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{{Stub}}
{{Infobox ET}}
{{ED intro}}
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!Degrees
!Degrees
! colspan="2" |Enneatonic
! colspan="2" |Enneatonic
!ed43\36
! colspan="2" |ed11\9~ed7/3
!Pyrite<sub>v</sub>
!ed35\29 (r¢<sub>Aeolian 29[[edIX]]</sub>)~8ed5/4
!''ed29\24=r¢<sub>v</sub>''
!29ed9/4~ed23\19
!Pyrite<sub>r¢</sub>
!25ed1213¢
!ed17\14
!Golden<sub>v</sub>
!ed11\9~ed7/3
!30ed(11φ+5\9φ+4)~18ed(5/3)
!ed16/13
!ed37\30
!ed21\17
!24ed1187¢~2ed18/17
!25ed1240¢
!10ed4/3~ed91\73
!''ed5\4=r¢<sub>^</sub>''
|-
|-
|1
|1
|G+/Jbd
|G+/Jbd
|''G+/Abd''
|''G+/Abd''
|47.7778
|48.{{Overline|8}}
|47.9265
|48.8957
|48.2759
48.2892
|''48.3333''
|48.4107 48.42105
|48.489
|48.52
|48.5714
|48.6617
|48.8889
48.8957
|49.1283
49.131
|49.2308
|49.3333
|49.4118
|49.4583
49.4773
|49.6
|49.8045
 
49.863
|''50''
|-
|-
|2
|2
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|95.5556
|97.{{Overline|7}}
|95.853
|97.7914
|96.5517
96.5784
|''96.6667''
|96.8214
 
96.8421
|96.97795
|97.04
|97.1429
|97.3234
|97.7778
97.7914
|98.25665
98.2621
|98.4615
|98.6667
|98.8235
|98.9167
98.9546
|99.2
|99.609
99.7261
|''100''
|-
|-
|3
|3
|G#+/Jd
|G#+/Jd
|''G#+/Ad''
|''G#+/Ad''
|143.3333
|146.{{Overline|6}}
|143.7794
|146.6871
|144.8276
144.8676
|''145''
|145.2321 145.2632
|145.4669
|145.56
|145.7143
|145.985
|146.6667
146.6871
|147.385
147.3931
|147.6923
|148
|148.2353
|148.375
148.4319
|148.8
|149.4135
 
149.589
|''150''
|-
|-
|4
|4
|J
|J
|''A''
|''A''
|191.1111
|195.{{Overline|5}}
|191.7059
|195.5828
|193.10345
193.1569
|''193.3333''
|193.6428 193.6842
|193.9559
|194.08
|194.2857
|194.6468
|195.5556
195.5828
|196.5133
196.5241
|196.9231
|197.3333
|197.6471
|197.8333
197.9092
|198.4
|199.218
199.4521
|''200''
|-
|-
|5
|5
|J+/Abd
|J+/Abd
|''A+/Bbd''
|''A+/Bbd''
|238.8889
|244.{{Overline|4}}
|239.6324
|244.4785
|241.3793
241.4461
|''241.6667''
|242.0534 242.1053
|242.4449
|242.6
|242.8571
|243.3085
|244.4444
244.4785
|245.6416
245.6552
|246.15385
|246.6667
|247.0588
|247.2917
247.3865
|248
|249.0225
 
249.3151
|''250''
|-
|-
|6
|6
|J#/Ab
|J#/Ab
|''A#/Bb''
|''A#/Bb''
|286.6667
|293.{{Overline|3}}
|287.5589
|293.3742
|289.6552
289.7353
|''290''
|290.4641 290.5263
|290.9339
|291.12
|291.4286
|291.9702
|293.3333
293.3742
|294.7699
294.7862
|295.3845
|296
|296.4706
|296.75
296.8638
|297.6
|298.827
299.1781
|''300''
|-
|-
|7
|7
|J#+/Ad
|J#+/Ad
|''A#+/Bd''
|''A#+/Bd''
|334.4444
|342.{{Overline|2}}
|335.48535
|342.2699
|337.931
338.0245
|''338.3333''
|338.8748 338.9474
|339.4228
|339.64
|340
|340.6319
|342.2222
342.2699
|343.8983
343.9173
|344.6154
|345.3333
|345.88235
|346.2083
346.3411
|347.2
|348.6315
 
349.0411
|''350''
|-
|-
|8
|8
|A
|A
|''B''
|''B''
|382.2222
|391.{{Overline|1}}
|383.4118
|391.1656
|386.2069
386.3137
|''386.6667''
|387.2855 387.3684
|387.9118
|388.16
|388.5714
|389.2936
|391.1111
391.1656
|393.0266
393.0483
|393.84615
|394.6667
|395.2941
|395.6667
395.8184
|396.8
|398.436
398.9041
|''400''
|-
|-
|9
|9
|A+/Bd
|A+/Bd
|''B+/Cd''
|''B+/Cd''
|430
|440
|431.3383
|440.0613
|434.4828
434.6029
|''435''
|435.6962 435.7895
|436.4008
|436.68
|437.1429
|437.95525
|440(.0613)
|442.1549
442.1794
|443.0769
|444
|444.7647
|445.125
445.2957
|446.4
|448.2405
 
448.7671
|''450''
|-
|-
|10
|10
|B
|B
|''C''
|''C''
|477.7778
|488.{{Overline|8}}
|479.2648
|488.957
|482.7586
482.8921
|''483.3333''
|484.1069 484.2105
|484.8898
|485.2
|485.7143
|486.61695
|488.8889
488.957
|491.2832
491.3104
|492.3077
|493.3333
|494.11765
|494.5833
494.773
|496
|498.045
498.6301
|''500''
|-
|-
|11
|11
|B+/Cbd
|B+/Cbd
|''C+/Qbd''
|''C+/Qbd''
|525.5556
|537.{{Overline|7}}
|527.1913
|537.8527
|531.0345
531.1814
|''531.6667''
|532.5176 532.6316
|533.37875
|533.72
|534.2857
|535.2786
|537.7778
537.8527
|540.41155
540.4414
|541.5385
|542.6667
|543.5294
|544.0417
544.2503
|545.6
|547.8495
 
548.4932
|''550''
|-
|-
|12
|12
|B#/Cb
|B#/Cb
|''C#/Qb''
|''C#/Qb''
|573.3333
|586.{{Overline|6}}
|575.1177
|586.7484
|579.3103
579.4706
|''580''
|580.9283 581.0526
|581.8677
|582.24
|582.8571
|583.9403
|586.6667
586.7484
|589.5399
589.5725
|590.7692
|592
|592.9412
|593.5
593.72755
|595.2
|597.654
598.3562
|''600''
|-
|-
|13
|13
|B#+/Cd
|B#+/Cd
|''C#+/Qd''
|''C#+/Qd''
|621.1111
|635.{{Overline|5}}
|623.0442
|635.6441
|627.5862
627.7598
|''628.3333''
|629.3390 629.4737
|630.3567
|630.76
|631.4286
|632.602
|635.5556
635.6441
|638.6682
638.7035
|640
|641.3333
|642.3529
|642.9583
643.20485
|644.8
|647.4585
 
648.2192
|''650''
|-
|-
|14
|14
|C
|C
|''Q''
|''Q''
|668.8889
|684.{{Overline|4}}
|670.9706
|684.5398
|675.8621
676.049
|''676.6667''
|677.7497 677.8947
|678.8457
|679.28
|680
|681.2637
|684.4444
684.5398
|687.7965
687.83455
|689.2308
|690.6667
|691.7647
|692.68215
|694.4
|697.263
698.0822
|''700''
|-
|-
|15
|15
|C+/Qbd
|C+/Qbd
|''Q+/Dbd''
|''Q+/Dbd''
|716.6667
|733.{{Overline|3}}
|718.8972
|733.43545
|724.1379
724.3382
|''725''
|726.16035 726.3158
|727.33466
|727.8
|728.5714
|729.9254
|733.3333
733.43545
|736.9248
736.9655
|738.4615
|740
|741.1765
|742.1594
|744
|846.6765
 
847.6712
|''750''
|-
|-
|16
|16
|C#/Qb
|C#/Qb
|''Q#/Db''
|''Q#/Db''
|764.4444
|782.{{Overline|2}}
|766.82365
|782.33115
|772.4138
772.6274
|''773.3333''
|774.571 774.7368
|775.8236
|776.32
|777.1429
|778.5871
|782.2222
782.33115
|786.0532
786.0966
|787.6923
|789.3333
|790.5882
|791.6367
|793.6
|796.872
797.8082
|''800''
|-
|-
|17
|17
|C#+/Qd
|C#+/Qd
|''Q#+/Dd''
|''Q#+/Dd''
|812.2222
|831.{{Overline|1}}
|814.7501
|831.22685
|820.6897
820.9166
|''821.6667''
|822.9817 823.1579
|824.31261
|824.84
|825.7143
|827.2488
|831.1111
831.22685
|835.1815
835.2277
|836.9231
|838.6667
|840
|841.114
|843.2
|946.2855
 
947.3973
|''850''
|-
|-
|18
|18
|Q
|Q
|''D''
|''D''
|860
|880
|862.6766
|880.1225
|868.9655
869.2059
|''870''
|871.3924 871.57895
|872.8016
|873.36
|874.2857
|875.9105
|880(.1225)
|884.3098
884.3587
|886.84615
|888
|889.4118
|890.5913
|892.8
|896.481
897.53425
|''900''
|-
|-
|19
|19
|Q+/Dd
|Q+/Dd
|''D+/Sd''
|''D+/Sd''
|907.7778
|928.{{Overline|8}}
|910.6031
|929.0182
|917.2414
917.4951
|''918.3333''
|919.8031
 
920
|921.29057
|921.88
|922.8571
|824.5722
|928.8889
929.0182
|933.4381
933.48975
|935.3845
|937.3333
|938.8235
|940.0686
|942.4
|946.2855
 
947.3973
|''950''
|-
|-
|20
|20
|D
|D
|''S''
|''S''
|955.5556
|977.{{Overline|7}}
|958.5296
|977.9139
|965.5172
965.7843
|''966.6667''
|968.2138 968.42105
|969.7795
|970.4
|971.4286
|972.2339
|977.7778
977.9139
|982.56645
982.6207
|984.6154
|986.6667
|988.2353
|989.5459
|992
|996.09
997.26027
|''1000''
|-
|-
| rowspan="2" |21
| rowspan="2" |21
|D+
|D+
|''S+''
|''S+''
| rowspan="2" |1003.3333
| rowspan="2" |1026.{{Overline|6}}
| rowspan="2" |1006.45605
| rowspan="2" |1026.8096
| rowspan="2" |1013.7931
1014.0735
| rowspan="2" |''1015''
| rowspan="2" |1016.6245 1016.8421
| rowspan="2" |1018.2685
| rowspan="2" |1018.92
| rowspan="2" |1020
| rowspan="2" |1021.8956
| rowspan="2" |1026.6667
1026.8096
| rowspan="2" |1031.6948
1301.7518
| rowspan="2" |1033.84615
| rowspan="2" |1037.3333
| rowspan="2" |1037.6471
| rowspan="2" |1039.0232
| rowspan="2" |1041.6
| rowspan="2" |1045.894
 
1047.123
| rowspan="2" |''1050''
|-
|-
| colspan="2" |Ebd
| colspan="2" |Ebd
Line 599: Line 140:
|D#
|D#
|''S#''
|''S#''
| rowspan="2" |1051.1111
| rowspan="2" |1075.{{Overline|5}}
| rowspan="2" |1054.3825
| rowspan="2" |1075.7053
| rowspan="2" |1062.069
1062.3627
| rowspan="2" |''1063.3333''
| rowspan="2" |1065.0352 1065.2632
| rowspan="2" |1066.7575
| rowspan="2" |1067.44
| rowspan="2" |1068.5714
| rowspan="2" |1070.5573
| rowspan="2" |1075.5556
1075.7053
| rowspan="2" |1080.8231
1080.8828
| rowspan="2" |1083.0769
| rowspan="2" |1085.3333
| rowspan="2" |1087.0588
| rowspan="2" |1088.5005
| rowspan="2" |1091.2
| rowspan="2" |1095.699
 
1096.9863
| rowspan="2" |''1100''
|-
|-
| colspan="2" |Eb
| colspan="2" |Eb
Line 628: Line 148:
|D#+
|D#+
|''S#+''
|''S#+''
| rowspan="2" |1098.8889
| rowspan="2" |1124.{{Overline|4}}
| rowspan="2" |1102.309
| rowspan="2" |1124.601
| rowspan="2" |1110.3448
1110.6519
| rowspan="2" |''1111.1667''
| rowspan="2" |1113.4459 1113.6842
| rowspan="2" |1115.2465
| rowspan="2" |1115.96
| rowspan="2" |1117.1429
| rowspan="2" |1119.219
| rowspan="2" |1124.4444
1124.601
| rowspan="2" |1129.9514
1130.0139
| rowspan="2" |1132.3077
| rowspan="2" |1134.6667
| rowspan="2" |1136.4706
| rowspan="2" |1137.9778
| rowspan="2" |1140.8
| rowspan="2" |1145.503
 
1146.849
| rowspan="2" |''1150''
|-
|-
| colspan="2" |Ed
| colspan="2" |Ed
Line 656: Line 155:
|24
|24
| colspan="2" |E
| colspan="2" |E
|1146.6667
|1173.{{Overline|3}}
|1150.2355
|1173.4967
|1158.621
1158.9411
|''1160''
|1161.8566 1162.1053
|1163.73545
|1164.48
|1165.7143
|1167.8807
|1173.3333
1173.4967
|1179.07976
1179.14495
|1181.5385
|1184
|1185.88235
|1187.4551
|1190.6
|1195.308
1196.7123
|''1200''
|-
|-
|25
|25
| colspan="2" |E+/Fbd
| colspan="2" |E+/Fbd
|1194.4444
|1222.{{Overline|2}}
|1198.162
|1222.3924
|1206.8966
1207.2304
|''1208.3333''
|1210.2672 1210.5263
|1212.2244
|1213
|1214.2857
|1216.5424
|1222.2222
1222.3924
|1228.208
1228.276
|1230.7692
|1233.3333
|1235.2941
|1236.9324
|1240
|1245.112
 
1246.575
|''1250''
|-
|-
|26
|26
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1242.2222
|1271.{{Overline|1}}
|1246.0884
|1271.2881
|1255.1724
1255.5196
|''1256.6667''
|1258.6779 1258.9474
|1260.7134
|1261.52
|1262.8571
|1265.2041
|1271.1111
1271.2881
|1277.3364
1277.407
|1280
|1282.6667
|1284.7059
|1286.4097
|1289.6
|1294.917
1296.4384
|''1300''
|-
|-
|27
|27
| colspan="2" |E#+/Fd
| colspan="2" |E#+/Fd
|1290
|1320
|1294.0149
|1320.1838
|1303.4483
1303.8088
|''1305''
|1307.0886 1307.3684
|1309.2024
|1310.04
|1311.4286
|1313.86575
|1320(.1838)
|1326.4647
1326.5381
|1329.2308
|1332
|1333.11765
|1335.887
|1339.2
|1344.721
 
1346.301
|''1350''
|-
|-
|28
|28
| colspan="2" |F
| colspan="2" |F
|1337.7778
|1368.{{Overline|8}}
|1341.9414
|1369.0795
|1351.7241
1352.098
|''1353.3333''
|1355.4993 1355.7895
|1357.6914
|1358.56
|1360
|1362.52745
|1368.8889
1369.0795
|1375.593
1375.6691
|1378.4615
|1381.3333
|1383.5294
|1385.3643
|1388.8
|1394.526
1396.1644
|''1400''
|-
|-
|29
|29
| colspan="2" |F+/Gd
| colspan="2" |F+/Gd
|1385.5556
|1417.{{Overline|7}}
|1389.8988
|1417.9725
|1400(.3872)
|''1401.1667''
|1403.91 1404.2105
|1406.1803
|1407.08
|1408.5714
|1411.1891
|1417.7778
1417.9725
|1424.7214
1424.8001
|1427.6923
|1430.6667
|1432.9412
|1434.8416
|1438.4
|1444.33
 
1446.027
|''1450''
|-
|-
|30
|30
| colspan="2" |G
| colspan="2" |G
|1433.3333
|1466.{{Overline|6}}
|1437.79435
|1466.8709
|1448.2759
|}
1448.6764
|''1450''
|1452.3207


1452.6316
== Harmonics ==
|1454.6693
{{Harmonics in equal
|1455.6
| steps = 30
|1457.1429
| num = 7
|1459.8508
| denom = 3
|1466.6667
}}
1466.8709
{{Harmonics in equal
|1473.8497
| steps = 30
1473.9312
| num = 7
|1476.9231
| denom = 3
|1480
| start = 12
|1482.3529
| collapsed = 1
|1484.3189
}}
|1488
|1494.135
1495.8904
|''1500''
|}

Latest revision as of 07:47, 5 October 2024

This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 29ed7/3 30ed7/3 31ed7/3 →
Prime factorization 2 × 3 × 5
Step size 48.8957 ¢ 
Octave 25\30ed7/3 (1222.39 ¢) (→ 5\6ed7/3)
Twelfth 39\30ed7/3 (1906.93 ¢) (→ 13\10ed7/3)
Consistency limit 3
Distinct consistency limit 3

30 equal divisions of 7/3 (abbreviated 30ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 30 equal parts of about 48.9 ¢ each. Each step represents a frequency ratio of (7/3)1/30, or the 30th root of 7/3.

Intervals

Degrees Enneatonic ed11\9~ed7/3
1 G+/Jbd G+/Abd 48.8 48.8957
2 G#/Jb G#/Ab 97.7 97.7914
3 G#+/Jd G#+/Ad 146.6 146.6871
4 J A 195.5 195.5828
5 J+/Abd A+/Bbd 244.4 244.4785
6 J#/Ab A#/Bb 293.3 293.3742
7 J#+/Ad A#+/Bd 342.2 342.2699
8 A B 391.1 391.1656
9 A+/Bd B+/Cd 440 440.0613
10 B C 488.8 488.957
11 B+/Cbd C+/Qbd 537.7 537.8527
12 B#/Cb C#/Qb 586.6 586.7484
13 B#+/Cd C#+/Qd 635.5 635.6441
14 C Q 684.4 684.5398
15 C+/Qbd Q+/Dbd 733.3 733.43545
16 C#/Qb Q#/Db 782.2 782.33115
17 C#+/Qd Q#+/Dd 831.1 831.22685
18 Q D 880 880.1225
19 Q+/Dd D+/Sd 928.8 929.0182
20 D S 977.7 977.9139
21 D+ S+ 1026.6 1026.8096
Ebd
22 D# S# 1075.5 1075.7053
Eb
23 D#+ S#+ 1124.4 1124.601
Ed
24 E 1173.3 1173.4967
25 E+/Fbd 1222.2 1222.3924
26 E#/Fb 1271.1 1271.2881
27 E#+/Fd 1320 1320.1838
28 F 1368.8 1369.0795
29 F+/Gd 1417.7 1417.9725
30 G 1466.6 1466.8709

Harmonics

Approximation of harmonics in 30ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +22.4 +5.0 -4.1 +0.7 -21.5 +5.0 +18.3 +10.0 +23.1 +4.8 +0.9
Relative (%) +45.8 +10.2 -8.4 +1.5 -44.0 +10.2 +37.4 +20.4 +47.3 +9.9 +1.8
Steps
(reduced) 		25
(25) 		39
(9) 		49
(19) 		57
(27) 		63
(3) 		69
(9) 		74
(14) 		78
(18) 		82
(22) 		85
(25) 		88
(28)
Approximation of harmonics in 30ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +9.0 -21.5 +5.7 -8.2 -15.4 -16.5 -12.4 -3.4 +10.0 -21.7 -0.9
Relative (%) +18.4 -44.0 +11.7 -16.8 -31.5 -33.8 -25.3 -6.9 +20.4 -44.4 -1.7
Steps
(reduced) 		91
(1) 		93
(3) 		96
(6) 		98
(8) 		100
(10) 		102
(12) 		104
(14) 		106
(16) 		108
(18) 		109
(19) 		111
(21)
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