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{{interwiki
{{interwiki
| de = 19edo
| de = 19-EDO
| en = 19edo
| en = 19edo
| es =  
| es = 19 EDO
| ja = 19平均律
| ja = 19平均律
}}
}}
{{Infobox ET
{{Infobox ET}}
| Prime factorization = 19
{{Wikipedia|19 equal temperament}}
| Subgroup = 2.3.5.7.13
{{ED intro}}
| Step size = 63.158
 
| Fifth type = [[Meantone]] 11\19 694.737¢ (-7.218¢)
== History ==
| Common uses = extended third-comma meantone, semaphore
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.
| Important MOS = [[meantone]] diatonic 5*3-2*2 (11\19, 1\1)<br/>[[semaphore]] 5*3-4*1 (4\19, 1\1)<br/>[[sensi]] 3*3-5*2 (7\19, 1\1)
}}


In music, '''19 equal temperament''', called 19-TET, 19-[[EDO]], or 19-ET, is the scale derived by dividing the [[octave]] into 19 [[Equal|equally]] large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[cent|cents]]. It is the 8th [[prime numbers|prime]] [[prime EDO|edo]], following [[17edo]] and coming before [[23edo]].
In 1577, music theorist Francisco de Salinas proposed [[1/3-comma meantone]], in which the fifth is 694.786{{c}}; the fifth of 19edo is 694.737{{c}}, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which comes within less than one cent of closing exactly, so that his suggestion is effectively 19edo.
 
In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).


== Theory ==
== Theory ==
=== History ===
19edo is the second edo, after [[12edo]], which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.


Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts.  Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.
It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.  


In 1577 music theorist Francisco de Salinas proposed [[1-3 Syntonic Comma Meantone|1/3-comma meantone]], in which the fifth is of size 694.786 cents; the fifth of 19-et is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which fails to close by less than a cent, so that his suggestion is effectively 19edo.
=== Prime harmonics ===
{{Harmonics in equal|19|columns=12}}


In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).
=== As an approximation of other temperaments ===
Besides meantone, 19edo is also suitable for [[magic]]/[[muggles]] temperament, because five of its major thirds are equivalent to one of its twelfths. Its 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 major sixth.  


=== As an approximation of other temperaments ===
For all of these there are more optimal tunings: the fifth of 19edo is flatter than the usual for meantone, and [[31edo]] is more optimal. Similarly, the generating interval of magic temperament is a major third, and again 19edo's is flatter; [[41edo]] more closely matches it. It does make for a good tuning for muggles, but in 19edo it is the same as magic. Finally, 19edo can be used as a tuning for sensi, though [[46edo]] provides a better sensi tuning.


The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone family|meantone]] temperament. It is also suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its ''twelfths.'' For all of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic. 19edo's 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 minor sixth, though [[27edo]] and [[46edo]] are better sensi tunings.
However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built. 19edo also has the advantage of being excellent for [[negri]], [[keemun]], [[godzilla]], muggles, and [[triton]]/[[liese]]. Keemun and negri are of particular note for being very simple 7-limit temperaments, with their [[mos scale]]s in 19edo offering a great abundance of septimal tetrads. The [[Graham complexity]] of the [[4:5:6:7|7-odd-limit tetrad]] is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles, and 13 for sensi.


However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7/6]]), and a septimal whole tone ([[8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi.
=== As a means of extending harmony ===
Because 19edo's 5-limit chords are more blended and concordant than those of 12edo, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. [[William Lynch]] suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non-diatonic chord extensions which tend to clash in 12edo blend much better in 19edo.


Being a zeta integral tuning, the 13-limit is represented relatively well, though only the 2.3.5.7.13 subgroup is represented [[consistent]]ly. Practically 19-edo can be used ''adaptively'' on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th and 13th harmonics are all tuned flat. The same cannot be said of 12edo, in which the 5th and 7th are - not only farther than they are in 19, but fairly sharp already. 19edo's [[negri]], [[sensi]] and [[semaphore]] scales have many 13-limit chords. (You can think of the sensi[8] [[3L 5s]] [[MOS]] scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but sensi[8] gives you additional ratios of 7 and 13.)
In addition, [[Joseph Yasser]] talks about the idea of a 12-tone supra-diatonic scale where the 7-tone major scale in 19edo becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased "A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe." Yasser believed that music would eventually move to a 19-tone system with a 12-note supra-diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend tonality without sounding too alien.


Another option would be to use a stretched octave; the [[The Riemann Zeta Function and Tuning|zeta function]]-optimal tuning has an octave of roughly 1203 cents. Stringed instruments, in particular the piano, are frequently tuned with stretched octaves anyway due to the inharmonicity inherent in strings, which makes 19edo a promising option for them. Octave stretching also means that an out-of-tune interval can be replaced with a compounded or inverted version of it which is near-just. For instance, if we're using [[93ed30]] (a variant of 19edo in which 30:1 is just), then we have near-just minor thirds (6:5), compound major thirds (as 5:1), and compound fifths (as 6:1), giving us versions of everything in the 5-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well.
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.


=== As a means of extending harmony ===
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.


Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. William Lynch suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non diatonic chord extensions which tend to clash in 12 EDO blend much better in 19 EDO.
=== Adaptive tuning ===
The no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L&nbsp;5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].


In addition, Joseph Yasser talks about the idea of a 12 tone supra diatonic scale where the 7 tone major scale in 19 EDO becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased "A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe. " Yasser believed that music would eventually move to a 19 tone system with a 12 note supra diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend tonality without sounding too alien.
Practically 19edo can be used ''adaptively'' on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th, and 13th harmonics are all tuned flat. This is in contrast to 12edo, where this is not possible since the 5th and 7th harmonics are not only much farther from just than they are in 19edo, but fairly sharp already.  


19 EDO 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 19 EDO.
Another option would be to use [[octave stretching]], which has similar benefits to adaptive use, but it also works for fixed-pitch Instruments. For more on that see the [[19edo#Octave stretch or compression|section on octave stretch]].


The narrow whole tones and wide diatonic semitones of 19edo give the diatonic scale a somewhat duller quality, but has the opposite effect on the pentatonic scale, which becomes much more expressive owing to the 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.
=== Subsets and supersets ===
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]].  


== Intervals ==
[[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]].


Standard 12edo notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes.
=== Miscellaneous properties ===
19edo has the flattest possible fifth of any edo that can possibly be [[diamond monotone]] in the [[15-odd-limit]]. Using 11\19 as the fifth, the sharpest possible mapping of [[5/4]] where [[10/9]] is no greater than [[9/8]] is 6\19, so the sharpest possible [[15/8]] is 17\19. Here [[16/15]] is a quarter of [[4/3]] (as in any [[negri]] tuning), so [[15/14]], [[14/13]], and [[13/12]] must all be equated with [[16/15]] to 2\19 for them to be monotone in size. If the fifth were any flatter, 5/4 and 15/8 would have to be flatter, and 16/15 would have to be sharper, so diamond monotone in the 15-odd-limit becomes impossible. 19edo is, in fact, diamond monotone in the 15-odd-limit, and even the [[17-odd-limit]] (see [[Monotonicity limits of small EDOs]]). The sharpest fifth where 15-odd-limit is possible is [[37edo#Miscellaneous properties|22\37]].


{| class="wikitable right-1 right-2 center-4 center-6 center-7"
== Intervals ==
! Degree
{| class="wikitable center-1 right-2"
! Cents
|-
! colspan="3" | Interval
! [[Degree|#]]
! Solfege
! [[Cent]]s
! Dodecatonic notation
! Note
! Ratios*
! 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
| 0.0000
| 0.0
| unison
| P1
| D
| D
| do
| [[1/1]]
| P1
| Unison (prime)
| 1/1
|-
|-
| 1
| 1
| 63.1579
| 63.2
| aug 1sn, dim 2nd
| D♯
| A1, d2
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| D#, Ebb
| Augmented unison
| di
| A1, m2
| [[25/24]], [[28/27]], [[26/25]]
|-
|-
| 2
| 2
| 126.3157
| 126.3
| minor 2nd
| E♭
| m2
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| Eb
| Minor second
| ra
| M2, m3
| [[15/14]], [[16/15]], [[13/12]], [[14/13]]
|-
|-
| 3
| 3
| 189.4737
| 189.5
| major 2nd
| M2
| E
| E
| re
| [[9/8]], [[10/9]]
| M3
| Major second
| [[9/8]], [[10/9]], [[6272/5625]]
|-
|-
| 4
| 4
| 252.6316
| 252.6
| aug 2nd, dim 3rd
| E♯/F♭
| A2, d3
| E#, Fb
| ri/ma
| m4, a3
| [[7/6]], [[8/7]], [[15/13]]
| [[7/6]], [[8/7]], [[15/13]]
| Augmented second/<br>Diminished third
|-
|-
| 5
| 5
| 315.7895
| 315.8
| minor 3rd
| m3
| F
| F
| me
| M4, m5
| [[6/5]]
| [[6/5]]
| Minor third
|-
|-
| 6
| 6
| 378.9474
| 378.9
| major 3rd
| F♯
| M3
| F#
| mi
| M5
| [[5/4]], [[16/13]], [[56/45]]
| [[5/4]], [[16/13]], [[56/45]]
| Major third
|-
|-
| 7
| 7
| 442.1053
| 442.1
| aug 3rd, dim 4th
| F𝄪/G♭
| A3, d4
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
| Fx, Gb
| Augmented third/<br>Diminished fourth
| mo
| A5, d6
| [[32/25]], [[9/7]], [[13/10]]
|-
|-
| 8
| 8
| 505.2632
| 505.3
| perfect 4th
| P4
| G
| G
| fa
| P6
| [[4/3]], [[75/56]]
| [[4/3]], [[75/56]]
| Perfect fourth
|-
| 9
| 568.4
| G♯
| [[7/5]], [[18/13]], [[25/18]]
| Augmented fourth<br>(Small [[tritone]])
|-
| 10
| 631.6
| A♭
| [[10/7]], [[13/9]], [[36/25]]
| Diminished fifth<br>(Large [[tritone]])
|-
| 11
| 694.7
| A
| [[3/2]], [[112/75]]
| Perfect fifth
|-
| 12
| 757.9
| A♯/B𝄫
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
| Augmented fifth/<br>Diminished sixth
|-
| 13
| 821.1
| B♭
| [[8/5]], [[13/8]], [[45/28]]
| Minor sixth
|-
| 14
| 884.2
| B
| [[5/3]]
| Major sixth
|-
| 15
| 947.4
| B♯/C♭
| [[7/4]], [[12/7]], [[26/15]]
| Augmented sixth<br>Diminished seventh
|-
| 16
| 1010.5
| C
| [[9/5]], [[16/9]]
| Minor seventh
|-
| 17
| 1073.7
| C♯
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| Major seventh
|-
| 18
| 1136.8
| D♭
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Augmented seventh
|-
| 19
| 1200.0
| D
| [[2/1]]
| Octave
|}
<references group="note"/>
=== Proposed interval names and solfèges ===
{| class="wikitable right-1 right-2 center-3 center-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! [[Solfège]]
! colspan="2" | [[SKULO interval names]]
|-
| 0
| 0.0
| Do
| Unison
| P1
|-
| 1
| 63.2
| Di/Ro
| Super unison, subminor second
| S1, sm2
|-
| 2
| 126.3
| Ra
| Minor second
| m2
|-
| 3
| 189.5
| Re
| Major second
| M2
|-
| 4
| 252.6
| Ri/Ma
| Supermajor second, subminor third
| SM2, sm3
|-
| 5
| 315.8
| Me
| Minor third
| m3
|-
| 6
| 378.9
| Mi
| Major third
| M3
|-
| 7
| 442.1
| Mo/Fe
| Supermajor third, sub fourth
| SM3, s4
|-
| 8
| 505.3
| Fa
| Perfect fourth
| P4
|-
|-
| 9
| 9
| 568.4211
| 568.4
| aug 4th
| Fi
| Augmented fourth
| A4
| A4
| G#
| fi
| A6, m7
| [[25/18]], [[7/5]], [[18/13]]
|-
|-
| 10
| 10
| 631.5789
| 631.6
| dim 5th
| Se
| Diminished fifth
| d5
| d5
| Ab
| se
| M7, d8
| [[36/25]], [[10/7]], [[13/9]]
|-
|-
| 11
| 11
| 694.7368
| 694.7
| perfect 5th
| So
| Perfect fifth
| P5
| P5
| A
| sol
| P8
| [[3/2]], [[112/75]]
|-
|-
| 12
| 12
| 757.8947
| 757.9
| aug 5th, dim 6th
| Si/Lo
| A5, d6
| Super fifth, subminor sixth
| A#, Bbb
| S5, sm6
| lo
| A8, m9
| [[25/16]], [[14/9]], [[20/13]]
|-
|-
| 13
| 13
| 821.0526
| 821.1
| minor 6th
| Le
| Minor sixth
| m6
| m6
| Bb
| le
| M9, m10
| [[8/5]], [[13/8]], 45/28
|-
|-
| 14
| 14
| 884.2105
| 884.2
| major 6th
| La
| Major sixth
| M6
| M6
| B
| la
| M10
| [[5/3]]
|-
|-
| 15
| 15
| 947.3684
| 947.4
| aug 6th, dim 7th
| Li/Ta
| A6, d7
| Supermajor sixth, subminor seventh
| B#, Cb
| SM6, sm7
| li/ta
| m11, A10
| [[7/4]], [[12/7]], [[26/15]]
|-
|-
| 16
| 16
| 1010.5263
| 1010.5
| minor 7th
| Te
| Minor seventh
| m7
| m7
| C
| te
| M11, m12
| [[9/5]], [[16/9]], [[5625/3136]]
|-
|-
| 17
| 17
| 1073.6843
| 1073.7
| major 7th
| Ti
| Major seventh
| M7
| M7
| C#
| ti
| M12
| [[15/8]], [[13/7]], [[28/15]], [[24/13]]
|-
|-
| 18
| 18
| 1136.8421
| 1136.8
| aug 7th, dim 8ve
| To/Da
| A7, d8
| Supermajor seventh, sub octave
| Cx, Db
| SM7, s8
| da
| A12, d13
| [[48/25]], [[27/14]], [[25/13]]
|-
|-
| 19
| 19
| 1200.0000
| 1200.0
| perfect 8ve
| Do
| Octave
| P8
| P8
| D
| do
| P13
| [[2/1]]
|}
|}
<nowiki>*</nowiki> based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.


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


{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center;"
! quality
! [[color name]]
! monzo format
! examples
|-
|-
| diminished
! Quality
! Color name
! Monzo format
! Examples
|-
| Diminished
| zo
| zo
| {a, b, 0, 1}
| {{nowrap|(''a'', ''b'', 0, 1)}}
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| minor
| rowspan="2" | Minor
| fourthward wa
| fourthward wa
| {a, b}, b &lt; -1
| (''a'',&nbsp;''b''), {{nowrap|''b'' < −1}}
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| "
| gu
| gu
| {a, b, -1}
| {{nowrap|(''a'', ''b'', −1)}}
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| major
| rowspan="2" | Major
| yo
| yo
| {a, b, 1}
| {{nowrap|(''a'', ''b'', 1)}}
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| "
| fifthward wa
| fifthward wa
| {a, b}, b &gt; 1
| (''a'',&nbsp;''b''), {{nowrap| ''b'' > 1 }}
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| augmented
| Augmented
| ru
| ru
| {a, b, 0, -1}
| {{nowrap|(''a'', ''b'', 0, −1)}}
| 9/7, 12/7
| 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 Bbb would have double-flats on B and E, and flats on C, D, F, G, and A. Thinking of rewriting this key as A# 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.
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𝄫 would have double-flats on B and E, and flats on C, D, F, G, and A. Thinking of rewriting this key as A♯ 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.


== Chord Names ==
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished seconds, thirds, sixths and sevenths. Here are the zo, gu, yo and ru triads:
 
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"
{| class="wikitable center-1 center-2 center-3 center-4"
! [[Kite's color notation|color of the 3rd]]
|-
! Color of the third
! JI chord
! JI chord
! notes as edosteps
! Edosteps
! notes of C chord
! Notes of C chord
! written name
! Written name
! spoken name
! Spoken name
|-
|-
| zo
| zo (7-over)
| 6:7:9
| 6:7:9
| 0-4-11
| 0–4–11
| C Ebb G
| C–E𝄫–G
| C(b3) or C(d3)
| Cm(♭3) or Cmin(♭3) or C(d3)
| C flat-three or C dim-three
| C subminor, C minor flat-three, C dim-three
|-
|-
| gu
| gu (5-under)
| 10:12:15
| 10:12:15
| 0-5-11
| 0–5–11
| C Eb G
| C–E♭–G
| Cm
| Cm or Cmin
| C minor
| C minor
|-
|-
| yo
| yo (5-over)
| 4:5:6
| 4:5:6
| 0-6-11
| 0–6–11
| C E G
| C–E–G
| C
| C or Cmaj
| C major or C
| C, C major
|-
|-
| ru
| ru (7-under)
| 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 Cmaj(♯3) or C(A3)
| C sharp-three or C aug-three
| C supermajor, C major sharp-three, C aug-three
|-
| yo (5-over)
| 4:5:6:7
| 0–6–11–15
| C–E–G–B𝄫
| Ch7 or C,d7 or Cadd(d7)
| C harmonic 7, C (major) add dim-seven
|-
| gu (5-under)
| 1/(12:10:8:7)<br>(1–6/5–3/2–12/7)
| 0–5–11–15
| C–E♭–G–A♯
| Cm♯6 or CmA6 or Cm(add(♯6)) or Cm(add(A6))
| C minor (add) sharp-six, C minor (add) aug-six
|}
|}


0-6-11-15 = C E G Bbb = C,bb7 or C,d7 = C double-flat-seven or C major dim-seven or C add dim-seven = 4:5:6:7
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.


0-5-11-15 = C Eb G A# is Cm,#6 or Cm,A6 = C minor sharp-six or C minor aug-six = 1/(4:5:6:7) = 1/1 - 6/5 - 3/2 - 12/7
For a more complete list, see [[19edo chords #Ups and downs notation]] and [[Kite's ups and downs notation #Chords and chord progressions]].


The last two chords illustrate how the 15\19 interval can be considered as either 7/4 or 12/7, and how 19edo tends to conflate zo and ru ratios.


For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|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), solfège, or sargam. Note that D# and Eb are two different notes.


== Just approximation ==
Any 19edo note or interval can be [[enharmonic unison|respelled enharmonically]] by adding a double-diminished second 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.


=== Selected just intervals by error ===
{| class="wikitable right-1 right-2 center-3 center-4"
 
|+ style="font-size: 105%;" | Notation of 19edo
{| class="wikitable" style="text-align:center;"
! colspan="2" |
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 23
|-
|-
! rowspan="2" | Error
! rowspan="2" | [[Degree|#]]
! absolute ([[cent|¢]])
! rowspan="2" | [[Cent]]s
| 0.0
! colspan="2" | [[Chain-of-fifths notation|Standard notation]]
| -7.2
| -7.4
| -21.5
| +17.1
| -19.5
| +3.3
|-
|-
! [[Relative error|relative]] (%)
! [[5L 2s|Diatonic interval names]]
| 0.0
! Note names<br>on D
| -11.4
| -11.7
| -34.0
| +27.1
| -30.8
| +5.2
|-
|-
! colspan="2" | [[fifthspan]]
| 0
| 0
| +1
| 0.0
| +4
| '''Perfect unison (P1)'''
| -9
| '''D'''
| +6
| -4
| -6
|}
 
==== 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''. 
 
{| class="wikitable center-1 right-2"
|+Direct mapping (even if inconsistent)
! Interval, complement
! Error (abs, [[cent|¢]])
|-
|-
| [[6/5]], [[5/3]]
| 1
| 0.148
| 63.2
| Augmented unison (A1)<br>Diminished second (d2)
| D#<br>Ebb
|-
|-
| [[14/13]], [[13/7]]
| 2
| 1.982
| 126.3
| Doubly augmented unison (AA1)<br>Minor second (m2)
| Dx<br>Eb
|-
|-
| [[15/13]], [[26/15]]
| 3
| 4.891
| 189.5
| '''Major second (M2)'''<br>Doubly diminished third (dd3)
| '''E'''<br>Fbb
|-
|-
| [[18/13]], [[13/9]]
| 4
| 5.039
| 252.6
| Augmented second (A2)<br>Diminished third (d3)
| E#<br>Fb
|-
|-
| [[15/14]], [[28/15]]
| 5
| 6.873
| 315.8
| Doubly augmented second (AA2)<br>'''Minor third (m3)'''
| Ex<br>'''F'''
|-
|-
| [[9/7]], [[14/9]]
| 6
| 7.021
| 378.9
| '''Major third (M3)'''<br>Doubly diminished fourth (dd4)
| '''F#'''<br>Gbb
|-
|-
| [[10/9]], [[9/5]]
| 7
| 7.070
| 442.1
| Augmented third (A3)<br>Diminished fourth (d4)
| Fx<br>Gb
|-
|-
| '''[[4/3]], [[3/2]]'''
| 8
| '''7.218'''
| 505.3
| '''Perfect fourth (P4)'''
| '''G'''
|-
|-
| '''[[5/4]], [[8/5]]'''
| 9
| '''7.366'''
| 568.4
| Augmented fourth (A4)<br>Doubly diminished fifth (dd5)
| G#<br>Abb
|-
|-
| [[13/10]], [[20/13]]
| 10
| 12.109
| 631.6
| Doubly augmented fourth (AA4)<br>Diminished fifth (d5)
| Gx<br>Ab
|-
|-
| [[13/12]], [[24/13]]
| 11
| 12.257
| 694.7
| '''Perfect fifth (P5)'''
| '''A'''
|-
|-
| [[7/5]], [[10/7]]
| 12
| 14.091
| 757.9
| Augmented fifth (A5)<br>Diminished sixth (d6)
| A#<br>Bbb
|-
|-
| [[7/6]], [[12/7]]
| 13
| 14.239
| 821.1
| Doubly augmented fifth (AA5)<br>Minor sixth (m6)
| Ax<br>Bb
|-
|-
| [[9/8]], [[16/9]]
| 14
| 14.436
| 884.2
| '''Major sixth (M6)'''<br>Doubly diminished seventh (dd7)
| '''B'''<br>Cbb
|-
|-
| [[16/15]], [[15/8]]
| 15
| 14.585
| 947.4
| Augmented sixth (A6)<br>Diminished seventh (d7)
| B#<br>Cb
|-
|-
| '''[[11/8]], [[16/11]]'''
| 16
| '''17.103'''
| 1010.5
| Doubly augmented sixth (AA6)<br>'''Minor seventh (m7)'''
| Bx<br>'''C'''
|-
|-
| '''[[16/13]], [[13/8]]'''
| 17
| '''19.475'''
| 1073.7
| Major seventh (M7)<br>Doubly diminished octave (dd8)
| C#<br>Dbb
|-
|-
| '''[[8/7]], [[7/4]]'''
| 18
| '''21.457'''
| 1136.8
| Augmented seventh (A7)<br>Diminished octave (d8)
| Cx<br>Db
|-
|-
| [[12/11]], [[11/6]]
| 19
| 24.321
| 1200.0
|-
| '''Perfect octave (P8)'''
| [[11/10]], [[20/11]]
| '''D'''
| 24.469
|-
| ''[[14/11]], [[11/7]]''
| ''24.597''
|-
| ''[[13/11]], [[22/13]]''
| ''26.580''
|-
| ''[[15/11]], [[22/15]]''
| ''31.470''
|-
| [[11/9]], [[18/11]]
| 31.539
|}
|}


{| class="wikitable center-1 right-2"
In 19edo:
|+Patent val mapping
* [[Ups and downs notation]] is identical to standard notation;
! Interval, complement
* Mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (♯) and flats (♭) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.
! Error (abs, [[cent|¢]])
 
{{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 ====
{{Sagittal chart|Evo}}
 
Because it includes no Sagittal symbols, this Evo Sagittal notation is identical to conventional notation.
 
==== Revo flavor ====
{{Sagittal chart}}
 
=== Dodecatonic notation ===
{| class="wikitable right-1 right-2 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Dodecatonic notation of 19edo
|-
|-
| [[6/5]], [[5/3]]
! [[Degree|#]]
| 0.148
! [[Cent]]s
! Interval names
|-
|-
| [[14/13]], [[13/7]]
| 0
| 1.982
| 0.0
| P1
|-
|-
| [[15/13]], [[26/15]]
| 1
| 4.891
| 63.2
| A1, m2
|-
|-
| [[18/13]], [[13/9]]
| 2
| 5.039
| 126.3
| M2, m3
|-
|-
| [[15/14]], [[28/15]]
| 3
| 6.873
| 189.5
| M3
|-
|-
| [[9/7]], [[14/9]]
| 4
| 7.021
| 252.6
| m4, A3
|-
|-
| [[10/9]], [[9/5]]
| 5
| 7.070
| 315.8
| M4, m5
|-
|-
| '''[[4/3]], [[3/2]]'''
| 6
| '''7.218'''
| 378.9
| M5
|-
|-
| '''[[5/4]], [[8/5]]'''
| 7
| '''7.366'''
| 442.1
| A5, d6
|-
|-
| [[13/10]], [[20/13]]
| 8
| 12.109
| 505.3
| P6
|-
|-
| [[13/12]], [[24/13]]
| 9
| 12.257
| 568.4
| A6, m7
|-
|-
| [[7/5]], [[10/7]]
| 10
| 14.091
| 631.6
| M7, d8
|-
| 11
| 694.7
| P8
|-
|-
| [[7/6]], [[12/7]]
| 12
| 14.239
| 757.9
| A8, m9
|-
|-
| [[9/8]], [[16/9]]
| 13
| 14.436
| 821.1
| M9, m10
|-
|-
| [[16/15]], [[15/8]]
| 14
| 14.585
| 884.2
| M10
|-
|-
| '''[[11/8]], [[16/11]]'''
| 15
| '''17.103'''
| 947.4
| m11, A10
|-
|-
| '''[[16/13]], [[13/8]]'''
| 16
| '''19.475'''
| 1010.5
| M11, m12
|-
|-
| '''[[8/7]], [[7/4]]'''
| 17
| '''21.457'''
| 1073.7
| M12
|-
|-
| [[12/11]], [[11/6]]
| 18
| 24.321
| 1136.8
| A12, d13
|-
|-
| [[11/10]], [[20/11]]
| 19
| 24.469
| 1200.0
| P13
|}
 
== Approximation to JI ==
[[File:19ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 19edo]]
 
=== Interval mappings ===
{{Q-odd-limit intervals|19}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
|-
| [[11/9]], [[18/11]]
! rowspan="2" | [[Subgroup]]
| 31.539
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
| ''[[15/11]], [[22/15]]''
! [[TE error|Absolute]] (¢)
| ''31.688''
! [[TE simple badness|Relative]] (%)
|-
|-
| ''[[13/11]], [[22/13]]''
| 2.3
| ''36.578''
| {{monzo| -30 19 }}
| {{mapping| 19 30 }}
| +2.277
| 2.277
| 3.612
|-
|-
| ''[[14/11]], [[11/7]]''
| 2.3.5
| ''38.561''
| 81/80, 3125/3072
|}
| {{mapping| 19 30 44 }}
 
| +2.578
==== Selected 17-limit intervals ====
| 1.911
[[File:19ed2-001.svg|alt=alt : Your browser has no SVG support.]]
| 3.025
 
=== Temperament measures ===
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 19et.  
{| class="wikitable center-all"
! colspan="2" |
!3-limit
!5-limit
!7-limit
!2.3.5.7.13
|-
|-
! colspan="2" |Octave stretch (¢)
| 2.3.5.7
| +2.28
| 49/48, 81/80, 126/125
| +2.58
| {{mapping| 19 30 44 53 }}
| +3.85
| +3.848
| +4.14
| 2.755
| 4.362
|-
|-
! rowspan="2" |Error
| 2.3.5.7.13
![[TE error|absolute]] (¢)
| 49/48, 65/64, 81/80, 91/90
|2.28
| {{mapping| 19 30 44 53 70 }}
|1.91
| +4.135
|2.76
| 2.530
|2.53
| 4.006
|-
|-
![[TE simple badness|relative]] (%)
| 2.3.5.7.13.23
|3.61
| 49/48, 65/64, 70/69, 81/80, 91/90
|3.02
| {{mapping| 19 30 44 53 70 86 }}
|4.35
| +3.319
|3.99
| 2.936
| 4.649
|}
|}
* 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]].


* 19et has a lower relative error than any previous ETs in the 5- and 7-limit. The next ET that does better in these subgroups is 34 and 31, respectively.
=== Uniform maps ===
* 19et is most prominent in the 2.3.5.7.13 subgroup, and the next ET that does better in this is 53.
{{Uniform map|edo=19}}


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


19 EDO [[tempering out|tempers out]] the following [[Comma|commas]]. (Note: This assumes the [[val]] {{val| 19 30 44 53 66 70 }}.)
{| class="commatable wikitable center-all left-3 right-4 left-6"
 
|-
{| class="wikitable center-all left-3 right-4 left-6"
! [[Harmonic limit|Prime<br>limit]]
! [[Harmonic limit|Prime<br>Limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Ratio]]
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
! [[Color notation/Temperament Names|Color Name]]
! [[Color notation/Temperament names|Color name]]
! Name(s)
! Name
|-
| 3
| <abbr title="1162261467/1073741824">(20 digits)</abbr>
| {{monzo| -30 19 }}
| 137.14
| Trilawa
| [[19-comma]]
|-
|-
| 5
| 5
| 16875/16384
| [[16875/16384]]
| {{Monzo| -14 3 4 }}
| {{monzo| -14 3 4 }}
| 51.12
| 51.12
| Laquadyo
| Laquadyo
| Negri comma, double augmentation diesis
| Negri comma
|-
| 5
| <abbr title="1594323/1562500">(14 digits)</abbr>
| {{monzo| -2 13 -8}}
| 34.91
| Laquadbigu
| [[Unicorn comma]]
|-
|-
| "
| 5
| 3125/3072
| [[3125/3072]]
| {{Monzo| -10 -1 5 }}
| {{monzo| -10 -1 5 }}
| 29.61
| 29.61
| Laquinyo
| Laquinyo
| Small diesis, magic comma
| Magic comma
|-
|-
| "
| 5
| [[81/80]]
| [[81/80]]
| {{Monzo| -4 4 -1 }}
| {{monzo| -4 4 -1 }}
| 21.51
| 21.51
| Gu
| Gu
| [[Syntonic comma]], Didymus comma, meantone comma
| Syntonic comma
|-
|-
| "
| 5
| 78732/78125
| [[78732/78125]]
| {{Monzo| 2 9 -7 }}
| {{monzo| 2 9 -7 }}
| 13.40
| 13.40
| Sepgu
| Sepgu
| Medium semicomma, sensipent comma
| Sensipent comma
|-
|-
| "
| 5
| 15625/15552
| [[15625/15552]]
| {{Monzo| -6 -5 6 }}
| {{monzo| -6 -5 6 }}
| 8.11
| 8.11
| Tribiyo
| Tribiyo
| Kleisma, semicomma majeur
| Kleisma
|-
|-
| "
| 5
|  
| <abbr title="1224440064/1220703125">(20 digits)</abbr>
| {{Monzo| 8 14 -13 }}
| {{monzo| 8 14 -13 }}
| 5.29
| 5.29
| Thegu
| Thegu
| Parakleisma
| [[Parakleisma]]
|-
|-
| "
| 5
|  
| <abbr title="19073486328125/19042491875328">(28 digits)</abbr>
| {{Monzo| -14 -19 19 }}
| {{monzo| -14 -19 19 }}
| 2.82
| 2.82
| Neyo
| Neyo
| Enneadeca, 19-tone-comma
| [[Enneadeca]]
|-
|-
| 7
| 7
| 1029/1000
| [[59049/57344]]
| {{Monzo| -3 1 -3 3 }}
| {{monzo| -13 10 0 -1 }}
| 50.72
| Laru
| Harrison's comma
|-
| 7
| [[1029/1000]]
| {{monzo| -3 1 -3 3 }}
| 49.49
| 49.49
| Trizogu
| Trizogu
| Keega
| Keega
|-
|-
| "
| 7
| 525/512
| [[525/512]]
| {{Monzo| -9 1 2 1 }}
| {{monzo| -9 1 2 1 }}
| 43.41
| 43.41
| Lazoyoyo
| Lazoyoyo
| Avicennma, Avicenna's enharmonic diesis
| Avicennma
|-
|-
| "
| 7
| [[49/48]]
| [[49/48]]
| {{Monzo| -4 -1 0 2 }}
| {{monzo| -4 -1 0 2 }}
| 35.70
| 35.70
| Zozo
| Zozo
| Slendro diesis
| Semaphoresma, slendro diesis
|-
|-
| "
| 7
| 686/675
| [[3645/3584]]
| {{Monzo| 1 -3 -2 3 }}
| {{monzo| -9 6 1 -1 }}
| 29.22
| Laruyo
| Schismean comma
|-
| 7
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| 27.99
| Trizo-agugu
| Trizo-agugu
| Senga
| Senga
|-
|-
| "
| 7
| 875/864
| [[875/864]]
| {{Monzo| -5 -3 3 1 }}
| {{monzo| -5 -3 3 1 }}
| 21.90
| 21.90
| Zotrigu
| Zotrigu
| Keema
| Keema
|-
|-
| "
| 7
| [[245/243]]
| [[245/243]]
| {{Monzo| 0 -5 1 2 }}
| {{monzo| 0 -5 1 2 }}
| 14.19
| 14.19
| Zozoyo
| Zozoyo
| Sensamagic
| Sensamagic comma
|-
|-
| "
| 7
| [[126/125]]
| [[126/125]]
| {{Monzo| 1 2 -3 1 }}
| {{monzo| 1 2 -3 1 }}
| 13.79
| 13.79
| Zotrigu
| Zotrigu
| Septimal semicomma, starling comma
| Starling comma
|-
|-
| "
| 7
| [[225/224]]
| [[225/224]]
| {{Monzo| -5 2 2 -1 }}
| {{monzo| -5 2 2 -1 }}
| 7.71
| 7.71
| Ruyoyo
| Ruyoyo
| Septimal kleisma, marvel comma
| Marvel comma
|-
|-
| "
| 7
| 19683/19600
| [[19683/19600]]
| {{Monzo| -4 9 -2 -2 }}
| {{monzo| -4 9 -2 -2 }}
| 7.32
| 7.32
| Labirugu
| Labirugu
| Cataharry
| Cataharry comma
|-
|-
| "
| 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 comma
|-
|-
| "
| 7
| 3136/3125
| [[3136/3125]]
| {{Monzo| 6 0 -5 2 }}
| {{monzo| 6 0 -5 2 }}
| 6.08
| 6.08
| Zozoquingu
| Zozoquingu
| Hemimean
| Hemimean comma
|-
|-
| "
| 7
|  
| <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
| [[Metric comma]]
|-
|-
| "
| 7
| 4375/4374
| [[4375/4374]]
| {{Monzo| -1 -7 4 1 }}
| {{monzo| -1 -7 4 1 }}
| 0.40
| 0.40
| Zoquadyo
| Zoquadyo
| Ragisma
| 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
| 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
| 896/891
| [[896/891]]
| {{Monzo| 7 -4 0 1 -1 }}
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| 9.69
| Saluzo
| Saluzo
| Pentacircle
| Pentacircle comma
|-
|-
| "
| 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
| [[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
| 540/539
| [[540/539]]
| {{Monzo| 2 3 1 -2 -1 }}
| {{monzo| 2 3 1 -2 -1 }}
| 3.21
| 3.21
| Lururuyo
| Lururuyo
Line 755: Line 928:
|-
|-
| 13
| 13
| 65/64
| [[39/38]]
| {{Monzo| -6 0 1 0 0 1 }}
| {{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
| 26.84
| Thoyo
| Thoyo
| Wilsorma
|-
| 13
| [[343/338]]
| {{monzo| -1 0 0 3 0 -2 }}
| 25.42
| Thuthutrizo
|  
|  
|-
|-
| "
| 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 comma, biome comma
|-
|-
| "
| 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
| Parizeksma
| 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 -1 }}
| 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
|}
|}
<references group="note" />


== 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]]


Since 19 is prime, all rank two 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.


{| class="wikitable right-1 right-2"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! Degree
! Degree
! Cents
! Cents
! Interval
! Interval
! Generator for
! Mos scales
! Temperaments
|-
|-
| 1
| 1
| 63.1579
| 63.16
| A1, d2
| A1, d2
| Unicorn/rhinocerus
|  
| [[Unicorn]] / [[Rhinoceros]]
|-
|-
| 2
| 2
| 126.3157
| 126.32
| m2
| m2
| [[1L&nbsp;8s]], [[9L&nbsp;1s]]
| [[Negri]]
| [[Negri]]
|-
|-
| 3
| 3
| 189.4737
| 189.47
| M2
| M2
| Deutone (2-meantone) / spell
| [[1L&nbsp;5s]], [[6L&nbsp;1s]], [[6L&nbsp;7s]]
| [[Deutone]] <br>[[Xenial]] / [[Sensamagic clan #Xenia|Xenia]] <br>[[Spell]]
|-
|-
| 4
| 4
| 252.6316
| 252.63
| A2, d3
| A2, d3
| [[Godzilla]]
| [[1L&nbsp;3s]], [[4L&nbsp;1s]], <br>[[5L&nbsp;4s]], [[5L&nbsp;9s]]
| [[Godzilla]] / [[Helayo]]
|-
|-
| 5
| 5
| 315.7895
| 315.79
| m3
| m3
| [[Kleismic]] ([[Hanson]], [[Keemun]], [[catakleismic]])
| [[3L&nbsp;1s]], [[4L&nbsp;3s]], <br>[[4L&nbsp;7s]], [[4L&nbsp;11s]]
| [[Cata]] / [[keemun]]
|-
|-
| 6
| 6
| 378.9474
| 378.95
| M3
| M3
| [[Magic]]/charisma/glamour
| [[3L&nbsp;1s]], [[3L&nbsp;4s]], [[3L&nbsp;7s]], <br>[[3L&nbsp;10s]], [[3L&nbsp;13s]]
| [[Magic]] / [[muggles]]
|-
|-
| 7
| 7
| 442.1053
| 442.11
| A3, d4
| A3, d4
| [[3L&nbsp;2s]], [[3L&nbsp;5s]], [[8L&nbsp;3s]]
| [[Sensi]]
| [[Sensi]]
|-
|-
| 8
| 8
| 505.2632
| 505.26
| P4
| P4
| [[Meantone]]/[[Flattone]]/[[meanennedecal|meanenneadecal]]/[[Meanpop]]
| [[2L&nbsp;3s]], [[5L&nbsp;2s]], [[7L&nbsp;5s]]
| [[Meantone]] / [[flattone]]
|-
|-
| 9
| 9
| 568.4211
| 568.42
| A4
| A4
| [[Liese]]/[[Triton]]/lisa
| [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], <br>[[2L&nbsp;9s]], [[2L&nbsp;11s]], [[2L&nbsp;13s]], <br>[[2L&nbsp;15s]]
| [[Liese]] <br>[[Triton]] / [[pycnic]]
|}
|}
== Octave stretch or compression ==
19edo is a promising option as a meantone tuning for pianos if split sharps are acceptable, since pianos are frequently tuned with stretched octaves due to the slight [[inharmonicity]] inherent in their strings. It also works well with harpsichords, since many have been, and are, built with split sharps.
Octave stretching also means that an out-of-tune interval can be replaced with a compounded or inverted version of it which is near-[[just]]. For example, if we are using [[49ed6]] or [[30edt]] (which tune 6:1 and 3:1 just and have octaves stretched by 2.8 and 4.57{{c}}, respectively), then we have near-just minor thirds (6:5), compound major thirds (as 5:1), and compound fifths (as 6:1), giving us versions of everything in the 5-odd-limit [[tonality diamond]]. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. Another possible choice is [[ZPI|65zpi]].
== Scales ==
=== MOS scales ===
{{Main|List of MOS scales in {{PAGENAME}}}}
==== Octave-equivalent mosses ====
* [[Meantone]] pentic, [[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 ===
{{Main|19edo modes}}
* Meantone harmonic minor: 3 2 3 3 2 4 2
* Meantone melodic minor: 3 2 3 3 3 3 2 (ascending), 3 2 3 3 2 3 3 (descending)
* 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 ==
== 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=19-EDO 5 string Bass 34"-37" scale length|frame|19-EDO bass conversion by Ron Sword.|none]]
[[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 }}
{{Catrel| 19edo tracks }}


* [http://micro.soonlabel.com/19-ET/ XA 19-ET Index]
; [http://micro.soonlabel.com/19-ET/ XA 19-ET Index]
* [https://xenharmonicgod.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)], an album of xenharmonic Christmas covers played by [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel], many are in 19edo
; A number of compositions that were perfomed at the [http://midwestmicrofest.org/concerts.html midwestmicrofest concert in 2007]{{dead link}}
* [https://soundcloud.com/aaron-krister-johnson/the-juggler The Juggler] by [[Aaron Krister Johnson]]
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=1008195 Foum] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3 play] by [[Jacob Barton]]
* [http://music.columbia.edu/%7Echris/sand.html Sand] by [[Christopher Bailey]]
* [http://works.music.columbia.edu/%7Echris/19mix1.mp3 Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me] by Christopher Bailey
* [http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3 Ditty] by Christopher Bailey
* [http://micro.soonlabel.com/gene_ward_smith/misc/Guillaume%20Costeley%20-%20Seigneur%20Dieu%20ta%20piti%e9.mp3 Seigneur Dieu ta pitié] by [[Guillaume Costeley]]
* [http://micro.soonlabel.com/0-hosted-albums/ivor/02%20Prelude%202%20for%2019%20tone%20guitar.mp3 Prelude 2 for 19 tone guitar] by [[Ivor Darreg]]
* [http://sethares.engr.wisc.edu/mp3s/sympathetic.html Sympathetic Metaphor] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3 play] by [[William Sethares]] [http://www.webcitation.org/5zFdC6u4V Permalink]
* [http://sethares.engr.wisc.edu/mp3s/truthonabus.html Truth on a bus] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3 play] by William Sethares [http://www.webcitation.org/5zFdSw1g4 Permalink]
* [http://www.h-pi.com/mp3/Rondo19ET.mp3 Rondo in 19ET] by [[Aaron Andrew Hunt]]
* [https://soundcloud.com/uz1kt3k/fuga-in-19et-2020 Fugue in 19ET (2020) - SoundCloud] by Aaron Andrew Hunt
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3 Citified Notions] and
* [http://archive.org/download/LimpOffToSchool/LimpOffToSchool19tet.mp3 Limp Off to School] by [[John Starrett]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/betelgeuse.mp3 The Light Of My Betelgeuse] by [[Mykhaylo Khramov]]
* [http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/01.Undines.mp3 Undines] by [[Jon Lyle Smith]]
* [http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/02.Sylphs.mp3 Sylphs] by Jon Lyle Smith
* [http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/03.Gnomes.mp3 Gnomes] by Jon Lyle Smith
* [http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/04.Salamanders.mp3 Salamanders] by Jon Lyle Smith
* [http://archive.org/details/AnotherAireForLute Another Aire For Lute] by Jon Lyle Smith
* A number of compositions that were perfomed at the [http://midwestmicrofest.org/concerts.html midwestmicrofest concert in 2007]
* Fanfare in 19-note Equal Tuning by Easley Blackwood
* [http://www.uvnitr.cz/flaoyg/flao_yg/zvire.mp3 Zvíře] by [http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html Milan Guštar]
* [http://www.ziaspace.com/ZIA/sections/music.html 19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/14%20-%2014.%2019%20octave.mp3 Comets Over Flatland 14] [[Randy Winchester]]
* [http://chrisvaisvil.com/?p=865 Forgetting Even Her Beauty blog] [http://micro.soonlabel.com/19-ET/daily20110516-19-forgetting_even_her_beauty.mp3 play Forgetting Even Her Beauty] by [[Chris Vaisvil]]
* [http://chrisvaisvil.com/?p=855 19 Black Hawks for Osama blog] [http://www.youtube.com/watch?v=gGO0R381HQs play video for 19 Black Hawks for Osama] by Chris Vaisvil
* [http://chrisvaisvil.com/?p=823 Summer Song blog] [http://micro.soonlabel.com/19-ET/daily20110501-19-summer_song_mix3.mp3 play Summer Song] by [[Trevor]] (The TwoRegs) and [[Norm Harris]] and Chris Vaisvil
* [http://chrisvaisvil.com/?p=820 19 ImprovFridays blog] [http://www.youtube.com/watch?v=-KaRXFoYwT4 play video of performance of 19 ImprovFridays] by Chris Vaisvil
* [http://chrisvaisvil.com/?p=800 The World has Changed blog] [http://micro.soonlabel.com/19-ET/daily20110429-19edo-the_world_has_changed3.mp3 play The World has Changed] by Chris Vaisvil
* [http://chrisvaisvil.com/?p=883 jjj] [http://micro.soonlabel.com/19-ET/daily20110523-19take2.mp3 play] by Chris Vaisvil
* [http://soundcloud.com/omega9/chip-chamber Now listen! Pitch!] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Now%20listen%21%20Pitch%21.mp3 play] by [[Omega9]]
* [https://www.youtube.com/watch?v=mlvme3ukPLE Cordas (19-edo version)] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas.mp3 play] by Omega9
* [http://www.youtube.com/watch?v=DSOGF4gDYu8 A Piece in 19edo] by Omega9
* [http://soundcloud.com/omega9/a-piece-in-19edo-version-3 A Piece in 19edo (ver.3)] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20A%20Piece%20in%2019edo.mp3 play] by Omega9
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/WTC2-24/19-edo-A-Prelude.mp3 Bach’s Prelude number 24 from Well Tempered Clavier, Book II] rendered by [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/WTC2-24/19-edo-B-Fugue.mp3 Bach’s Fugue number 24 from Well Tempered Clavier, Book II] rendered by [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/_Movi_Nove__by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 Movi-Nove] by [https://soundcloud.com/lois-lancaster/movi-nove Roncevaux (Löis Lancaster)]
* [https://soundcloud.com/rewarrp/psychedelic-delt Psychedelic Delt] by [[Rewarrp]]
* [https://soundcloud.com/camtaylor-1/17-out-of-19edo-bright-objects Bright Objects] - 17-tone fifths chain in 19EDO by [[Cam Taylor]]
* [https://soundcloud.com/cam-taylor-2-1/17-out-of-19edo-wurly-minor-thirds-minor-sevens Minor Thirds, Minor Sevens] - 17-tone fifths chain in 19EDO by Cam Taylor
* [https://soundcloud.com/camtaylor-1/wurly-minors-and-enharmonic-tetrachords-17-out-of-19edo Wurly Minors and Enharmonic Tetrachords] - 17-tone fifths chain in 19EDO by Cam Taylor
* [https://www.youtube.com/watch?v=JTpF2MifP5Y Brain for Breakfast] - 19-EDO piece (first movement uses 19 tone serialism) and
* [https://www.youtube.com/watch?v=arn08IsWGzY Psychoclowns] - 19-EDO pseudo-rondo by [[Bostjan Zupancic]]


== See also ==
== See also ==
 
* [[19edo modes]]
* [[19edo Modes]]
* [[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]]
* [[Extraclassical tonality]]
* [[Lumatone mapping for 19edo]]


=== Articles ===
== 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.


* [http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen] by [[Ivor Darreg]] [http://www.webcitation.org/5xZzBtDGF Permalink]
== External links ==
* [http://www.microstick.net/nineteenarticle.htm Nineteen for the Nineties] by Ivor Darreg
* [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://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications] by Hubert S. Howe Jr. [http://www.webcitation.org/5xbMKVaqa Permalink]
* [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://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar] by William A. Sethares [http://www.webcitation.org/5xeCbEPZ0 Permalink]
* [http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Bailey, Morrison, Pearson and Parncutt [http://www.webcitation.org/5xeDFQDvn Permalink]
* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory] [http://tonalsoft.com/enc/number/19edo.aspx Permalink]
* [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].
* [http://www.ronsword.com/books.html Enneadecaphonic Scales for Guitar] by [[Ron Sword]]
* [[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]  
* Here is a [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, ''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.


[[Category:19-tone]]
[[Category:19-tone scales]]
[[Category:19edo]]
[[Category:Godzilla]]
[[Category:Equal divisions of the octave]]
[[Category:Golden meantone]]
[[Category:Golden]]
[[Category:Kleismic]]
[[Category:Intervals]]
[[Category:Listen]]
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Prime EDO]]
[[Category:Magic]]
[[Category:Negri]]
[[Category:Semaphore]]
[[Category:Sensi]]
[[Category:Teentuning]]
[[Category:Teentuning]]
[[Category:Zeta]]
[[Category:Historical]]
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