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=<span style="background-color: #e5e5e5; color: #008693; font-family: 'Times New Roman',Times,serif; font-size: 113%;">38 tone equal temperament</span>=
'''38edo''' divides the octave into 38 equal parts of 31.579 [[cent|cents]]. Since 38 = 2*19, it can be thought of as two parallel [[19edo|19edos]]. It [[tempering_out|tempers out]] the same [[5-limit]] commas as [[19edo|19]], namely 81/80, 3125/3072 and 15625/15552. In the [[7-limit]], we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone_family|injera temperament]], for which 38 is the [[Optimal_patent_val|optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175.


'''38edo''' divides the octave into 38 equal parts of 31.579 [[cent|cent]]s. Since 38 = 2*19, it can be thought of as two parallel [[19edo|19edo]]s. It [[tempering_out|tempers out]] the same [[5-limit|5-limit]] commas as [[19edo|19]], namely 81/80, 3125/3072 and 15625/15552. In the [[7-limit|7-limit]], we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone_family|injera temperament]], for which 38 is the [[Optimal_patent_val|optimal patent val]]. In the [[11-limit|11-limit]], we can add 121/120 and 176/175.
== Intervals ==


===38-EDO Intervals:===
{| class="wikitable center-1 right-2"
 
{| class="wikitable"
|-
|-
| '''Step'''
! Step
|'''Cents'''
! Cents
|-
|-
| 0
| 0
|0.0000
| 0.0000
|-
|-
| | 1
| 1
| | 31.57895
| 31.5789
|-
|-
| | 2
| 2
| |63.1579
| 63.1579
|-
|-
| | 3
| 3
| | 94.7368
| 94.7368
|-
|-
| | 4
| 4
| |126.3157
| 126.3157
|-
|-
| | 5
| 5
| | 157.8947
| 157.8947
|-
|-
| | 6
| 6
| |189.4737
| 189.4737
|-
|-
| | 7
| 7
| | 221.0526
| 221.0526
|-
|-
| | 8
| 8
| |252.6316
| 252.6316
|-
|-
| | 9
| 9
| | 284.2105
| 284.2105
|-
|-
| | 10
| 10
| |315.7895
| 315.7895
|-
|-
| | 11
| 11
| | 347.3684
| 347.3684
|-
|-
| | 12
| 12
| |378.9474
| 378.9474
|-
|-
| | 13
| 13
| | 410.5263
| 410.5263
|-
|-
| | 14
| 14
| |442.1053
| 442.1053
|-
|-
| | 15
| 15
| | 473.6843
| 473.6843
|-
|-
| | 16
| 16
| |505.2632
| 505.2632
|-
|-
| | 17
| 17
| | 536.8421
| 536.8421
|-
|-
| | 18
| 18
| |568.42105
| 568.4211
|-
|-
| | 19
| 19
| | 600
| 600.0000
|-
|-
| | 20
| 20
| |631.57895
| 631.5789
|-
|-
| | 21
| 21
| | 663.1579
| 663.1579
|-
|-
| | 22
| 22
| |694.7368
| 694.7368
|-
|-
| | 23
| 23
| | 726.3157
| 726.3157
|-
|-
| | 24
| 24
| |757.8947
| 757.8947
|-
|-
| | 25
| 25
| | 789.4737
| 789.4737
|-
|-
| | 26
| 26
| |821.0526
| 821.0526
|-
|-
| | 27
| 27
| | 852.6316
| 852.6316
|-
|-
| | 28
| 28
| |884.2105
| 884.2105
|-
|-
| | 29
| 29
| | 915.7895
| 915.7895
|-
|-
| | 30
| 30
| |947.3684
| 947.3684
|-
|-
| | 31
| 31
| | 978.9474
| 978.9474
|-
|-
| | 32
| 32
| |1010.5263
| 1010.5263
|-
|-
| | 33
| 33
| | 1042.1053
| 1042.1053
|-
|-
| | 34
| 34
| |1073.6843
| 1073.6843
|-
|-
| | 35
| 35
| | 1105.2632
| 1105.2632
|-
|-
| | 36
| 36
| |1136.8421
| 1136.8421
|-
|-
| | 37
| 37
| | 1168.42105
| 1168.4211
|-
|-
|38
| 38
|1200
| 1200.0000
|}
|}
[[Category:edo]]
[[Category:edo]]
[[Category:theory]]
[[Category:theory]]
Retrieved from "https://en.xen.wiki/w/38edo"