5 vD
14 925-932 [[72]] [[73]] 977.455 980 982.737 [[74]] [[75]] [[76]] 1002.1053 1036-1043 D
15 991.0714-998.5714 1033.3333 1042.2238 1047.27 1050 1052.9325 1055.45405 1058.7832 1063.5972 1073.6842 1110-1117.5 ^D, vE
16 1057.1429-1065.1429 1102.2222 1111.7054 1117.09 1120 1123.128 1125.81765 1129.3688 1134.5037 1145.2632 1184-1192 E
17 1123.2143-1131.7143 1171.1111 1181.187 1186.91 1190 1193.3235 1196.18125 1199.9543 1205.4102 1216.8451 1258-1268.5 ^E, vF
18 1189.2857-1198.2857 1240 1250.6686 1256.73 1260 1263.519 1266.5449 1270.5398 1276.3166 1288.42105 1332-1341 F
19 1255.3571-1263.8571 1308.8889 1320.1502 1326.545 1330 1333.7145 1336.9085 1341.1254 1347.2231 1360 1406-1415.5 ^F, vC
20 1321.4286-1331.4286 1377.7778 1389.6318 1396.36 1400 1403.91 1407.272 1411.7109 1418.1296 1431.57895 1480-1490 C

Music

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