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| ja = 19平均律
| ja = 19平均律
}}
}}
{{Infobox ET}}
{{Infobox ET|debug=1}}
{{Wikipedia|19 equal temperament}}
{{Wikipedia|19 equal temperament}}
= Main page =
{{ED intro}}
{{ED intro}}


Line 28: Line 30:
19edo also closely approximates most of the intervals of [[Bozuji tuning]], a 21st century tuning based on Gioseffo Zarlino's approach to just intonation. with most of the adjacent diatonic diminished and augmented intervals of Bozuji tuning represented enharmonically by one interval in 19edo.
19edo also closely approximates most of the intervals of [[Bozuji tuning]], a 21st century tuning based on Gioseffo Zarlino's approach to just intonation. with most of the adjacent diatonic diminished and augmented intervals of Bozuji tuning represented enharmonically by one interval in 19edo.


Due to the narrow whole tones and wide diatonic semitones, 19edo's diatonic scale tends to sound somewhat dull compared to 12edo, but the pentatonic scale is said by many to sound much more expressive owing to the significantly larger contrast between the narrow whole tone and wide minor third. While 12edo has an expressive diatonic and dull pentatonic, the reverse is true in 19. Pentatonicism thus becomes more important in 19edo, and one option is to use the pentatonic scale as a sort of "super-chord", with "chord progressions" being modulations between pentatonic subsets of the superdiatonic scale.
Due to the narrow whole tones and wide diatonic semitones, 19edo's diatonic scale tends to sound somewhat dull compared to 12edo, but the pentatonic scale is said by many to sound much more expressive owing to the significantly larger contrast between the narrow whole tone and wide minor third. Pentatonicism thus becomes more important in 19edo, and one option is to use the pentatonic scale as a sort of "super-chord", with "chord progressions" being modulations between pentatonic subsets of the superdiatonic scale.


=== Prime harmonics ===
=== Prime harmonics ===
Line 45: Line 47:
[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. See [[undevigintone]]. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[meanmag]].
[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. See [[undevigintone]]. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[meanmag]].


== Intervals ==
== Instruments ==
[[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]]
 
== Music ==
{{Main| 19edo/Music }}
{{Catrel| 19edo tracks }}
 
; [http://micro.soonlabel.com/19-ET/ XA 19-ET Index]
; A number of compositions that were perfomed at the [http://midwestmicrofest.org/concerts.html midwestmicrofest concert in 2007]{{dead link}}
 
== See also ==
* [[19edo modes]]
* [[19edo chords]]
* [[Strictly proper 19edo scales]]
* [[How to tune a 19edo guitar by ear]]
* [[Primer for 19edo]]
* [[Mason Green's New Common Practice Notation]]
* [[Extraclassical tonality]]
* [[Lumatone mapping for 19edo]]
* [[List of 19et rank two temperaments by badness]]
* [[List of 19et rank two temperaments by complexity]]
* [[List of edo-distinct 19et rank two temperaments]]
* [[Syntonic–kleismic equivalence continuum]]
 
== Further reading ==
* [[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).
* 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.
* [[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.
 
== 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://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].
* [[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]
 
=== Notes ===
<references group="note" />
 
=== References ===
* 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.
 
= Intervals (delisted page) =
 
== Degrees ==
{| class="wikitable right-1 right-2 center-5 center-8"
{| class="wikitable right-1 right-2 center-5 center-8"
|-
|-
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! Approximated [[Just intonation|JI]] Intervals<ref group="note">{{sg|limit=2.3.5.7.13 subgroup}}</ref>
! Approximated [[Just intonation|JI]] Intervals<ref group="note">{{sg|limit=2.3.5.7.13 subgroup}}</ref>
! [[Solfege]]
! [[Solfege]]
! colspan="2" | [[SKULO interval names|SKULO Interval]]
|-
|-
| 0
| 0
Line 60: Line 110:
| [[1/1]]
| [[1/1]]
| Do
| Do
| unison
| P1
|-
|-
| 1
| 1
Line 68: Line 116:
| [[25/24]], [[26/25]], [[28/27]]
| [[25/24]], [[26/25]], [[28/27]]
| Di/Ro
| Di/Ro
| super unison, subminor second
| S1, sm2
|-
|-
| 2
| 2
Line 76: Line 122:
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| Ra
| Ra
| minor second
| m2
|-
|-
| 3
| 3
Line 84: Line 128:
| [[9/8]], [[10/9]]
| [[9/8]], [[10/9]]
| Re
| Re
| major second
| M2
|-
|-
| 4
| 4
Line 92: Line 134:
| [[7/6]], [[8/7]], [[15/13]]
| [[7/6]], [[8/7]], [[15/13]]
| Ri/Ma
| Ri/Ma
| supermajor second, subminor third
| SM2, sm3
|-
|-
| 5
| 5
Line 100: Line 140:
| [[6/5]]
| [[6/5]]
| Me
| Me
| minor third
| m3
|-
|-
| 6
| 6
Line 108: Line 146:
| [[5/4]], [[16/13]], [[56/45]]
| [[5/4]], [[16/13]], [[56/45]]
| Mi
| Mi
| major third
| M3
|-
|-
| 7
| 7
Line 116: Line 152:
| [[9/7]], [[13/10]], [[32/25]]
| [[9/7]], [[13/10]], [[32/25]]
| Mo/Fe
| Mo/Fe
| supermajor third, sub fourth
| SM3, s4
|-
|-
| 8
| 8
Line 124: Line 158:
| [[4/3]], [[75/56]]
| [[4/3]], [[75/56]]
| Fa
| Fa
| perfect fourth
| P4
|-
|-
| 9
| 9
Line 132: Line 164:
| [[7/5]], [[18/13]], [[25/18]]
| [[7/5]], [[18/13]], [[25/18]]
| Fi
| Fi
| augmented fourth
| A4
|-
|-
| 10
| 10
Line 140: Line 170:
| [[10/7]], [[13/9]], [[36/25]]
| [[10/7]], [[13/9]], [[36/25]]
| Se
| Se
| diminished fifth
| d5
|-
|-
| 11
| 11
Line 148: Line 176:
| [[3/2]], [[112/75]]
| [[3/2]], [[112/75]]
| So
| So
| perfect fifth
| P5
|-
|-
| 12
| 12
Line 156: Line 182:
| [[14/9]], [[20/13]], [[25/16]]
| [[14/9]], [[20/13]], [[25/16]]
| Si/Lo
| Si/Lo
| super fifth, subminor sixth
| S5, sm6
|-
|-
| 13
| 13
Line 164: Line 188:
| [[8/5]], [[13/8]], [[45/28]]
| [[8/5]], [[13/8]], [[45/28]]
| Le
| Le
| minor sixth
| m6
|-
|-
| 14
| 14
Line 172: Line 194:
| [[5/3]]
| [[5/3]]
| La
| La
| major sixth
| M6
|-
|-
| 15
| 15
Line 180: Line 200:
| [[7/4]], [[12/7]], [[26/15]]
| [[7/4]], [[12/7]], [[26/15]]
| Li/Ta
| Li/Ta
| supermajor sixth, subminor seventh
| SM6, sm7
|-
|-
| 16
| 16
Line 188: Line 206:
| [[9/5]], [[16/9]]
| [[9/5]], [[16/9]]
| Te
| Te
| minor seventh
| m7
|-
|-
| 17
| 17
Line 196: Line 212:
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| Ti
| Ti
| major seventh
| M7
|-
|-
| 18
| 18
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| [[25/13]], [[27/14]], [[48/25]]
| [[25/13]], [[27/14]], [[48/25]]
| To/Da
| To/Da
| supermajor seventh, sub octave
| SM7, s8
|-
|-
| 19
| 19
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| [[2/1]]
| [[2/1]]
| Do
| Do
| octave
| P8
|}
=== Interval quality and chord names in color notation ===
Using [[color notation]], qualities can be loosely associated with colors:
{| class="wikitable" style="text-align: center;"
|-
! Quality
! [[Color name|Color Name]]
! Monzo Format
! Examples
|-
| diminished
| zo
| (a, b, 0, 1)
| 7/6, 7/4
|-
| rowspan="2" | minor
| fourthward wa
| (a, b), b &lt; -1
| 32/27, 16/9
|-
| gu
| (a, b, -1)
| 6/5, 9/5
|-
| rowspan="2" | major
| yo
| (a, b, 1)
| 5/4, 5/3
|-
| fifthward wa
| (a, b), b &gt; 1
| 9/8, 27/16
|-
| augmented
| ru
| (a, b, 0, -1)
| 9/7, 12/7
|}
Key signatures are the same, but with the extra notes and different enharmonic equivalents, some key signatures can get messy.  For example, the key of B&#x1D12B; would have double-flats on B and E, and flats on C, D, F, G, and A.  Thinking of rewriting this key as A&#x266F; might seem better, but then the key signature would contain double-sharps on C, F, and G, and sharps on A, B, D, and E, which is actually worse.
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads:
{| class="wikitable center-1 center-2 center-3 center-4"
|-
! [[Kite's color notation|Color of the 3rd]]
! JI Chord
! Edosteps
! Notes of C Chord
! Written Name
! Spoken Name
|-
| zo (7-over)
| 6:7:9
| 0–4–11
| C–E&#x1D12B;–G
| Cm(&#x266D;3) or Cmin(&#x266D;3) or C(d3)
| C subminor, C minor flat-three, C dim-three
|-
| gu (5-under)
| 10:12:15
| 0–5–11
| C–E&#x266D;–G
| Cm or Cmin
| C minor
|-
| yo (5-over)
| 4:5:6
| 0–6–11
| C–E–G
| C or Cmaj
| C, C major
|-
| ru (7-under)
| 14:18:21
| 0–7–11
| C–E&#x266F;–G
| C(&#x266F;3) or Cmaj(&#x266F;3) or C(A3)
| C supermajor, C major sharp-three, C aug-three
|-
| yo (5-over)
| 4:5:6:7
| 0–6–11–15
| C–E–G–B&#x1D12B;
| Ch7 or C,d7 or Cadd(d7)
| C harmonic 7, C (major) add dim-seven
|-
| gu (5-under)
| 12:10:8:7 or 1:6/5:3/2:12/7
| 0–5–11–15
| C–E&#x266D;–G–A&#x266F;
| Cm&#x266F;6 or CmA6 or Cm(add(&#x266F;6)) or Cm(add(A6))
| C minor (add) sharp-six, C minor (add) aug-six
|}
The last two chords illustrate how the 15\19 interval can be considered as either 7/4 or 12/7, and how 19edo conflates zo and ru ratios.
For a more complete list, see [[19edo Chord Names]] and [[Ups and downs notation #Chords and Chord Progressions]].
== Notation ==
=== Standard 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.
Any 19edo note or interval can be [[Enharmonic unison|respelled enharmonically]] by adding a double-diminished 2nd to it or subtracting one from it. Adding a dd2 is equivalent to finding the 12edo equivalent with a higher degree, then diminishing it. For example, C# becomes Db, which is diminished to become Dbb.
{| class="wikitable right-1 right-2 center-3 center-4"
|+ style="font-size: 105%;" | Notation of 19edo
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Chain-of-fifths notation|Standard Notation]]
|-
! [[5L 2s|Diatonic Interval Names]]
! Note Names<br />on D
|-
| 0
| 0.00
| '''Perfect unison (P1)'''
| '''D'''
|-
| 1
| 63.16
| Augmented unison (A1)<br />Diminished second (d2)
| D#<br />Ebb
|-
| 2
| 126.32
| Doubly augmented unison (AA1)<br />Minor second (m2)
| Dx<br />Eb
|-
| 3
| 189.47
| '''Major second (M2)'''<br />Doubly diminished third (dd3)
| '''E'''<br />Fbb
|-
| 4
| 252.63
| Augmented second (A2)<br />Diminished third (d3)
| E#<br />Fb
|-
| 5
| 315.79
| Doubly augmented second (AA2)<br />'''Minor third (m3)'''
| Ex<br />'''F'''
|-
| 6
| 378.95
| '''Major third (M3)'''<br />Doubly diminished fourth (dd4)
| '''F#'''<br />Gbb
|-
| 7
| 442.11
| Augmented third (A3)<br />Diminished fourth (d4)
| Fx<br />Gb
|-
| 8
| 505.26
| '''Perfect fourth (P4)'''
| '''G'''
|-
| 9
| 568.42
| Augmented fourth (A4)<br />Doubly diminished fifth (dd5)
| G#<br />Abb
|-
| 10
| 631.58
| Doubly augmented fourth (AA4)<br />Diminished fifth (d5)
| Gx<br />Ab
|-
| 11
| 694.74
| '''Perfect fifth (P5)'''
| '''A'''
|-
| 12
| 757.89
| Augmented fifth (A5)<br />Diminished sixth (d6)
| A#<br />Bbb
|-
| 13
| 821.05
| Doubly augmented fifth (AA5)<br />Minor sixth (m6)
| Ax<br />Bb
|-
| 14
| 884.21
| '''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)
| '''B'''<br />Cbb
|-
| 15
| 947.37
| Augmented sixth (A6)<br />Diminished seventh (d7)
| B#<br />Cb
|-
| 16
| 1010.53
| Doubly augmented sixth (AA6)<br />'''Minor seventh (m7)'''
| Bx<br />'''C'''
|-
| 17
| 1073.68
| Major seventh (M7)<br />Doubly diminished octave (dd8)
| C#<br />Dbb
|-
| 18
| 1136.84
| Augmented seventh (A7)<br />Diminished octave (d8)
| Cx<br />Db
|-
| 19
| 1200.00
| '''Perfect octave (P8)'''
| '''D'''
|}
In 19edo:
* [[Ups and downs notation]] is identical to standard notation;
* Mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (&#x266F;) and flats (&#x266D;) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.
{{Sharpness-sharp1}}
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[5edo#Sagittal notation|5]], [[12edo#Sagittal notation|12]], and [[26edo#Sagittal notation|26]], and is a subset of the notations for EDOs [[38edo#Sagittal notation|38]], [[57edo#Sagittal notation|57]], and [[76edo#Sagittal notation|76]].
==== Evo flavor ====
<imagemap>
File:19-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 327 0 487 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
default [[File:19-EDO_Evo_Sagittal.svg]]
</imagemap>
Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.
==== Revo flavor ====
<imagemap>
File:19-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 367 0 527 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
default [[File:19-EDO_Revo_Sagittal.svg]]
</imagemap>
=== Dodecatonic notation ===
{| class="wikitable right-1 right-2 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Dodecatonic Notation of 19edo
|-
! [[Degree]]
! [[Cent]]s
! Interval Names
|-
| 0
| 0.00
| P1
|-
| 1
| 63.16
| A1, m2
|-
| 2
| 126.32
| M2, m3
|-
| 3
| 189.47
| M3
|-
| 4
| 252.63
| m4, A3
|-
| 5
| 315.79
| M4, m5
|-
| 6
| 378.95
| M5
|-
| 7
| 442.11
| A5, d6
|-
| 8
| 505.26
| P6
|-
| 9
| 568.42
| A6, m7
|-
| 10
| 631.58
| M7, d8
|-
| 11
| 694.74
| P8
|-
| 12
| 757.89
| A8, m9
|-
| 13
| 821.05
| M9, m10
|-
| 14
| 884.21
| M10
|-
| 15
| 947.37
| m11, A10
|-
| 16
| 1010.53
| M11, m12
|-
| 17
| 1073.68
| M12
|-
| 18
| 1136.84
| A12, d13
|-
| 19
| 1200.00
| P13
|}
|}


Line 555: Line 231:
=== Interval mappings ===
=== Interval mappings ===
{{Q-odd-limit intervals|19}}
{{Q-odd-limit intervals|19}}
=== Zeta peak index ===
{{ZPI
| zpi = 65
| steps = 18.9480867166984
| step size = 63.3309324546460
| tempered height = 5.980169
| pure height = 5.214351
| integral = 1.313799
| gap = 16.699651
| octave = 1203.28771663827
| consistent = 10
| distinct = 7
}}
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -30 19 }}
| {{mapping| 19 30 }}
| +2.28
| 2.28
| 3.61
|-
| 2.3.5
| 81/80, 3125/3072
| {{mapping| 19 30 44 }}
| +2.58
| 1.91
| 3.02
|-
| 2.3.5.7
| 49/48, 81/80, 126/125
| {{mapping| 19 30 44 53 }}
| +3.85
| 2.76
| 4.35
|-
| 2.3.5.7.13
| 49/48, 65/64, 81/80, 91/90
| {{mapping| 19 30 44 53 70 }}
| +4.14
| 2.53
| 3.99
|-
| 2.3.5.7.13.23
| 49/48, 65/64, 70/69, 81/80, 91/90
| {{mapping| 19 30 44 53 70 86 }}
| +3.32
| 2.93
| 4.64
|}
* 19et is lower in relative error than any previous equal temperaments in the 5-, 7-, 13-, 17-, and 19-limit&mdash;''both'' 19 and 19e val achieve this in the case of 13-limit, 19eg val in the 17-limit, and 19egh val in the 19-limit. The next equal temperaments doing better in those subgroups are [[34edo|34]], [[31edo|31]], [[27edo|27e]], [[22edo|22]], and [[26edo|26]], respectively.
* 19et is best in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]].
=== Uniform maps ===
{{Uniform map|edo=19}}
=== Commas ===
19et [[tempering out|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"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cents]]
! [[Color notation/Temperament names|Color name]]
! Name
|-
| 3
| <abbr title="1162261467/1073741824">(20 digits)</abbr>
| {{monzo| -30 19 }}
| 137.14
| Trilawa
| [[19-comma]]
|-
| 5
| [[16875/16384]]
| {{monzo| -14 3 4 }}
| 51.12
| Laquadyo
| Negri comma
|-
| 5
| <abbr title="1594323/1562500">(14 digits)</abbr>
| {{monzo| -2 13 -8}}
| 34.91
| Laquadbigu
| [[Unicorn comma]]
|-
| 5
| [[3125/3072]]
| {{monzo| -10 -1 5 }}
| 29.61
| Laquinyo
| Magic comma
|-
| 5
| [[81/80]]
| {{monzo| -4 4 -1 }}
| 21.51
| Gu
| Syntonic comma
|-
| 5
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma
|-
| 5
| [[15625/15552]]
| {{monzo| -6 -5 6 }}
| 8.11
| Tribiyo
| Kleisma
|-
| 5
| <abbr title="1224440064/1220703125">(20 digits)</abbr>
| {{monzo| 8 14 -13 }}
| 5.29
| Thegu
| [[Parakleisma]]
|-
| 5
| <abbr title="19073486328125/19042491875328">(28 digits)</abbr>
| {{monzo| -14 -19 19 }}
| 2.82
| Neyo
| [[Enneadeca]]
|-
| 7
| [[59049/57344]]
| {{monzo| -13 10 0 -1 }}
| 50.72
| Laru
| Harrison's comma
|-
| 7
| [[1029/1000]]
| {{monzo| -3 1 -3 3 }}
| 49.49
| Trizogu
| Keega
|-
| 7
| [[525/512]]
| {{monzo| -9 1 2 1 }}
| 43.41
| Lazoyoyo
| Avicennma
|-
| 7
| [[49/48]]
| {{monzo| -4 -1 0 2 }}
| 35.70
| Zozo
| Semaphoresma, slendro diesis
|-
| 7
| [[3645/3584]]
| {{monzo| -9 6 1 -1 }}
| 29.22
| Laruyo
| Schismean comma
|-
| 7
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
| 7
| [[875/864]]
| {{monzo| -5 -3 3 1 }}
| 21.90
| Zotrigu
| Keema
|-
| 7
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.79
| Zotrigu
| Starling comma
|-
| 7
| [[225/224]]
| {{monzo| -5 2 2 -1 }}
| 7.71
| Ruyoyo
| Marvel comma
|-
| 7
| [[19683/19600]]
| {{monzo| -4 9 -2 -2 }}
| 7.32
| Labirugu
| Cataharry comma
|-
| 7
| [[10976/10935]]
| {{monzo| 5 -7 -1 3 }}
| 6.48
| Satrizo-agu
| Hemimage comma
|-
| 7
| [[3136/3125]]
| {{monzo| 6 0 -5 2 }}
| 6.08
| Zozoquingu
| Hemimean comma
|-
| 7
| <abbr title="703125/702464">(12 digits)</abbr>
| {{monzo| -11 2 7 -3 }}
| 1.63
| Latriru-asepyo
| [[Metric comma]]
|-
| 7
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
| 11
| [[45/44]]
| {{monzo| -2 2 1 0 -1 }}
| 38.91
| Luyo
| Undecimal fifth tone
|-
| 11
| [[56/55]]
| {{monzo| 3 0 -1 1 -1 }}
| 31.19
| Luzogu
| Undecimal tritonic comma
|-
| 11
| [[100/99]]
| {{monzo| 2 -2 2 0 -1 }}
| 17.40
| Luyoyo
| Ptolemisma
|-
| 11
| [[896/891]]
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle comma
|-
| 11
| [[65536/65219]]
| {{monzo| 16 0 0 -2 -3 }}
| 8.39
| Satrilu-aruru
| Orgonisma
|-
| 11
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
| 11
| [[540/539]]
| {{monzo| 2 3 1 -2 -1 }}
| 3.21
| Lururuyo
| Swetisma
|-
| 13
| [[39/38]]
| {{monzo| -1 1 0 0 0 1 0 -1 }}
| 44.97
| Nutho
| Undevicesimal two-ninth tone
|-
| 13
| [[65/64]]
| {{monzo| -6 0 1 0 0 1 }}
| 26.84
| Thoyo
| Wilsorma
|-
| 13
| [[343/338]]
| {{monzo| -1 0 0 3 0 -2 }}
| 25.42
| Thuthutrizo
|
|-
| 13
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
| 13
| [[676/675]]
| {{monzo| 2 -3 -2 0 0 2 }}
| 2.56
| Bithogu
| Island comma
|-
| 13
| [[1001/1000]]
| {{monzo| -3 0 -3 1 1 1 }}
| 1.73
| Tholozotrigu
| Fairytale comma, sinbadma
|-
| 23
| [[2187/2116]]
| {{monzo| -2 7 0 0 0 0 0 0 -2 }}
| 57.14
| Labitwethu
| Lipsett comma
|-
| 23
| [[70/69]]
| {{monzo| 1 -1 1 1 0 0 0 0 -}}
| 24.91
| Twethuzoyo
| Small vicesimotertial eighth tone
|-
| 23
| 256/253
| {{monzo| 8 0 0 0 -1 0 0 0 -1 }}
| 20.41
| Twethulu
| 253rd subharmonic
|-
| 23
| [[161/160]]
| {{monzo| -5 0 -1 1 0 0 0 0 1 }}
| 10.79
| Twethozogu
| Major kirnbergisma
|-
| 23
| [[208/207]]
| {{monzo| 4 -2 0 0 0 1 0 0 -1 }}
| 8.34
| Twethutho
| Vicetone comma
|-
| 23
| [[529/528]]
| {{monzo| -4 -1 0 0 -1 0 0 0 2 }}
| 3.28
| Bitwetho-alu
| Preziosisma
|-
| 23
| [[576/575]]
| {{monzo| 6 2 -2 0 0 0 0 0 -1 }}
| 3.01
| Twethugugu
| Worcester comma
|-
| 23
| [[1288/1287]]
| {{monzo| 3 -2 0 1 -1 -1 0 0 1 }}
| 1.34
| Twethothuluzo
| Triaphonisma
|}
=== Linear temperaments ===
* [[List of 19et rank two temperaments by badness]]
* [[List of 19et rank two temperaments by complexity]]
* [[List of edo-distinct 19et rank two temperaments]]
* [[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.
{| class="wikitable center-1 right-2 center-3"
|-
! Degree
! Cents
! Interval
! Mos scales
! Temperaments
|-
| 1
| 63.16
| A1, d2
|
| [[Unicorn]] / [[Rhinoceros]]
|-
| 2
| 126.32
| m2
| [[1L&nbsp;8s]], [[9L&nbsp;1s]]
| [[Negri]]
|-
| 3
| 189.47
| M2
| [[1L&nbsp;5s]], [[6L&nbsp;1s]], [[6L&nbsp;7s]]
| [[Deutone]]<br>[[Spell]]
|-
| 4
| 252.63
| A2, d3
| [[1L&nbsp;3s]], [[4L&nbsp;1s]], <br>[[5L&nbsp;4s]], [[5L&nbsp;9s]]
| [[Godzilla]]
|-
| 5
| 315.79
| m3
| [[3L&nbsp;1s]], [[4L&nbsp;3s]], <br>[[4L&nbsp;7s]], [[4L&nbsp;11s]]
| [[Cata]] / [[keemun]]
|-
| 6
| 378.95
| M3
| [[3L&nbsp;1s]], [[3L&nbsp;4s]], [[3L&nbsp;7s]], <br>[[3L&nbsp;10s]], [[3L&nbsp;13s]]
| [[Magic]] / [[muggles]]
|-
| 7
| 442.11
| A3, d4
| [[3L&nbsp;2s]], [[3L&nbsp;5s]], [[8L&nbsp;3s]]
| [[Sensi]]
|-
| 8
| 505.26
| P4
| [[2L&nbsp;3s]], [[5L&nbsp;2s]], [[7L&nbsp;5s]]
| [[Meantone]] / [[flattone]]
|-
| 9
| 568.42
| A4
| [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], <br>[[2L&nbsp;9s]], [[2L&nbsp;11s]], [[2L&nbsp;13s]], <br>[[2L&nbsp;15s]]
| [[Liese]] / [[pycnic]]<br>[[Triton]]
|}
== Scales ==
=== MOS scales ===
{{Main|List of MOS scales in {{PAGENAME}}}}
==== Octave-equivalent mosses ====
* [[meantone]] pentatonic, [[2L 3s]] (gen = 11\19): 3 3 5 3 5
* [[meantone]] diatonic, [[5L 2s]] (gen = 11\19): 3 3 2 3 3 3 2
* [[meantone]] chromatic, [[7L 5s]] (gen = 11\19): 2 1 2 1 2 2 1 2 1 2 1 2
* [[semaphore]][5], [[4L 1s]] (gen = 4\19): 4 4 3 4 4
* [[semaphore]][9], [[5L 4s]] (gen = 4\19): 3 1 3 1 3 3 1 3 1
* [[semaphore]][14], [[5L 9s]] (gen = 4\19): 2 1 2 1 1 2 1 1 2 1 1 2 1 1
* [[sensi]][5], [[2L 3s]] (gen = 7\19): 5 2 5 2 5
* [[sensi]][8], [[3L 5s]] (gen = 7\19): 2 3 2 2 3 2 2 3
* [[sensi]][11], [[8L 3s]] (gen = 7\19): 2 2 1 2 2 2 1 2 2 2 1
* [[negri]][9], [[1L 8s]] (gen = 2\19): 2 2 2 2 3 2 2 2 2
* [[negri]][10], [[9L 1s]] (gen = 2\19): 2 2 2 2 2 1 2 2 2 2
* [[kleismic]][7], [[4L 3s]] (gen = 5\19): 1 4 1 4 1 4 4
* [[kleismic]][11], [[4L 7s]] (gen = 5\19): 1 3 1 1 3 1 1 3 1 3 1
* [[kleismic]][15], [[4L 11s]] (gen = 5\19): 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1
* [[magic]][7], [[3L 4s]] (gen = 6\19): 5 1 5 1 5 1 1
* [[magic]][10], [[3L 7s]] (gen = 6\19): 4 1 1 4 1 1 4 1 1 1
* [[magic]][13], [[3L 10s]] (gen = 6\19): 3 1 1 1 3 1 1 1 3 1 1 1 1
* [[magic]][16], [[3L 13s]] (gen = 6\19): 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1
* [[liese]][17], [[2L 15s]] (gen = 9\19): 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
=== Other scales ===
* Meantone harmonic minor: 3 2 3 3 2 4 2
* Meantone melodic minor: 3 2 3 3 3 3 2
* Meantone harmonic major: 3 3 2 3 2 4 2
* chromatic octave species - Meantone / [[marvel double harmonic major]] (subset of Negri[9]): 2 4 2 3 2 4 2
* chromatic octave species (subset of Negri[9]): 2 2 4 3 2 2 4
* chromatic octave species - [[Sahara]] septatonic (subset of Negri[9]): 4 2 2 3 4 2 2
* [[Marvel hexatonic]] (subset of Negri[9]): 4 2 5 2 4 2
* enharmonic pentatonic: 2 6 3 2 6
* enharmonic pentatonic: 6 2 3 6 2
* enharmonic octave species: 1 1 6 3 1 1 6
* enharmonic octave species: 6 1 1 3 6 1 1
* enharmonic octave species: 1 6 1 3 1 6 1
* [[Pinetone#Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 3 2 3 1 2 3 2 3 (subset of Meantone[12])
* [[Pinetone#Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 3 2 1 3 2 3 3 2 (subset of Meantone[12])
* [[Pinetone#Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 2 3 1 3 2 3 2 3
* [[Pinetone#Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 2 3 1 4 1 3 2 3
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of Meantone[7]): 1 2 3 2 1 2 3 2 1 2
* [[Antipental blues]]: 4 4 1 2 4 4
* [[Semiquartal]] 3|5 b2: 1 3 3 1 3 1 3 3 1
* [[5-odd-limit]] tonality diamond: 5 1 2 3 2 1 5
* [[7-odd-limit]] tonality diamond: 4 1 1 2 1 1 1 2 1 1 4
* [[9-odd-limit]] tonality diamond: 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3
== Instruments ==
[[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]]
== Music ==
{{Main| 19edo/Music }}
{{Catrel| 19edo tracks }}
; [http://micro.soonlabel.com/19-ET/ XA 19-ET Index]
; A number of compositions that were perfomed at the [http://midwestmicrofest.org/concerts.html midwestmicrofest concert in 2007]{{dead link}}
== See also ==
* [[19edo modes]]
* [[19edo chords]]
* [[Strictly proper 19edo scales]]
* [[How to tune a 19edo guitar by ear]]
* [[Primer for 19edo]]
* [[Mason Green's New Common Practice Notation]]
* [[Extraclassical tonality]]
* [[Lumatone mapping for 19edo]]
== Further reading ==
* [[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).
* 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.
* [[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.
== 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://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].
* [[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]
=== Notes ===
<references group="note" />
=== References ===
* 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.
[[Category:19-tone scales]]
[[Category:19-tone scales]]
[[Category:Godzilla]]
[[Category:Godzilla]]
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