Xenharmonic Wiki

19edo: Difference between revisions

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Added errors to each approximated JI interval; moved 19edo notation into separate category. Spaced out 19edo intervals table for a better look.
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== Intervals ==
== Intervals ==
{| class="wikitable right-1 right-2 center-5 center-7 center-8"
{| class="wikitable right-1 right-2 center-5 center-7 center-8"
![[Degree]]
! [[Degree]]
![[Cent|Cents]]
! [[Cent]]s
![[Interval region|Interval Region]]
! [[Interval region|Interval Region]]
!Approximated [[Just intonation|JI]] Intervals* (error in [[¢]])
! Approximated [[Just intonation|JI]] Intervals* (error in [[¢]])
![[Solfege]]
! [[Solfege]]
!Dodecatonic Notation
! Dodecatonic Notation
|-
|-
|0
| 0
|0.00
| 0.00
 
| Unison (prime)
|Unison (prime)
| [[1/1]] (just)
 
| Do
|[[1/1]] (just)
| P1
|Do
|P1
|-
|-
|1
| 1
|63.16
| 63.16
|Augmented unison
| Augmented unison
 
| [[25/24]] (-7.515)<br>[[28/27]] (+0.197)<br>[[26/25]] (-4.742)<br>[[648/625]] (+0.593)
|[[25/24]] (-7.515)  
| Di/Ro
[[28/27]] (+0.197)  
| A1, m2
 
[[26/25]] (-4.742)
 
[[648/625]] (+0.593)
|Di/Ro
|A1, m2
|-
|-
|2
| 2
|126.32
| 126.32
|Minor second
| Minor second
 
| [[15/14]] (+6.873)<br>[[16/15]] (+14.584)<br>[[13/12]] (-12.257)<br>[[14/13]] (-1.982)
|[[15/14]] (+6.873)
| Ra
[[16/15]] (+14.584)  
| M2, m3
 
[[13/12]] (-12.257)
 
[[14/13]] (-1.982)
|Ra
|M2, m3
|-
|-
|3
| 3
|189.47
| 189.47
|Major second
| Major second
 
| [[9/8]] (-14.436)<br>[[10/9]] (+7.070)<br>[[125/112]] (-0.641)
|[[9/8]] (-14.436)
[[10/9]] (+7.070)
 
[[125/112]] (-0.641)
| Re
| Re
|M3
| M3
|-
|-
|4
| 4
|252.63
| 252.63
|Diminished third
| Diminished third
 
| [[7/6]] (-14.239)<br>[[8/7]] (+21.457)<br>[[15/13]] (+4.891)
|[[7/6]] (-14.239)
[[8/7]] (+21.457)
 
[[15/13]] (+4.891)
| Ri/Ma
| Ri/Ma
|m4, A3
| m4, A3
|-
|-
|5
| 5
|315.79
| 315.79
 
| Minor third
| Minor third
 
| [[6/5]] (+0.148)
|[[6/5]] (+0.148)
| Me
|Me
| M4, m5
|M4, m5
|-
|-
|6
| 6
|378.95
| 378.95
|Major third
| Major third
 
| [[5/4]] (-7.366)<br>[[16/13]] (+19.475)<br>[[56/45]] (+0.345)
|[[5/4]] (-7.366)  
| Mi
[[16/13]] (+19.475)  
| M5
 
[[56/45]] (+0.345)
|Mi
|M5
|-
|-
| 7
| 7
|442.11
| 442.11
|Augmented third
| Augmented third
 
| [[32/25]] (+14.733)<br>[[9/7]] (+7.021)<br>[[13/10]] (-12.109)
|[[32/25]] (+14.733)  
| Mo/Fe
[[9/7]] (+7.021)  
| A5, d6
 
[[13/10]] (-12.109)
|Mo/Fe
|A5, d6
|-
|-
|8
| 8
| 505.26
| 505.26
 
| Perfect fourth
|Perfect fourth
| [[4/3]] (+7.218)<br>[[75/56]] (-0.493)
 
| Fa
|[[4/3]] (+7.218)
[[75/56]] (-0.493)
|Fa
| P6
| P6
|-
|-
|9
| 9
|568.42
| 568.42
|Augmented fourth
| Augmented fourth<br>(Small [[tritone]])
 
| [[25/18]] (-0.296)<br>[[7/5]] (-14.091)<br>[[18/13]] (+5.039)<br>[[11/8]] (+17.103)
(Small [[tritone]])
| Fi
 
| A6, m7
|[[25/18]] (-0.296)  
[[7/5]] (-14.091)
 
[[18/13]] (+5.039)
 
[[11/8]] (+17.103)
|Fi
|A6, m7
|-
|-
|10
| 10
|631.58
| 631.58
|Diminished fifth
| Diminished fifth<br>(Large [[tritone]])
 
| [[36/25]] (+0.296)<br>[[10/7]] (+14.091)<br>[[13/9]] (-5.039)<br>[[16/11]] (-17.103)
(Large [[tritone]])
| Se
 
| M7, d8
|[[36/25]] (+0.296)
[[10/7]] (+14.091)
 
[[13/9]] (-5.039)
 
[[16/11]] (-17.103)
|Se
|M7, d8
|-
|-
|11
| 11
|694.74
| 694.74
 
| Perfect fifth
|Perfect fifth
| [[3/2]] (-7.218)<br>[[112/75]] (+0.493)
 
| So
|[[3/2]] (-7.218)
| P8
[[112/75]] (+0.493)
|So
|P8
|-
|-
|12
| 12
|757.89
| 757.89
|Augmented fifth
| Augmented fifth
 
| [[25/16]] (-14.733)<br>[[14/9]] (-7.021)<br>[[20/13]] (+12.109)
|[[25/16]] (-14.733)
[[14/9]] (-7.021)
 
[[20/13]] (+12.109)
| Si/Lo
| Si/Lo
|A8, m9
| A8, m9
|-
|-
|13
| 13
| 821.05
| 821.05
| Minor sixth
| Minor sixth
 
| [[8/5]] (+7.366)<br>[[13/8]] (-19.475)<br>[[45/28]] (-0.345)
|[[8/5]] (+7.366)
| Le
[[13/8]] (-19.475)
| M9, m10
 
[[45/28]] (-0.345)
|Le
|M9, m10
|-
|-
| 14
| 14
| 884.21
| 884.21
 
| Major sixth
|Major sixth
| [[5/3]] (-0.148)
 
| La
|[[5/3]] (-0.148)
| M10
|La
|M10
|-
|-
|15
| 15
|947.37
| 947.37
|Diminished seventh
| Diminished seventh
 
| [[7/4]] (-21.457)<br>[[12/7]] (+14.239)<br>[[26/15]] (-4.891)
|[[7/4]] (-21.457)
| Li/Ta
[[12/7]] (+14.239)
| m11, A10
 
[[26/15]] (-4.891)
|Li/Ta
|m11, A10
|-
|-
|16
| 16
|1010.53
| 1010.53
|Minor seventh
| Minor seventh
 
| [[9/5]] (-7.070)<br>[[16/9]] (+14.436)<br>[[224/125]] (+0.641)
|[[9/5]] (-7.070)
| Te
[[16/9]] (+14.436)
| M11, m12
 
[[224/125]] (+0.641)
|Te
|M11, m12
|-
|-
|17
| 17
|1073.68
| 1073.68
|Major seventh
| Major seventh
 
| [[15/8]] (-14.584)<br>[[13/7]] (+1.982)<br>[[28/15]] (-6.873)<br>[[24/13]] (+12.257)
|[[15/8]] (-14.584)
| Ti
[[13/7]] (+1.982)
| M12
 
[[28/15]] (-6.873)
 
[[24/13]] (+12.257)
|Ti
|M12
|-
|-
|18
| 18
|1136.84
| 1136.84
| Augmented seventh
| Augmented seventh
 
| [[48/25]] (+7.515)<br>[[27/14]] (-0.197)<br>[[25/13]] (+4.742)<br>[[625/324]] (-0.593)
|[[48/25]] (+7.515)
[[27/14]] (-0.197)
 
[[25/13]] (+4.742)
 
[[625/324]] (-0.593)
| To/Da
| To/Da
|A12, d13
| A12, d13
|-
|-
|19
| 19
| 1200.00
| 1200.00
 
| Octave
|Octave
| [[2/1]] (just)
 
|[[2/1]] (just)
| Do
| Do
|P13
| P13
|}
|}
<nowiki>*</nowiki> based on treating 19edo as a 2.3.5.7.13 subgroup temperament; other approaches are possible.
<nowiki>*</nowiki> based on treating 19edo as a 2.3.5.7.13 subgroup temperament; other approaches are possible.


===Interval quality and chord names in color notation===
=== Interval quality and chord names in color notation ===
Using [[color notation]], qualities can be loosely associated with colors:
Using [[color notation]], qualities can be loosely associated with colors:


{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Quality
! Quality
![[Color name]]
! [[Color name|Color Name]]
!Monzo Format
! Monzo Format
!Examples
! Examples
|-
|-
|diminished
| diminished
|zo
| zo
|(a, b, 0, 1)
| (a, b, 0, 1)
|7/6, 7/4
| 7/6, 7/4
|-
|-
| rowspan="2" |minor
| rowspan="2" | minor
|fourthward wa
| fourthward wa
|(a, b), b &lt; -1
| (a, b), b &lt; -1
|32/27, 16/9
| 32/27, 16/9
|-
|-
|gu
| gu
|(a, b, -1)
| (a, b, -1)
|6/5, 9/5
| 6/5, 9/5
|-
|-
| rowspan="2" |major
| rowspan="2" | major
|yo
| yo
|(a, b, 1)
| (a, b, 1)
|5/4, 5/3
| 5/4, 5/3
|-
|-
|fifthward wa
| fifthward wa
|(a, b), b &gt; 1
| (a, b), b &gt; 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| augmented
| augmented
|ru
| ru
|(a, b, 0, -1)
| (a, b, 0, -1)
|9/7, 12/7
| 9/7, 12/7
|}
|}


Line 322: Line 236:


{| class="wikitable center-1 center-2 center-3 center-4"
{| class="wikitable center-1 center-2 center-3 center-4"
![[Kite's color notation|Color of the 3rd]]
! [[Kite's color notation|Color of the 3rd]]
! JI Chord
! JI Chord
!Edosteps
! Edosteps
!Notes of C Chord
! Notes of C Chord
!Written Name
! Written Name
!Spoken Name
! Spoken Name
|-
|-
|zo
| zo
|6:7:9
| 6:7:9
|0-4-11
| 0-4-11
|C Ebb G
| C Ebb G
|C(b3) or C(d3)
| C(b3) or C(d3)
|C flat-three or C dim-three
| C flat-three or C dim-three
|-
|-
|gu
| gu
|10:12:15
| 10:12:15
|0-5-11
| 0-5-11
|C Eb G
| C Eb G
|Cm
| Cm
|C minor
| C minor
|-
|-
|yo
| yo
|4:5:6
| 4:5:6
|0-6-11
| 0-6-11
|C E G
| C E G
|C
| C
|C major or C
| C major or C
|-
|-
|ru
| ru
|14:18:21
| 14:18:21
|0-7-11
| 0-7-11
| C E# G
| C E# G
|C(#3) or C(A3)
| C(#3) or C(A3)
|C sharp-three or C aug-three
| C sharp-three or C aug-three
|}
|}


Line 365: Line 279:


For a more complete list, see [[19edo Chord Names]] and [[Ups and downs notation #Chords and Chord Progressions]].
For a more complete list, see [[19edo Chord Names]] and [[Ups and downs notation #Chords and Chord Progressions]].
==Notation==
==Notation==
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter [[chain-of-fifths notation]] (with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes.
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter [[chain-of-fifths notation]] (with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes.
{| class="wikitable"
{| class="wikitable"
|+Notation of 19edo
|+Notation of 19edo
![[Degree]]
! [[Degree]]
![[Cent|Cents]]
! [[Cent|Cents]]
![[5L 2s|Diatonic]] interval names
! [[5L 2s|Diatonic]] interval names
!Note names (on D)
! Note names (on D)
|-
|-
|0
| 0
|0.00
| 0.00
|'''Perfect unison (P1)'''
| '''Perfect unison (P1)'''
|'''D'''
| '''D'''
|-
|-
|1
| 1
|63.16
| 63.16
|'''Augmented unison (A1)'''
| '''Augmented unison (A1)'''<br>Diminished second (d2)
Diminished second (d2)
| '''D#'''<br>Ebb
|'''D#'''
Ebb
|-
|-
|2
| 2
|126.32
| 126.32
|Doubly augmented unison (AA1)
| Doubly augmented unison (AA1)<br>'''Minor second (m2)'''
'''Minor second (m2)'''
| Dx<br>'''Eb'''
|Dx
'''Eb'''
|-
|-
|3
| 3
|189.47
| 189.47
|'''Major second (M2)'''
| '''Major second (M2)'''<br>Doubly diminished third (dd3)
Doubly diminished third (dd3)
| '''E'''<br>Fbb
|'''E'''
Fbb
|-
|-
|4
| 4
|252.63
| 252.63
|Augmented second (A2)
| Augmented second (A2)<br>'''Diminished third (d3)'''
'''Diminished third (d3)'''
| E#<br>'''Fb'''
|E#
'''Fb'''
|-
|-
|5
| 5
|315.79
| 315.79
|Doubly augmented second (AA2)
| Doubly augmented second (AA2)<br>'''Minor third (m3)'''
'''Minor third (m3)'''
| Ex<br>'''F'''
|Ex
'''F'''
|-
|-
|6
| 6
|378.95
| 378.95
|'''Major third (M3)'''
| '''Major third (M3)'''<br>Doubly diminished fourth (dd4)
Doubly diminished fourth (dd4)
| '''F#'''<br>Gbb
|'''F#'''
Gbb
|-
|-
|7
| 7
|442.11
| 442.11
|'''Augmented third (A3)'''
| '''Augmented third (A3)'''<br>Diminished fourth (d4)
Diminished fourth (d4)
| '''Fx'''<br>Gb
|'''Fx'''
Gb
|-
|-
|8
| 8
|505.26
| 505.26
|'''Perfect fourth (P4)'''
| '''Perfect fourth (P4)'''
|'''G'''
| '''G'''
|-
|-
|9
| 9
|568.42
| 568.42
|'''Augmented fourth (A4)'''
| '''Augmented fourth (A4)'''<br>Doubly diminished fifth (dd5)
Doubly diminished fifth (dd5)
| '''G#'''<br>Abb
|'''G#'''
Abb
|-
|-
|10
| 10
|631.58
| 631.58
|Doubly augmented fourth (AA4)
| Doubly augmented fourth (AA4)<br>'''Diminished fifth (d5)'''
'''Diminished fifth (d5)'''
| Gx<br>'''Ab'''
|Gx
'''Ab'''
|-
|-
|11
| 11
|694.74
| 694.74
|'''Perfect fifth (P5)'''
| '''Perfect fifth (P5)'''
|'''A'''
| '''A'''
|-
|-
|12
| 12
|757.89
| 757.89
|'''Augmented fifth (A5)'''
| '''Augmented fifth (A5)'''<br>Diminished sixth (d6)
Diminished sixth (d6)
| '''A#'''<br>Bbb
|'''A#'''
Bbb
|-
|-
|13
| 13
|821.05
| 821.05
|Doubly augmented fifth (AA5)
| Doubly augmented fifth (AA5)<br>'''Minor sixth (m6)'''
'''Minor sixth (m6)'''
| Ax<br>'''Bb'''
|Ax
'''Bb'''
|-
|-
|14
| 14
|884.21
| 884.21
|'''Major sixth (M6)'''
| '''Major sixth (M6)'''<br>Doubly diminished seventh (dd7)
Doubly diminished seventh (dd7)
| '''B'''<br>Cbb
|'''B'''
Cbb
|-
|-
|15
| 15
|947.37
| 947.37
|Augmented sixth (A6)
| Augmented sixth (A6)<br>'''Diminished seventh (d7)'''
'''Diminished seventh (d7)'''
| B#<br>'''Cb'''
|B#
'''Cb'''
|-
|-
|16
| 16
|1010.53
| 1010.53
|Doubly augmented sixth (AA6)
| Doubly augmented sixth (AA6)<br>'''Minor seventh (m7)'''
'''Minor seventh (m7)'''
| Bx<br>'''C'''
|Bx
'''C'''
|-
|-
|17
| 17
|1073.68
| 1073.68
|'''Major seventh (M7)'''
| '''Major seventh (M7)'''<br>Doubly diminished octave (dd8)
Doubly diminished octave (dd8)
| '''C#'''<br>Dbb
|'''C#'''
Dbb
|-
|-
|18
| 18
|1136.84
| 1136.84
|'''Augmented seventh (A7)'''
| '''Augmented seventh (A7)'''<br>Diminished octave (d8)
Diminished octave (d8)
| '''Cx'''<br>Db
|'''Cx'''
Db
|-
|-
|19
| 19
|1200.00
| 1200.00
|'''Perfect octave (P8)'''
| '''Perfect octave (P8)'''
|'''D'''
| '''D'''
|}
|}


==JI approximation==
== JI approximation ==
===15-odd-limit interval mappings===
=== 15-odd-limit interval mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 19edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.   
The following table shows how [[15-odd-limit intervals]] are represented in 19edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.   


{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="white-space:nowrap" |15-odd-limit intervals by direct approximation (even if inconsistent)
|+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)
!Interval, complement
! Interval, complement
!Error (abs, [[Cent|¢]])
! Error (abs, [[Cent|¢]])
!Error (rel, [[Relative cent|%]])
! Error (rel, [[Relative cent|%]])
|-
|-
|[[6/5]], [[5/3]]
| [[6/5]], [[5/3]]
|0.148
| 0.148
|0.2
| 0.2
|-
|-
|[[14/13]], [[13/7]]
| [[14/13]], [[13/7]]
|1.982
| 1.982
|3.1
| 3.1
|-
|-
|[[15/13]], [[26/15]]
| [[15/13]], [[26/15]]
|4.891
| 4.891
|7.7
| 7.7
|-
|-
|[[18/13]], [[13/9]]
| [[18/13]], [[13/9]]
| 5.039
| 5.039
|8.0
| 8.0
|-
|-
|[[15/14]], [[28/15]]
| [[15/14]], [[28/15]]
|6.873
| 6.873
|10.9
| 10.9
|-
|-
|[[9/7]], [[14/9]]
| [[9/7]], [[14/9]]
|7.021
| 7.021
|11.1
| 11.1
|-
|-
|[[10/9]], [[9/5]]
| [[10/9]], [[9/5]]
|7.070
| 7.070
|11.2
| 11.2
|-
|-
|'''[[4/3]], [[3/2]]'''
| '''[[4/3]], [[3/2]]'''
|'''7.218'''
| '''7.218'''
|'''11.4'''
| '''11.4'''
|-
|-
|'''[[5/4]], [[8/5]]'''
| '''[[5/4]], [[8/5]]'''
|'''7.366'''
| '''7.366'''
|'''11.7'''
| '''11.7'''
|-
|-
|[[13/10]], [[20/13]]
| [[13/10]], [[20/13]]
|12.109
| 12.109
|19.2
| 19.2
|-
|-
|[[13/12]], [[24/13]]
| [[13/12]], [[24/13]]
|12.257
| 12.257
|19.4
| 19.4
|-
|-
|[[7/5]], [[10/7]]
| [[7/5]], [[10/7]]
|14.091
| 14.091
|22.3
| 22.3
|-
|-
|[[7/6]], [[12/7]]
| [[7/6]], [[12/7]]
|14.239
| 14.239
|22.5
| 22.5
|-
|-
|[[9/8]], [[16/9]]
| [[9/8]], [[16/9]]
|14.436
| 14.436
|22.9
| 22.9
|-
|-
|[[16/15]], [[15/8]]
| [[16/15]], [[15/8]]
|14.585
| 14.585
|23.1
| 23.1
|-
|-
|'''[[11/8]], [[16/11]]'''
| '''[[11/8]], [[16/11]]'''
|'''17.103'''
| '''17.103'''
|'''27.1'''
| '''27.1'''
|-
|-
|'''[[16/13]], [[13/8]]'''
| '''[[16/13]], [[13/8]]'''
|'''19.475'''
| '''19.475'''
|'''30.8'''
| '''30.8'''
|-
|-
|'''[[8/7]], [[7/4]]'''
| '''[[8/7]], [[7/4]]'''
|'''21.457'''
| '''21.457'''
|'''34.0'''
| '''34.0'''
|-
|-
|[[12/11]], [[11/6]]
| [[12/11]], [[11/6]]
| 24.321
| 24.321
|38.5
| 38.5
|-
|-
|[[11/10]], [[20/11]]
| [[11/10]], [[20/11]]
|24.469
| 24.469
|38.7
| 38.7
|-
|-
|''[[14/11]], [[11/7]]''
| ''[[14/11]], [[11/7]]''
|''24.597''
| ''24.597''
|''38.9''
| ''38.9''
|-
|-
|''[[13/11]], [[22/13]]''
| ''[[13/11]], [[22/13]]''
|''26.580''
| ''26.580''
|''42.1''
| ''42.1''
|-
|-
|''[[15/11]], [[22/15]]''
| ''[[15/11]], [[22/15]]''
|''31.470''
| ''31.470''
|''49.8''
| ''49.8''
|-
|-
|[[11/9]], [[18/11]]
| [[11/9]], [[18/11]]
| 31.539
| 31.539
| 49.9
| 49.9
Line 616: Line 497:
{{15-odd-limit|19}}
{{15-odd-limit|19}}


===Selected 17-limit intervals ===
=== Selected 17-limit intervals ===
[[File:19ed2-001.svg|alt=alt : Your browser has no SVG support.]]
[[File:19ed2-001.svg|alt=alt : Your browser has no SVG support.]]


==Regular temperament properties==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo| -30 19 }}
| {{monzo| -30 19 }}
|[{{val| 19 30 }}]
| [{{val| 19 30 }}]
| +2.28
| +2.28
|2.28
| 2.28
|3.61
| 3.61
|-
|-
|2.3.5
| 2.3.5
|81/80, 3125/3072
| 81/80, 3125/3072
|[{{val| 19 30 44 }}]
| [{{val| 19 30 44 }}]
| +2.58
| +2.58
|1.91
| 1.91
|3.02
| 3.02
|-
|-
| 2.3.5.7
| 2.3.5.7
|49/48, 81/80, 126/125
| 49/48, 81/80, 126/125
|[{{val| 19 30 44 53 }}]
| [{{val| 19 30 44 53 }}]
| +3.85
| +3.85
|2.76
| 2.76
|4.35
| 4.35
|-
|-
|2.3.5.7.13
| 2.3.5.7.13
|49/48, 65/64, 81/80, 91/90
| 49/48, 65/64, 81/80, 91/90
|[{{val| 19 30 44 53 70 }}]
| [{{val| 19 30 44 53 70 }}]
| +4.14
| +4.14
|2.53
| 2.53
|3.99
| 3.99
|}
|}


Line 663: Line 544:
19et is prominent in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]].
19et is prominent in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]].


===Uniform maps===
=== Uniform maps ===
{{Uniform map|13|18.5|19.5}}
{{Uniform map|13|18.5|19.5}}


===Commas===
=== Commas ===
19et [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 19 30 44 53 66 70 }}.)
19et [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 19 30 44 53 66 70 }}.)


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
![[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>Limit]]
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Monzo]]
! [[Monzo]]
![[Cents]]
! [[Cents]]
![[Color notation/Temperament Names|Color Name]]
! [[Color notation/Temperament Names|Color Name]]
!Name
! Name
|-
|-
| 3
| 3
|<abbr title="1162261467/1073741824">(20 digits)</abbr>
| <abbr title="1162261467/1073741824">(20 digits)</abbr>
|{{monzo| -30 19 }}
| {{monzo| -30 19 }}
|137.14
| 137.14
|
|  
|
|  
|-
|-
|5
| 5
|[[16875/16384]]
| [[16875/16384]]
|{{monzo| -14 3 4 }}
| {{monzo| -14 3 4 }}
|51.12
| 51.12
| Laquadyo
| Laquadyo
|Negri comma
| Negri comma
|-
|-
|5
| 5
|[[3125/3072]]
| [[3125/3072]]
|{{monzo| -10 -1 5 }}
| {{monzo| -10 -1 5 }}
|29.61
| 29.61
|Laquinyo
| Laquinyo
|Magic comma
| Magic comma
|-
|-
|5
| 5
|[[81/80]]
| [[81/80]]
|{{monzo| -4 4 -1 }}
| {{monzo| -4 4 -1 }}
|21.51
| 21.51
|Gu
| Gu
| Syntonic comma
| Syntonic comma
|-
|-
|5
| 5
|[[78732/78125]]
| [[78732/78125]]
|{{monzo| 2 9 -7 }}
| {{monzo| 2 9 -7 }}
|13.40
| 13.40
|Sepgu
| Sepgu
|Sensipent comma
| Sensipent comma
|-
|-
|5
| 5
|[[15625/15552]]
| [[15625/15552]]
|{{monzo| -6 -5 6 }}
| {{monzo| -6 -5 6 }}
|8.11
| 8.11
|Tribiyo
| Tribiyo
|Kleisma
| Kleisma
|-
|-
| 5
| 5
|<abbr title="1224440064/1220703125">(20 digits)</abbr>
| <abbr title="1224440064/1220703125">(20 digits)</abbr>
|{{monzo| 8 14 -13 }}
| {{monzo| 8 14 -13 }}
|5.29
| 5.29
|Thegu
| Thegu
|[[Parakleisma]]
| [[Parakleisma]]
|-
|-
|5
| 5
|<abbr title="19073486328125/19042491875328">(28 digits)</abbr>
| <abbr title="19073486328125/19042491875328">(28 digits)</abbr>
|{{monzo| -14 -19 19 }}
| {{monzo| -14 -19 19 }}
|2.82
| 2.82
| Neyo
| Neyo
|[[Enneadeca]]
| [[Enneadeca]]
|-
|-
|7
| 7
|[[1029/1000]]
| [[1029/1000]]
|{{monzo| -3 1 -3 3 }}
| {{monzo| -3 1 -3 3 }}
|49.49
| 49.49
|Trizogu
| Trizogu
|Keega
| Keega
|-
|-
|7
| 7
|[[525/512]]
| [[525/512]]
|{{monzo| -9 1 2 1 }}
| {{monzo| -9 1 2 1 }}
|43.41
| 43.41
|Lazoyoyo
| Lazoyoyo
|Avicennma
| Avicennma
|-
|-
| 7
| 7
|[[49/48]]
| [[49/48]]
|{{monzo| -4 -1 0 2 }}
| {{monzo| -4 -1 0 2 }}
|35.70
| 35.70
|Zozo
| Zozo
|Slendro diesis
| Slendro diesis
|-
|-
|7
| 7
|[[686/675]]
| [[686/675]]
|{{monzo| 1 -3 -2 3 }}
| {{monzo| 1 -3 -2 3 }}
|27.99
| 27.99
|Trizo-agugu
| Trizo-agugu
|Senga
| Senga
|-
|-
|7
| 7
|[[875/864]]
| [[875/864]]
|{{monzo| -5 -3 3 1 }}
| {{monzo| -5 -3 3 1 }}
|21.90
| 21.90
|Zotrigu
| Zotrigu
| Keema
| Keema
|-
|-
|7
| 7
|[[245/243]]
| [[245/243]]
|{{monzo| 0 -5 1 2 }}
| {{monzo| 0 -5 1 2 }}
| 14.19
| 14.19
|Zozoyo
| Zozoyo
|Sensamagic
| Sensamagic
|-
|-
|7
| 7
|[[126/125]]
| [[126/125]]
|{{monzo| 1 2 -3 1 }}
| {{monzo| 1 2 -3 1 }}
|13.79
| 13.79
|Zotrigu
| Zotrigu
|Starling comma
| Starling comma
|-
|-
|7
| 7
|[[225/224]]
| [[225/224]]
|{{monzo| -5 2 2 -1 }}
| {{monzo| -5 2 2 -1 }}
|7.71
| 7.71
|Ruyoyo
| Ruyoyo
|Marvel comma
| Marvel comma
|-
|-
|7
| 7
|[[19683/19600]]
| [[19683/19600]]
|{{monzo| -4 9 -2 -2 }}
| {{monzo| -4 9 -2 -2 }}
|7.32
| 7.32
|Labirugu
| Labirugu
|Cataharry
| Cataharry
|-
|-
|7
| 7
|[[10976/10935]]
| [[10976/10935]]
|{{monzo| 5 -7 -1 3 }}
| {{monzo| 5 -7 -1 3 }}
|6.48
| 6.48
|Satrizo-agu
| Satrizo-agu
|Hemimage
| Hemimage
|-
|-
|7
| 7
|[[3136/3125]]
| [[3136/3125]]
|{{monzo| 6 0 -5 2 }}
| {{monzo| 6 0 -5 2 }}
|6.08
| 6.08
|Zozoquingu
| Zozoquingu
|Hemimean
| Hemimean
|-
|-
|7
| 7
|<abbr title="703125/702464">(12 digits)</abbr>
| <abbr title="703125/702464">(12 digits)</abbr>
|{{monzo| -11 2 7 -3 }}
| {{monzo| -11 2 7 -3 }}
| 1.63
| 1.63
|Latriru-asepyo
| Latriru-asepyo
|[[Meter]]
| [[Meter]]
|-
|-
|7
| 7
|[[4375/4374]]
| [[4375/4374]]
|{{monzo| -1 -7 4 1 }}
| {{monzo| -1 -7 4 1 }}
|0.40
| 0.40
|Zoquadyo
| Zoquadyo
| Ragisma
| Ragisma
|-
|-
|11
| 11
|[[100/99]]
| [[100/99]]
|{{monzo| 2 -2 2 0 -1 }}
| {{monzo| 2 -2 2 0 -1 }}
| 17.40
| 17.40
|Luyoyo
| Luyoyo
|Ptolemisma
| Ptolemisma
|-
|-
| 11
| 11
|[[896/891]]
| [[896/891]]
|{{monzo| 7 -4 0 1 -1 }}
| {{monzo| 7 -4 0 1 -1 }}
|9.69
| 9.69
|Saluzo
| Saluzo
|Pentacircle
| Pentacircle
|-
|-
|11
| 11
|[[65536/65219]]
| [[65536/65219]]
|{{monzo| 16 0 0 -2 -3 }}
| {{monzo| 16 0 0 -2 -3 }}
| 8.39
| 8.39
|Satrilu-aruru
| Satrilu-aruru
|Orgonisma
| Orgonisma
|-
|-
|11
| 11
|[[385/384]]
| [[385/384]]
|{{monzo| -7 -1 1 1 1 }}
| {{monzo| -7 -1 1 1 1 }}
|4.50
| 4.50
|Lozoyo
| Lozoyo
|Keenanisma
| Keenanisma
|-
|-
|11
| 11
|[[540/539]]
| [[540/539]]
|{{monzo| 2 3 1 -2 -1 }}
| {{monzo| 2 3 1 -2 -1 }}
|3.21
| 3.21
|Lururuyo
| Lururuyo
|Swetisma
| Swetisma
|-
|-
|13
| 13
|[[65/64]]
| [[65/64]]
|{{monzo| -6 0 1 0 0 1 }}
| {{monzo| -6 0 1 0 0 1 }}
|26.84
| 26.84
|Thoyo
| Thoyo
|Wilsorma
| Wilsorma
|-
|-
|13
| 13
|[[343/338]]
| [[343/338]]
|{{monzo| -1 0 0 3 0 -2 }}
| {{monzo| -1 0 0 3 0 -2 }}
| 25.42
| 25.42
|Thuthutrizo
| Thuthutrizo
|
|
|-
|-
|13
| 13
|[[91/90]]
| [[91/90]]
|{{monzo| -1 -2 -1 1 0 1 }}
| {{monzo| -1 -2 -1 1 0 1 }}
|19.13
| 19.13
| Thozogu
| Thozogu
|Superleap
| Superleap
|-
|-
|13
| 13
|[[676/675]]
| [[676/675]]
|{{monzo| 2 -3 -2 0 0 2 }}
| {{monzo| 2 -3 -2 0 0 2 }}
|2.56
| 2.56
|Bithogu
| Bithogu
|Island comma
| Island comma
|}
|}
<references />
<references/>


===Linear temperaments===
=== Linear temperaments ===
*[[List of 19et rank two temperaments by badness]]
* [[List of 19et rank two temperaments by badness]]
*[[List of 19et rank two temperaments by complexity]]
* [[List of 19et rank two temperaments by complexity]]
*[[List of edo-distinct 19et rank two temperaments]]
* [[List of edo-distinct 19et rank two temperaments]]
*[[Syntonic-kleismic equivalence continuum]]
* [[Syntonic-kleismic equivalence continuum]]


Since 19 is prime, all rank-2 temperaments in 19edo have one period per octave (i.e. are linear). Therefore you can make a correspondence between intervals and the linear temperaments they generate.
Since 19 is prime, all rank-2 temperaments in 19edo have one period per octave (i.e. are linear). Therefore you can make a correspondence between intervals and the linear temperaments they generate.
Line 899: Line 780:
{| class="wikitable center-1 right-2 center-3"
{| class="wikitable center-1 right-2 center-3"
|-
|-
!Degree
! Degree
!Cents
! Cents
! Interval
! Interval
!MOSes
! MOSes
!Temperaments
! Temperaments
|-
|-
|1
| 1
| 63.16
| 63.16
|A1, d2
| A1, d2
|
|  
|[[Unicorn]] / [[rhinocerus]]
| [[Unicorn]] / [[rhinocerus]]
|-
|-
|2
| 2
|126.32
| 126.32
|m2
| m2
|[[1L 8s]], [[9L 1s]]
| [[1L 8s]], [[9L 1s]]
|[[Negri]]
| [[Negri]]
|-
|-
|3
| 3
|189.47
| 189.47
|M2
| M2
|[[1L 5s]], [[6L 1s]], [[6L 7s]]
| [[1L 5s]], [[6L 1s]], [[6L 7s]]
|[[Deutone]]<br>[[Spell]]
| [[Deutone]]<br>[[Spell]]
|-
|-
| 4
| 4
|252.63
| 252.63
| A2, d3
| A2, d3
|[[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]
| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]
|[[Godzilla]]
| [[Godzilla]]
|-
|-
|5
| 5
|315.79
| 315.79
|m3
| m3
|[[3L 1s]], [[4L 3s]], <br>[[4L 7s]], [[4L 11s]]
| [[3L 1s]], [[4L 3s]], <br>[[4L 7s]], [[4L 11s]]
|[[Cata]] / [[keemun]]
| [[Cata]] / [[keemun]]
|-
|-
|6
| 6
|378.95
| 378.95
|M3
| M3
|[[3L 1s]], [[3L 4s]], [[3L 7s]], <br>[[3L 10s]], [[3L 13s]]
| [[3L 1s]], [[3L 4s]], [[3L 7s]], <br>[[3L 10s]], [[3L 13s]]
|[[Magic]] / [[muggles]]
| [[Magic]] / [[muggles]]
|-
|-
|7
| 7
|442.11
| 442.11
|A3, d4
| A3, d4
|[[3L 2s]], [[3L 5s]], [[8L 3s]]
| [[3L 2s]], [[3L 5s]], [[8L 3s]]
|[[Sensi]]
| [[Sensi]]
|-
|-
|8
| 8
|505.26
| 505.26
|P4
| P4
|[[2L 3s]], [[5L 2s]], [[7L 5s]]
| [[2L 3s]], [[5L 2s]], [[7L 5s]]
|[[Meantone]] / [[flattone]]
| [[Meantone]] / [[flattone]]
|-
|-
|9
| 9
| 568.42
| 568.42
|A4
| A4
|[[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]
| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]
|[[Liese]] / [[pycnic]]<br>[[Triton]]
| [[Liese]] / [[pycnic]]<br>[[Triton]]
|}
|}


==Scales==
== Scales ==
===MOS scales===
=== MOS scales ===
====Octave-equivalent mosses ====
==== Octave-equivalent mosses ====
*[[meantone]] pentatonic, [[2L 3s]] (gen = 11\19): 33535
* [[meantone]] pentatonic, [[2L 3s]] (gen = 11\19): 33535
*[[meantone]] diatonic, [[5L 2s]] (gen = 11\19): 3323332
* [[meantone]] diatonic, [[5L 2s]] (gen = 11\19): 3323332
*[[meantone]] chromatic, [[7L 5s]] (gen = 11\19): 212122121212
* [[meantone]] chromatic, [[7L 5s]] (gen = 11\19): 212122121212
*[[semaphore]][5], [[4L 1s]] (gen = 4\19): 44344
* [[semaphore]][5], [[4L 1s]] (gen = 4\19): 44344
*[[semaphore]][9], [[5L 4s]] (gen = 4\19): 313133131
* [[semaphore]][9], [[5L 4s]] (gen = 4\19): 313133131
*[[semaphore]][14], [[5L 9s]] (gen = 4\19): 21211211211211
* [[semaphore]][14], [[5L 9s]] (gen = 4\19): 21211211211211
*[[sensi]][5], [[2L 3s]] (gen = 7\19): 52525
* [[sensi]][5], [[2L 3s]] (gen = 7\19): 52525
*[[sensi]][8], [[3L 5s]] (gen = 7\19): 23223223
* [[sensi]][8], [[3L 5s]] (gen = 7\19): 23223223
*[[sensi]][11], [[8L 3s]] (gen = 7\19): 22122212221
* [[sensi]][11], [[8L 3s]] (gen = 7\19): 22122212221
*[[negri]][9], [[1L 8s]] (gen = 2\19): 222232222
* [[negri]][9], [[1L 8s]] (gen = 2\19): 222232222
*[[negri]][10], [[9L 1s]] (gen = 2\19): 2222212222
* [[negri]][10], [[9L 1s]] (gen = 2\19): 2222212222
*[[kleismic]][7], [[4L 3s]] (gen = 5\19): 1414144
* [[kleismic]][7], [[4L 3s]] (gen = 5\19): 1414144
*[[kleismic]][11], [[4L 7s]] (gen = 5\19): 13113113131
* [[kleismic]][11], [[4L 7s]] (gen = 5\19): 13113113131
*[[kleismic]][15], [[4L 11s]] (gen = 5\19): 121112111211211
* [[kleismic]][15], [[4L 11s]] (gen = 5\19): 121112111211211
*[[magic]][7], [[3L 4s]] (gen = 6\19): 5151511
* [[magic]][7], [[3L 4s]] (gen = 6\19): 5151511
*[[magic]][10], [[3L 7s]] (gen = 6\19): 4114114111
* [[magic]][10], [[3L 7s]] (gen = 6\19): 4114114111
*[[magic]][13], [[3L 10s]] (gen = 6\19): 3111311131111
* [[magic]][13], [[3L 10s]] (gen = 6\19): 3111311131111
*[[magic]][16], [[3L 13s]] (gen = 6\19): 2111121111211111
* [[magic]][16], [[3L 13s]] (gen = 6\19): 2111121111211111
*[[liese]][17], [[2L 15s]] (gen = 9\19): 2111111111211111111
* [[liese]][17], [[2L 15s]] (gen = 9\19): 2111111111211111111


===Other scales===
=== Other scales ===
*Meantone harmonic minor: 3233242
* Meantone harmonic minor: 3233242
*Meantone melodic minor: 3233332
* Meantone melodic minor: 3233332
*Meantone harmonic major: 3323242
* Meantone harmonic major: 3323242
*Meantone / [[marvel double harmonic major]]: 2423242 (subset of Negri[9])
* Meantone / [[marvel double harmonic major]]: 2423242 (subset of Negri[9])
*enharmonic pentatonic: 26326, 62362
* enharmonic pentatonic: 26326, 62362
*enharmonic octave species: 1163116, 6113611, 1613161
* enharmonic octave species: 1163116, 6113611, 1613161
*[[Semiquartal]] 3|5 b2: 133131331
* [[Semiquartal]] 3|5 b2: 133131331
*[[Marvel hexatonic]]: 425242 (subset of Negri[9])
* [[Marvel hexatonic]]: 425242 (subset of Negri[9])
*[[Antipental blues]]: 441244
* [[Antipental blues]]: 441244


==Instruments==
== Instruments ==
[[File:Vaisvil-19edo-guitar-IMG00145-1024x768.jpg|512x384px|thumb|none|19 note per octave Ibanez conversion by Brad Smith (Indianapolis)]]
[[File:Vaisvil-19edo-guitar-IMG00145-1024x768.jpg|512x384px|thumb|none|19 note per octave Ibanez conversion by Brad Smith (Indianapolis)]]
[[File:Bass19.jpg|alt=19edo 5 string Bass 34"-37" scale length|512x384px|thumb|none|19edo bass conversion by Ron Sword]]
[[File:Bass19.jpg|alt=19edo 5 string Bass 34"-37" scale length|512x384px|thumb|none|19edo bass conversion by Ron Sword]]


==Music==
== Music ==
{{Main| 19edo/Music}}
{{Main| 19edo/Music}}
{{Catrel|19edo tracks}}
{{Catrel|19edo tracks}}
Line 1,005: Line 886:
; [[Naegleria fowleri]] recorded all of their music in 19edo
; [[Naegleria fowleri]] recorded all of their music in 19edo


==See also==
== See also ==
*[[19edo modes]]
* [[19edo modes]]
*[[19edo chords]]
* [[19edo chords]]
*[[Strictly proper 19edo scales]]
* [[Strictly proper 19edo scales]]
*[[How to tune a 19edo guitar by ear]]
* [[How to tune a 19edo guitar by ear]]
*[[Primer for 19edo]]
* [[Primer for 19edo]]
*[[Mason Green's New Common Practice Notation]]
* [[Mason Green's New Common Practice Notation]]
*[[Arto and Tendo Theory]]
* [[Arto and Tendo Theory]]
*[[Lumatone mapping for 19edo]]
* [[Lumatone mapping for 19edo]]


===References===
=== References ===
*Bucht, Saku and Huovinen, Erkki, ''Perceived consonance of harmonic intervals in 19-tone equal temperament'', CIM04_proceedings.
* Bucht, Saku and Huovinen, Erkki, ''Perceived consonance of harmonic intervals in 19-tone equal temperament'', CIM04_proceedings.
*Levy, Kenneth J., ''Costeley's Chromatic Chanson'', Annales Musicologues: Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.
* Levy, Kenneth J., ''Costeley's Chromatic Chanson'', Annales Musicologues: Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.


==Further reading==
== Further reading ==
*[[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.
* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.
*Darreg, Ivor. ''[http://www.microstick.net/nineteenarticle.htm Nineteen for the Nineties]''{{dead link}}. (Unknown date of publication).
* Darreg, Ivor. ''[http://www.microstick.net/nineteenarticle.htm Nineteen for the Nineties]''{{dead link}}. (Unknown date of publication).
*Howe, Hubert S., Jr. [http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications]. c. 2004.
* Howe, Hubert S., Jr. [http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications]. c. 2004.
*[[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.
* [[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.
*[[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Enneadecaphonic Scales for Guitar: A Repository of Scales, Chord-Scales, Notations and Techniques for Nineteen Equal Divisions of the Octave]''. 2010.
* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Enneadecaphonic Scales for Guitar: A Repository of Scales, Chord-Scales, Notations and Techniques for Nineteen Equal Divisions of the Octave]''. 2010.
*Yasser, Joseph. ''[https://www.worldcat.org/fr/title/726192994 Theory of Evolving Tonality]''. 1932.
* Yasser, Joseph. ''[https://www.worldcat.org/fr/title/726192994 Theory of Evolving Tonality]''. 1932.


==External links==
== External links ==
*[http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on the [[Tonalsoft Encyclopedia]]
* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on the [[Tonalsoft Encyclopedia]]
*[http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Ingrid Pearson, Graham Hair, Dougie McGilvray, Nick Bailey, Amanda Morrison and Richard Parncutt (from n-ISM, the Network for Interdisciplinary Studies in Science, Technology, and Music)
* [http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Ingrid Pearson, Graham Hair, Dougie McGilvray, Nick Bailey, Amanda Morrison and Richard Parncutt (from n-ISM, the Network for Interdisciplinary Studies in Science, Technology, and Music)
*[http://mtg.redkeylabs.com/index.php?topic=6.0 Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar].
* [http://mtg.redkeylabs.com/index.php?topic=6.0 Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar].
*[[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/home/bostjan/microtones/19edo 19-EDO pages]
* [[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/home/bostjan/microtones/19edo 19-EDO pages]  
*[https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]
* [https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]


[[Category:19-tone scales]]
[[Category:19-tone scales]]
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