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19edo is the 8th [[prime edo]], following [[17edo]] and preceding [[23edo]]. As such, it does not contain any nontrivial subset edos, though it contains [[19ed4]].  
19edo is the 8th [[prime edo]], following [[17edo]] and preceding [[23edo]]. As such, it does not contain any nontrivial subset edos, though it contains [[19ed4]].  


[[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. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best.  
 
Large edos like [[190edo]], [[494edo]], [[665edo]], [[836edo]], [[1178edo]], and many others, contain 19edo and also exhibit high consistency in higher limits. These are also notable because they still temper out the [[enneadeca]], which preserves the precise [[6/5]] mapping 19edo has while improving upon it with microtemperaments.
 
See [[19th-octave temperaments]] for a detailed overview.


=== Miscellaneous properties ===
=== Miscellaneous properties ===
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== Intervals ==
== Intervals ==
{| class="wikitable right-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! [[Degree|#]]
! [[Degree|#]]
! [[Cent]]s
! [[Cent]]s
! [[Interval category|Interval categories]]
! Note
! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament.</ref>
! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament</ref>
! [[Interval category]]
|-
|-
| 0
| 0
| 0.0
| 0.0
| D
| [[1/1]]
| Unison (prime)
| Unison (prime)
| [[1/1]]
|-
|-
| 1
| 1
| 63.2
| 63.2
| D♯
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Augmented unison
| Augmented unison
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
|-
|-
| 2
| 2
| 126.3
| 126.3
| E♭
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| Minor second
| Minor second
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
|-
|-
| 3
| 3
| 189.5
| 189.5
| E
| [[9/8]], [[10/9]]
| Major second
| Major second
| [[9/8]], [[10/9]]
|-
|-
| 4
| 4
| 252.6
| 252.6
| Augmented second<br>Diminished third
| E♯/F♭
| [[7/6]], [[8/7]], [[15/13]]
| [[7/6]], [[8/7]], [[15/13]]
| Augmented second/<br>Diminished third
|-
|-
| 5
| 5
| 315.8
| 315.8
| F
| [[6/5]]
| Minor third
| Minor third
| [[6/5]]
|-
|-
| 6
| 6
| 378.9
| 378.9
| F♯
| [[5/4]], [[16/13]], [[56/45]]
| Major third
| Major third
| [[5/4]], [[16/13]], [[56/45]]
|-
|-
| 7
| 7
| 442.1
| 442.1
| Augmented third
| F𝄪/G♭
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
| Augmented third/<br>Diminished fourth
|-
|-
| 8
| 8
| 505.3
| 505.3
| G
| [[4/3]], [[75/56]]
| Perfect fourth
| Perfect fourth
| [[4/3]], [[75/56]]
|-
|-
| 9
| 9
| 568.4
| 568.4
| G♯
| [[7/5]], [[18/13]], [[25/18]]
| Augmented fourth<br>(Small [[tritone]])
| Augmented fourth<br>(Small [[tritone]])
| [[7/5]], [[18/13]], [[25/18]]
|-
|-
| 10
| 10
| 631.6
| 631.6
| A♭
| [[10/7]], [[13/9]], [[36/25]]
| Diminished fifth<br>(Large [[tritone]])
| Diminished fifth<br>(Large [[tritone]])
| [[10/7]], [[13/9]], [[36/25]]
|-
|-
| 11
| 11
| 694.7
| 694.7
| A
| [[3/2]], [[112/75]]
| Perfect fifth
| Perfect fifth
| [[3/2]], [[112/75]]
|-
|-
| 12
| 12
| 757.9
| 757.9
| Augmented fifth
| A♯/B𝄫
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
| Augmented fifth/<br>Diminished sixth
|-
|-
| 13
| 13
| 821.1
| 821.1
| B♭
| [[8/5]], [[13/8]], [[45/28]]
| Minor sixth
| Minor sixth
| [[8/5]], [[13/8]], [[45/28]]
|-
|-
| 14
| 14
| 884.2
| 884.2
| B
| [[5/3]]
| Major sixth
| Major sixth
| [[5/3]]
|-
|-
| 15
| 15
| 947.4
| 947.4
| B♯/C♭
| [[7/4]], [[12/7]], [[26/15]]
| Augmented sixth<br>Diminished seventh
| Augmented sixth<br>Diminished seventh
| [[7/4]], [[12/7]], [[26/15]]
|-
|-
| 16
| 16
| 1010.5
| 1010.5
| C
| [[9/5]], [[16/9]]
| Minor seventh
| Minor seventh
| [[9/5]], [[16/9]]
|-
|-
| 17
| 17
| 1073.7
| 1073.7
| C♯
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| Major seventh
| Major seventh
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
|-
|-
| 18
| 18
| 1136.8
| 1136.8
| D♭
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Augmented seventh
| Augmented seventh
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
|-
|-
| 19
| 19
| 1200.0
| 1200.0
| D
| [[2/1]]
| Octave
| Octave
| [[2/1]]
|}
|}
<references group="note"/>
<references group="note"/>
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For a more complete list, see [[19edo chords #Ups and downs notation]] and [[Kite's ups and downs notation #Chords and chord progressions]].
For a more complete list, see [[19edo chords #Ups and downs notation]] and [[Kite's ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
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[[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]]
Several [[Lumatone mapping for 19edo|Lumatone mappings for 19edo]] are available.


== Music ==
== Music ==
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* [[Mason Green's New Common Practice Notation]]
* [[Mason Green's New Common Practice Notation]]
* [[Extraclassical tonality]]
* [[Extraclassical tonality]]
* [[Lumatone mapping for 19edo]]
 


== Further reading ==
== Further reading ==
* [[Mandelbaum, Joel]]. ''[https://anaphoria.com/mandelbaum.html Multiple Division of the Octave and the Tonal Resources of 19-tone Temperament]''. 1961.
* [[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. ''[https://microstick.net/nineteen-for-the-nineties-by-ivor-darreg/ Nineteen for the Nineties]''. (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. [https://huberthowe.org/tone-theory/ 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://archive.org/details/theoryofevolving0000jose Theory of Evolving Tonality]''. 1932.


== External links ==
== External links ==
Line 1,165: Line 1,194:
* [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/khereb/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]


=== References ===
=== References ===
* Bucht, Saku and Huovinen, Erkki, ''Perceived consonance of harmonic intervals in 19-tone equal temperament'', CIM04_proceedings.
* Bucht, Saku and Huovinen, Erkki, [https://www.parncutt.org/CIM04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf ''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.


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