Xenharmonic Wiki

38edo: Difference between revisions

← Older edit
VisualWikitext
Contribution (talk | contribs)
3,348 edits
No edit summary
Overthink (talk | contribs)
autopatrolled
2,982 edits
→Theory: expand 38df paragraph
 
(74 intermediate revisions by 14 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|38}}
{{ED intro}}


==Theory==
== Theory ==
Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. While the halving of the step size lowers [[consistency]] and leaves it only mediocre in terms of overall [[Relative_errors_of_small_EDOs|relative error]], the fact that the 3rd & 5th harmonics are flat by almost exactly the same amount, while the 11th is double that means there are quite a few near perfect composite ratios, such as the the [[6/5]] it shares with 19edo, plus [[11/9]], [[15/11]] & [[25/22]], (and their inversions) while a single step nears [[55/54]]. This gives several interesting possibilities for unusual near-just chords such as 15:18:22:25:30. It [[tempers out]] the same [[5-limit]] commas as 19edo, 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 [[injera]] temperament, for which 38 is the [[optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175.  
Since 38 factors as {{nowrap|2 × 19}}, 38edo can be thought of as two parallel chains of [[19edo]]. It provides a possible correction to the [[11/1|11th harmonic]] of 19edo, which works well with 19edo's flat approximations of the [[3/1|3rd]] and [[5/1|5th]] harmonics, making it a decent [[2.3.5.11 subgroup|2.3.5.11-subgroup]] system. Compared to 19edo, the halving of the step size lowers [[consistency]], and leaves it only mediocre in terms of overall [[relative interval error|relative error]]. However, the fact that the 3rd and 5th harmonics are flat by almost exactly the same amount, while the 11th is close to double that, means there are quite a few near-perfect composite ratios, such as the the [[6/5]] it shares with 19edo, plus [[11/9]], [[15/11]], [[25/22]], and their [[octave complement]]s, while a single step nears [[55/54]]. The approximation to [[11/9]] in particular should be noted for forming a 10-strong [[consistent circle]]. This gives several interesting possibilities for unusual near-just chords such as 15:18:22:25:30.  


In [[Warts|38df]], every [[prime interval]] from 3 to 19 is characterized by a flat intonation. Furthermore, the mapping of all [[19-odd-limit]] intervals in 38df aligns with their closest approximations in 38edo, excepting for 7/4 and 13/8, along with their octave complements 8/7 and 16/13, which are by definition mapped to their secondary optimal steps within 38df.  
Using the [[patent val]], it [[tempering out|tempers out]] the same [[5-limit]] commas as 19edo, 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 [[injera]] temperament, for which 38 is the [[optimal patent val]] in the 7-limit. In the [[11-limit]], we can add [[121/120]] and [[176/175]], and in the [[13-limit]] we can add [[66/65]] and [[144/143]]. 38edo patently supports [[mohajira]] up to the 13-limit. While the [[7/1|7th]] and [[13/1|13th]] harmonics themselves are improved compared to 19edo, many other intervals involving these harmonics become less accurate, so whether 38edo actually corrects them is debatable.


Harmonic series in 38df (22 16 12 10 8 8 6 6 5 5 4 4 4 4 3 3 3 3): [[File:Harmonic_series_38df.mp3]] [[:File:Harmonic_series_38df.mp3|[File info]]]
Instead, the [[val]] {{val| 38 60 88 '''106''' 131 '''140''' 155 161 }} (38df in [[wart notation]]) can be used, where primes [[7/1|7]] and [[13/1|13]] use their second-best approximations, and are mapped the same as in 19edo. The [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] mapping of 19edo is preserved in 38df, while harmonics [[11/1|11]], [[17/1|17]], and [[19/1|19]] are mapped between steps of 19edo. In 38df, every [[odd harmonic]] from 3 to 19 is characterized by a flat intonation. Furthermore, the [[mapping]]s of all [[19-odd-limit]] intervals in 38df align with their closest approximations in 38edo, except for [[7/4]], [[13/8]], and their octave complements [[8/7]] and [[16/13]], which are by definition mapped to their second-closest steps within 38df. The 38df mapping thus creates a natural full [[19-limit]] extension to the 2.3.5.7.13-subgroup mapping of 19edo. It tempers out [[49/48]], [[65/64]], [[81/80]], [[225/224]], etc. as in 19edo, as well as [[121/120]], [[289/288]], [[324/323]], [[361/360]], and many more.


The harmonic series from 1 to 20 is approximated within 38df by the step sequence: {{nowrap| 38 22 16 12 10 8 8 6 6 5 5 4 4 4 4 3 3 3 3 }}
[[File:Harmonic_series_38df.mp3]] [[:File:Harmonic_series_38df.mp3|[Harmonic series 2-20 in 38df]]]
=== Prime harmonics ===
{{Harmonics in equal|38}}
{{Harmonics in equal|38}}


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! Step
! rowspan="3" | Step
! Cents
! rowspan="3" | Cents
!19-odd-limit ratios,
! colspan="3" | Approximated ratios
treated as 38df
! rowspan="3" colspan="3" | [[Ups and downs notation]]*<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vvd2)
! colspan="3" | [[Ups and Downs Notation]]*
|-
! rowspan="2" | Ratios of the <br>2.3.5.11.17.19 subgroup
! colspan="2" | Ratios of 7 and 13
|-
! Patent val
! 38df val
|-
|-
| 0
| 0
| 0.0000
| 0.0
|
| [[1/1]]
|
|  
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 29: Line 40:
|-
|-
| 1
| 1
| 31.5789
| 31.6
|
| [[55/54]], [[45/44]], ''[[33/32]]''
| [[64/63]], ''[[36/35]]''
| [[56/55]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 36: Line 49:
|-
|-
| 2
| 2
| 63.1579
| 63.2
|
| [[25/24]], [[34/33]]
| [[22/21]]
| [[28/27]], [[26/25]], [[27/26]]
| Aug 1sn, dim 2nd
| Aug 1sn, dim 2nd
| A1, d2
| A1, d2
Line 43: Line 58:
|-
|-
| 3
| 3
| 94.7368
| 94.7
|[[20/19]], [[19/18]], [[18/17]], [[17/16]]
| [[20/19]], [[19/18]], [[18/17]], [[17/16]]
| ''[[15/14]]'', [[21/20]]
|
| Upaug 1sn, downminor 2nd
| Upaug 1sn, downminor 2nd
| ^A1, vm2
| ^A1, vm2
Line 50: Line 67:
|-
|-
| 4
| 4
| 126.3157
| 126.3
|[[16/15]], [[15/14]], [[14/13]], [[13/12]]
| [[16/15]]
| [[14/13]]
| [[15/14]], [[14/13]], [[13/12]]
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 57: Line 76:
|-
|-
| 5
| 5
| 157.8947
| 157.9
|[[12/11]], [[11/10]]
| [[12/11]], [[11/10]]
| ''[[13/12]]'', [[35/32]]
|
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 64: Line 85:
|-
|-
| 6
| 6
| 189.4737
| 189.5
|[[10/9]], [[19/17]], [[9/8]]
| [[10/9]], [[19/17]], [[9/8]]
|
| [[28/25]]
| Major 2nd
| Major 2nd
| M2
| M2
Line 71: Line 94:
|-
|-
| 7
| 7
| 221.0526
| 221.1
|[[17/15]]
| [[25/22]], [[17/15]]
| [[8/7]], ''[[15/13]]''
|
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 78: Line 103:
|-
|-
| 8
| 8
| 252.6316
| 252.6
|[[8/7]], [[15/13]], [[22/19]], [[7/6]]
| [[22/19]]
|
| ''[[8/7]]'', [[15/13]], [[7/6]]
| Aug 2nd, Dim 3rd
| Aug 2nd, Dim 3rd
| A2, d3
| A2, d3
Line 85: Line 112:
|-
|-
| 9
| 9
| 284.2105
| 284.2
|[[20/17]], [[13/11]], [[19/16]]
| [[20/17]], [[19/16]]
| ''[[7/6]]''
| [[13/11]]
| Downminor 3rd
| Downminor 3rd
| vm3
| vm3
Line 92: Line 121:
|-
|-
| 10
| 10
| 315.7895
| 315.8
|[[6/5]]
| [[6/5]]
| ''[[13/11]]'', ''[[17/14]]''
|
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 99: Line 130:
|-
|-
| 11
| 11
| 347.3684
| 347.4
|[[17/14]], [[11/9]]
| [[11/9]]
| [[16/13]]
| [[17/14]]
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 106: Line 139:
|-
|-
| 12
| 12
| 378.9474
| 378.9
|[[16/13]], [[5/4]]
| [[5/4]]
|
| ''[[16/13]]''
| Major 3rd
| Major 3rd
| M3
| M3
Line 113: Line 148:
|-
|-
| 13
| 13
| 410.5263
| 410.5
|[[24/19]], [[19/15]], [[14/11]]
| [[24/19]], [[19/15]]
| ''[[9/7]]''
| [[14/11]]
| Upmajor 3rd, Downdim 4th
| Upmajor 3rd, Downdim 4th
| ^M3, vd4
| ^M3, vd4
Line 120: Line 157:
|-
|-
| 14
| 14
| 442.1053
| 442.1
|[[9/7]], [[22/17]], [[13/10]]
| [[22/17]], [[32/25]]
| ''[[14/11]]'', ''[[17/13]]''
| [[9/7]], [[13/10]], ''[[21/16]]''
| Aug 3rd, dim 4th
| Aug 3rd, dim 4th
| A3, d4
| A3, d4
Line 127: Line 166:
|-
|-
| 15
| 15
| 473.6843
| 473.7
|[[17/13]]
| [[25/19]]
| [[21/16]], ''[[13/10]]''
| [[17/13]]
| Down 4th
| Down 4th
| v4
| v4
Line 134: Line 175:
|-
|-
| 16
| 16
| 505.2632
| 505.3
|[[4/3]]
| [[4/3]]
| ''[[19/14]]''
|
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 141: Line 184:
|-
|-
| 17
| 17
| 536.8421
| 536.8
|[[19/14]], [[15/11]], [[26/19]], [[11/8]]
| [[15/11]], [[11/8]], [[34/25]]
| ''[[18/13]]''
| [[19/14]], [[26/19]]
| Up 4th
| Up 4th
| ^4
| ^4
Line 148: Line 193:
|-
|-
| 18
| 18
| 568.4211
| 568.4
|[[18/13]], [[7/5]]
| [[25/18]]
| ''[[26/19]]''
| [[18/13]], [[7/5]]
| Aug 4th
| Aug 4th
| A4
| A4
Line 155: Line 202:
|-
|-
| 19
| 19
| 600.0000
| 600.0
|[[24/17]], [[17/12]]
| [[24/17]], [[17/12]]
| [[7/5]], [[10/7]]
|
| Upaug 4th, downdim 5th
| Upaug 4th, downdim 5th
| ^A4, vd5
| ^A4, vd5
Line 162: Line 211:
|-
|-
| 20
| 20
| 631.5789
| 631.6
|[[10/7]], [[13/9]]
| [[36/25]]
| ''[[19/13]]''
| [[10/7]], [[13/9]]
| Dim 5th
| Dim 5th
| d5
| d5
Line 169: Line 220:
|-
|-
| 21
| 21
| 663.1579
| 663.2
|[[16/11]], [[19/13]], [[22/15]], [[28/19]]
| [[22/15]], [[16/11]], [[25/17]]
| ''[[13/9]]''
| [[19/13]], [[28/19]]
| Down 5th
| Down 5th
| v5
| v5
Line 176: Line 229:
|-
|-
| 22
| 22
| 694.7368
| 694.7
|[[3/2]]
| [[3/2]]
| ''[[28/19]]''
|
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 183: Line 238:
|-
|-
| 23
| 23
| 726.3157
| 726.3
|[[26/17]]
| [[38/25]]
| ''[[20/13]]''
| [[26/17]]
| Up 5th
| Up 5th
| ^5
| ^5
Line 190: Line 247:
|-
|-
| 24
| 24
| 757.8947
| 757.9
|[[20/13]], [[17/11]], [[14/9]]
| [[17/11]], [[25/16]]
| ''[[26/17]]'', ''[[11/7]]''
| [[14/9]], [[20/13]], ''[[32/21]]''
| Aug 5th, dim 6th
| Aug 5th, dim 6th
| A5, d6
| A5, d6
Line 197: Line 256:
|-
|-
| 25
| 25
| 789.4737
| 789.5
|[[11/7]], [[30/19]], [[19/12]]
| [[30/19]], [[19/12]]
| ''[[14/9]]''
| [[11/7]]
| Upaug 5th, downminor 6th
| Upaug 5th, downminor 6th
| ^A5, vm6
| ^A5, vm6
Line 204: Line 265:
|-
|-
| 26
| 26
| 821.0526
| 821.1
|[[8/5]], [[13/8]]
| [[8/5]]
|
| ''[[13/8]]''
| Minor 6th
| Minor 6th
| m6
| m6
Line 211: Line 274:
|-
|-
| 27
| 27
| 852.6316
| 852.6
|[[18/11]], [[28/17]]
| [[18/11]]
| [[13/8]]
| [[28/17]]
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 218: Line 283:
|-
|-
| 28
| 28
| 884.2105
| 884.2
|[[5/3]]
| [[5/3]]
| ''[[28/17]]'', ''[[22/13]]''
|
| Major 6th
| Major 6th
| M6
| M6
Line 225: Line 292:
|-
|-
| 29
| 29
| 915.7895
| 915.8
|[[32/19]], [[22/13]], [[17/10]]
| [[32/19]], [[17/10]]
|
| [[22/13]]
| Upmajor 6th
| Upmajor 6th
| ^M6
| ^M6
Line 232: Line 301:
|-
|-
| 30
| 30
| 947.3684
| 947.4
|[[12/7]], [[19/11]], [[26/15]], [[7/4]]
| [[19/11]]
|
| [[12/7]], [[26/15]], ''[[7/4]]''
| Aug 6th, dim 7th
| Aug 6th, dim 7th
| A6, d7
| A6, d7
Line 239: Line 310:
|-
|-
| 31
| 31
| 978.9474
| 978.9
|[[30/17]]
| [[44/25]], [[30/17]]
| ''[[26/15]]'', [[7/4]]
|
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 246: Line 319:
|-
|-
| 32
| 32
| 1010.5263
| 1010.5
|[[16/9]], [[34/19]], [[9/5]]
| [[16/9]], [[34/19]], [[9/5]]
|
| [[25/14]]
| Minor 7th
| Minor 7th
| m7
| m7
Line 253: Line 328:
|-
|-
| 33
| 33
| 1042.1053
| 1042.1
|[[20/11]], [[11/6]]
| [[20/11]], [[11/6]]
| ''[[24/13]]'', [[64/35]]
|
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 260: Line 337:
|-
|-
| 34
| 34
| 1073.6843
| 1073.7
|[[24/13]], [[13/7]], [[28/15]], [[15/8]]
| [[15/8]]
| [[13/7]]
| [[24/13]], [[13/7]], [[28/15]]
| Major 7th
| Major 7th
| M7
| M7
Line 267: Line 346:
|-
|-
| 35
| 35
| 1105.2632
| 1105.3
|[[32/17]], [[17/9]], [[36/19]], [[19/10]]
| [[32/17]], [[17/9]], [[36/19]], [[19/10]]
| ''[[28/15]]''
|
| Upmajor 7th, Downdim 8ve
| Upmajor 7th, Downdim 8ve
| ^M7, vd8
| ^M7, vd8
Line 274: Line 355:
|-
|-
| 36
| 36
| 1136.8421
| 1136.8
|
| [[33/17]], [[48/25]]
|
| [[27/14]], [[25/13]], [[52/27]]
| Aug 7th, dim 8ve
| Aug 7th, dim 8ve
| A7, d8
| A7, d8
Line 281: Line 364:
|-
|-
| 37
| 37
| 1168.4211
| 1168.4
|
| ''[[64/33]]'', [[88/45]], [[108/55]]
| [[63/32]]
| [[55/28]]
| Down 8ve
| Down 8ve
| v8
| v8
Line 288: Line 373:
|-
|-
| 38
| 38
| 1200.0000
| 1200.0
|
| [[2/1]]
|
|  
| Perfect 8ve
| Perfect 8ve
| P8
| P8
| D
| D
|}
|}
<nowiki>*</nowiki> Ups and downs may be substituted with semi-sharps and semi-flats, respectively
<nowiki/>* Ups and downs may be substituted with semi-sharps and semi-flats, respectively
 
== Notation ==
=== Ups and downs notation ===
Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp.
{{Ups and downs sharpness}}
 
=== Quarter-tone notation ===
Since a sharp raises by two steps, [[24edo#Notation|quarter-tone accidentals]] can also be used:
{{sharpness-sharp2}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[17edo#Sagittal notation|17]], [[24edo#Sagittal notation|24]], and [[31edo#Sagittal notation|31]], is a subset of the notation for [[76edo#Sagittal notation|76-EDO]], and is a superset of the notation for [[19edo#Sagittal notation|19-EDO]].
 
==== Evo flavor ====
<imagemap>
File:38-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 130 106 [[33/32]]
default [[File:38-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:38-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 703 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 130 106 [[33/32]]
default [[File:38-EDO_Revo_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:38-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 631 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 130 106 [[33/32]]
default [[File:38-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein-Zimmerman notation.
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals}}
{{Q-odd-limit intervals|37.9|apx=val|header=none|tag=none|title=15-odd-limit intervals by 38df val mapping}}
 
== Rank-2 temperaments ==
{| class="wikitable"
|+ [[Rank-2 temperament]]s in 38edo
|-
! Temperament !! Generator !! Periods per octave
|-
| [[Opossum]] || 5\38 || 1
|-
| [[Hemisensi]] || 7\38 || 1
|-
| [[Delorean]] / [[subkla]] || 9\38 || 1
|-
| [[Migration]] / [[mohajira]] / [[nethertone]] / [[ptolemy]] / [[subklei]] || 11\38 || 1
|-
| [[Hocus]] || 13\38 || 1
|-
| [[Buzzard]] || 15\38 || 1
|-
| [[Maquila]] / [[wilsec]] || 17\38 || 1
|-
| [[Bimeantone]] / [[injera]] || 3\38 || 2
|-
| [[Bison]] / [[hemikleismic]] || 5\38 || 2
|-
| [[Astrology]] / [[divination]] / [[horoscope]] || 7\38 || 2
|-
| [[Decimal]] || 8\38 || 2
|}
 
== Octave stretch or compression ==
38edo's approximation of [[JI]] can be improved by slightly [[octave stretch|stretching the octave]], as in [[ed5|88ed5]], [[zpi|166zpi]] or [[60edt]].
 
== Scales ==
; [[MOS scale]]s
* Astrology[22]: 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 2
* Buzzard[8]: 7 1 7 7 1 7 1 7
* Buzzard[13] 1 6 1 6 1 1 6 1 1 6 1 6 1
* Buzzard[18]: 1 5 1 1 1 5 1 1 1 5 1 1 5 1 1 1 5 1
* Buzzard[23]: 1 1 4 1 1 1 4 1 1 1 1 4 1 1 1 1 4 1 1 1 4 1 1
* Decimal[10]: 3 5 3 5 3 3 5 3 5 3
* Decimal[14]: 3 2 3 3 3 2 3 3 2 3 3 3 2 3
* Decimal[24]: 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2
* Hocus[23]: 1 1 1 6 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 6 1 1 1
* Injera[6]: 3 13 3 3 13 3
* Injera[8]: 3 3 10 3 3 3 10 3
* Injera[10]: 3 3 7 3 3 3 3 7 3 3
* Injera[12]: 3 3 3 4 3 3 3 3 3 4 3 3
* Injera[14]: 3 3 3 1 3 3 3 3 3 3 1 3 3 3
* Injera[26]: 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1
* Maquila[20]: 1 3 1 3 1 3 1 3 1 1 3 1 3 1 3 1 3 1 3 1
* Mohajira[7] (''a.k.a. quasi-[[equiheptatonic]]''): 5 6 5 6 5 6 5
* Mohajira[10]: 5 1 5 5 1 5 5 5 1 5
* Mohajira[17]: 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1
* Mohajira[24]: 1 3 1 1 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1 1 3 1
* Subkla[13]: 2 5 2 2 5 2 2 2 5 2 2 5 2
* Subkla[17]: 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2
* Subkla[21]: 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2
 
; MOS subsets
* ''of injera[12]''
** Quasi-major: 6 7 3 6 6 7 3
** Quasi-minor: 6 3 7 6 3 7 6
 
; [[MODMOS|MODMOS scales]]
{{Idiosyncratic terms}}
* ''of bison[22]''
** Tame bison: 3 1 1 1 1 3 3 1 1 1 3 3 1 1 1 3 3 1 1 1 1 3
 
* ''of hemisensi[11]''
** Hemisettled11: 3 3 3 4 3 6 3 3 3 4 3
 
* ''of hemisensi[16]''
** Hemisettled16: 5 1 3 3 1 3 1 1 3 1 5 1 3 3 1 3
 
* ''of opossum[23]''
** Tame possum: 3 3 2 2 2 3 2 2 2 3 2 2 2 3 3
 
; Others
{{Idiosyncratic terms}}
* [[Antipental blues]]: 9 7 2 4 9 7
* Ninteenplus: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2
* Quasi-[[equipentatonic]]: 8 8 6 8 8
* [[Well temperament|Well-tempered]] 19-in-38: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 2 2 2


== Instruments ==
== Instruments ==
*[[Lumatone mapping for 38edo]]
* [[Lumatone mapping for 38edo]]
*[[Skip fretting system 38 2 11]]
* [[Skip fretting system 38 2 11]]


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=Cw1Cz1ojoSw Canon at the Semitone on The Mother's Malison Theme for Cor Anglais and Violin] by [[Claudi Meneghin]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/rewy-32BfRs ''Spirit of the Night - Secret of Mana (microtonal cover in 38edo)''] (2025)
* [https://www.youtube.com/shorts/QcFEW45uxHY ''38edo improv''] (2025)
* ''waltz in 38edo'' (2026)
** [https://www.youtube.com/shorts/Gdx4hk7FKU0 <nowiki>[short]</nowiki>] (demonstrates Lumatone mapping)
** [https://www.youtube.com/watch?v=amukQrZuseY <nowiki>[full version]</nowiki>]
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=Cw1Cz1ojoSw Canon at the Semitone on The Mother's Malison Theme for Cor Anglais and Violin] (2022)


[[Category:38edo| ]]  <!-- main article -->
[[Category:38edo| ]]  <!-- Main article -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Listen]]
[[Category:Listen]]
[[Category:Todo:add rank 2 temperaments table]]
Retrieved from "https://en.xen.wiki/w/38edo"