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{{ED intro}}
{{ED intro}}


While 38ed7/3 fails to accurately represent low primes, it provides great approximations of the 13th, 17th, 19th, and a multitude of higher prime harmonics, and also handles the interval of [[5/3]] well. But 38ed7/3 should, most of all, be noted for the exceptional quality of its approximation to [[11/9]], which is a mere 0.0088 cents off from just. Its natural subgroup in the [[19-limit]] is 7/3.5/3.11/9.13.17.19, but this can extend to include higher primes, especially 29 and 31.
== Theory ==
While 38ed7/3 fails to accurately represent low [[prime interval|prime harmonics]], it provides great approximations of the [[13/1|13th]], [[17/1|17th]], [[19/1|19th]], and a multitude of higher primes, and also handles the interval of [[5/3]] well. But 38ed7/3 should, most of all, be noted for the exceptional quality of its approximation to [[11/9]], which is a mere 0.0088 cents off from just. Its natural subgroup in the [[19-limit]] is 5/3.7/3.11/9.13.17.19, but this can extend to include higher primes, especially [[29/1|29]], [[31/1|31]], and [[37/1|37]].


{{Harmonics in equal|38|7|3|prec=2|columns=15|intervals=prime}}
38ed7/3 possesses a shimmering octave at 31 steps in, therefore making this a potential octave-compressed version of [[31edo]], one that sacrifices its notable accuracy in the [[7-limit]] (though a number of 7-limit intervals are still portrayed passably due to the common flat tendency of harmonics 2, 3, 5, and 7) in favor of a huge number of high primes.
{{Harmonics in equal|38|7|3|prec=2|columns=15|intervals=odd}}
 
=== Harmonics ===
{{Harmonics in equal|38|7|3|columns=11}}
{{Harmonics in equal|38|7|3|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 38ed7/3 (continued)}}


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2"
!Degrees
! #
! colspan="2" |Enneatonic
! Cents
! colspan="2" |ed11\9~ed7/3
|-
| rowspan="2" |1
| colspan="2" |G^
| rowspan="2" |38.5965
| rowspan="2" |38.6019
|-
|Jbv
|''Abv''
|-
|2
|Jb
|''Ab''
|77.193
|77.2037
|-
| rowspan="2" |3
|Jb^
|''Ab^''
| rowspan="2" |115.7895
| rowspan="2" |115.8056
|-
| colspan="2" |G#v
|-
|4
| colspan="2" |G#
|154.386
|154.4075
|-
|-
| rowspan="2" |5
| 1
| colspan="2" |G#^
| 38.6
| rowspan="2" |192.98245
| rowspan="2" |193.0093
|-
|-
|Jv
| 2
|''Av''
| 77.2
|-
|-
|6
| 3
|J
| 115.8
|''A''
|231.57895
|231.6112
|-
|-
|7
| 4
|J^/Av
| 154.4
|''A^/Bv''
|270.1754
|270.2131
|-
|-
|8
| 5
|A
| 193.0
|''B''
|308.7719
|308.8149
|-
|-
|9
| 6
|A^/Bbv
| 231.6
|B^/Cbv
|347.3684
|347.4168
|-
|-
|10
| 7
|Bb
| 270.2
|''Cb''
|385.9649
|386.0187
|-
|-
|11
| 8
|Bb^/A#v
| 308.8
|''Cb^/B#''v
|424.5614
|424.6205
|-
|-
|12
| 9
|A#
| 347.4
|''B#''
|463.1579
|463.2224
|-
|-
|13
| 10
|A#^/Bv
| 386.0
|''B#^/Cv''
|501.7544
|502.6667
|-
|-
|14
| 11
|B
| 424.6
|''C''
|540.3509
|540.4261
|-
|-
|15
| 12
|B^/Cv
| 463.2
|''C^/Qv''
|578.9474
|579.028
|-
|-
|16
| 13
|C
| 502.7
|''Q''
|617.5439
|617.6299
|-
|-
|17
| 14
|C^/Qbv
| 540.4
|''Q^/Dbv''
|656.14035
|656.2317
|-
|-
|18
| 15
|Qb
| 579.0
|''Db''
|694.7368
|694.8336
|-
|-
|19
| 16
|Qb^/C#v
| 617.6
|''Db^/Q#v''
|733.{{Overline|3}}
|733.43545
|-
|-
|20
| 17
|C#
| 656.2
|''Q#''
|771.9298
|772.0373
|-
|-
|21
| 18
|C#^/Qv
| 694.8
|''Q#/Dv''
|810.5263
|810.6392
|-
|-
|22
| 19
|Q
| 733.4
|''D''
|849.1228
|849.24105
|-
|-
|23
| 20
|Q^/Dv
| 772.0
|''D^/Sv''
|887.7193
|887.8429
|-
|-
|24
| 21
|D
| 810.6
|''S''
|926.3158
|926.4448
|-
|-
| rowspan="2" |25
| 22
|D^
| 849.2
|''S^''
| rowspan="2" |964.9123
| rowspan="2" |965.04665
|-
|-
| colspan="2" |Ebv
| 23
| 887.8
|-
|-
|26
| 24
| colspan="2" |Eb
| 926.4
|1003.5088
|1003.6485
|-
|-
| rowspan="2" |27
| 25
| colspan="2" |Eb^
| 965.0
| rowspan="2" |1042.1053
| rowspan="2" |1042.2504
|-
|-
|D#v
| 26
|''S#v''
| 1003.6
|-
|-
|28
| 27
|D#
| 1042.3
|''S#''
|1080.70175
|1080.85225
|-
|-
| rowspan="2" |29
| 28
|D#^
| 1080.9
|''S#^''
| rowspan="2" |1119.29825
| rowspan="2" |1119.4541
|-
|-
| colspan="2" |Ev
| 29
| 1119.5
|-
|-
|30
| 30
| colspan="2" |E
| 1158.1
|1157.8947
|1158.0559
|-
|-
|31
| 31
| colspan="2" |E^/Fbv
| 1196.7
|1196.4912
|1196.6578
|-
|-
|32
| 32
| colspan="2" |Fb
| 1235.3
|1235.0877
|1235.2567
|-
|-
|33
| 33
| colspan="2" |Fb^/E#v
| 1273.9
|1273.68425
|1273.8616
|-
|-
|34
| 34
| colspan="2" |E#
| 1312.5
|1312.2807
|1312.4634
|-
|-
|35
| 35
| colspan="2" |E#^/Fv
| 1351.1
|1350.8772
|1351.0654
|-
|-
|36
| 36
| colspan="2" |F
| 1389.7
|1389.4737
|1389.6672
|-
|-
|37
| 37
| colspan="2" |F^/Gv
| 1428.3
|1428.0702
|1428.269
|-
|-
|38
| 38
| colspan="2" |G
| 1466.9
|1466.{{Overline|6}}
|1466.8709
|}
|}
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