19edo: Difference between revisions

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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.

In 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone|{{frac|1|3}}-comma meantone]], in which the fifth is 694.786 ~~cents~~; the fifth of 19edo is 694.737, 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 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone|{{frac|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]).

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19edo's most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for [[meantone]]. It is also suitable for [[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 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. 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 major sixth, though [[46edo]] is a better sensi tuning.

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 is in fact the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]]), and is the fifth [[zeta integral edo]], after 12edo. It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo 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 scale]]s in 19edo 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.

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 is in fact the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]]), and is the fifth [[zeta integral edo]], after 12edo. It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo 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 scale]]s in 19edo 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.

Being a zeta integral tuning, the no-11's 13-limit is represented relatively well and consistently. 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. 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.)

Another option would be to use [[octave stretching]]; the closest [[the Riemann zeta function and tuning #Optimal octave stretch|local zeta peak]] to 19 occurs at 18.9481, which makes the octaves 1203.29 ~~cents~~, and a step size of between 63.~~2 and 63~~.4 ~~cents~~ would be preferable in theory. Pianos are frequently tuned with stretched octaves anyway due to the slight inharmonicity inherent in their strings, which makes 19edo a promising option for pianos 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 [[30ed3]] (which tune 6:1 and 3:1 just and have octaves stretched by 2.8 and 4.57 ~~cents~~, 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-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. The most extreme of these options would be [[11edf]], which has octaves stretched by 12.47 ~~cents~~.

Another option would be to use [[octave stretching]]; the closest [[the Riemann zeta function and tuning #Optimal octave stretch|local zeta peak]] to 19 occurs at 18.9481, which makes the octaves 1203.29{{c}}, and a step size of between 63.2–63.4{{c}} would be preferable in theory. Pianos are frequently tuned with stretched octaves anyway due to the slight inharmonicity inherent in their strings, which makes 19edo a promising option for pianos 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 [[30ed3]] (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-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. The most extreme of these options would be [[11edf]], which has octaves stretched by 12.47{{c}}.

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

Because 19edo ~~allows for~~ more blended, consonant ~~harmonies~~ than 12edo ~~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 12edo blend much better in 19edo.

Because 19edo's 5-limit chords are more blended and consonant 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.

19edo's diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3 ~~cents~~ off [[23/16]].

19edo's 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 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.

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== Intervals ==

{| class="wikitable right-1 right-2 center-5 center-8"

|-

! [[Degree]]

! [[Cent]]s

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Using [[color notation]], qualities can be loosely associated with colors:

{| class="wikitable" style="text-align: center"

{| class="wikitable" style="text-align: center;"

|-

! Quality

! [[Color name|Color Name]]

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{| class="wikitable center-1 center-2 center-3 center-4"

|-

! [[Kite's color notation|Color of the 3rd]]

! JI Chord

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{| class="wikitable right-1 right-2 center-3 center-4"

|+ style="font-size: 105%;" |Notation of 19edo

|+ style="font-size: 105%;" | Notation of 19edo

|-

! rowspan="2" |[[Degree]]

! rowspan="2" | [[Degree]]

! rowspan="2" |[[Cent]]s

! rowspan="2" | [[Cent]]s

! colspan="2" |[[Chain-of-fifths notation|Standard Notation]]

! colspan="2" | [[Chain-of-fifths notation|Standard Notation]]

|-

![[5L 2s|Diatonic Interval Names]]

! [[5L 2s|Diatonic Interval Names]]

! Note Names on D

|-

| 0

| 0.00

|'''Perfect unison (P1)'''

| '''Perfect unison (P1)'''

|'''D'''

| '''D'''

|-

| 1

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| 3

| 189.47

|'''Major second (M2)''' Doubly diminished third (dd3)

| '''Major second (M2)''' Doubly diminished third (dd3)

|'''E''' Fbb

| '''E''' Fbb

|-

| 4

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| 6

| 378.95

|'''Major third (M3)''' Doubly diminished fourth (dd4)

| '''Major third (M3)''' Doubly diminished fourth (dd4)

|'''F#''' Gbb

| '''F#''' Gbb

|-

| 7

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| 8

| 505.26

|'''Perfect fourth (P4)'''

| '''Perfect fourth (P4)'''

|'''G'''

| '''G'''

|-

| 9

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| 11

| 694.74

|'''Perfect fifth (P5)'''

| '''Perfect fifth (P5)'''

|'''A'''

| '''A'''

|-

| 12

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| 14

| 884.21

|'''Major sixth (M6)''' Doubly diminished seventh (dd7)

| '''Major sixth (M6)''' Doubly diminished seventh (dd7)

|'''B''' Cbb

| '''B''' Cbb

|-

| 15

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| 19

| 1200.00

|'''Perfect octave (P8)'''

| '''Perfect octave (P8)'''

|'''D'''

| '''D'''

|}

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===Sagittal notation===

=== 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====~~

==== Evo flavor ====

File:19-EDO_Evo_Sagittal.svg

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Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.

~~====Revo flavor====~~

==== Revo flavor ====

File:19-EDO_Revo_Sagittal.svg

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|-

! [[Harmonic limit|Prime limit]]

! [[Ratio]]<ref group="note">{{rd~~|10~~}}</ref>

! [[Ratio]]<ref group="note">{{rd}}</ref>

! [[Monzo]]

! [[Cents]]

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| 126.32

| m2

| [[1L 8s]], [[9L 1s]]

| [[1L 8s]], [[9L 1s]]

| [[Negri]]

|-

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| 189.47

| M2

| [[1L 5s]], [[6L 1s]], [[6L 7s]]

| [[1L 5s]], [[6L 1s]], [[6L 7s]]

| [[Deutone]] [[Spell]]

|-

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| 252.63

| A2, d3

| [[1L 3s]], [[4L 1s]], [[5L 4s]], [[5L 9s]]

| [[1L 3s]], [[4L 1s]], [[5L 4s]], [[5L 9s]]

| [[Godzilla]]

|-

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| 315.79

| m3

| [[3L 1s]], [[4L 3s]], [[4L 7s]], [[4L 11s]]

| [[3L 1s]], [[4L 3s]], [[4L 7s]], [[4L 11s]]

| [[Cata]] / [[keemun]]

|-

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| 378.95

| M3

| [[3L 1s]], [[3L 4s]], [[3L 7s]], [[3L 10s]], [[3L 13s]]

| [[3L 1s]], [[3L 4s]], [[3L 7s]], [[3L 10s]], [[3L 13s]]

| [[Magic]] / [[muggles]]

|-

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| 442.11

| A3, d4

| [[3L 2s]], [[3L 5s]], [[8L 3s]]

| [[3L 2s]], [[3L 5s]], [[8L 3s]]

| [[Sensi]]

|-

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| 505.26

| P4

| [[2L 3s]], [[5L 2s]], [[7L 5s]]

| [[2L 3s]], [[5L 2s]], [[7L 5s]]

| [[Meantone]] / [[flattone]]

|-

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| 568.42

| A4

| [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], [[2L 13s]], [[2L 15s]]

| [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], [[2L 13s]], [[2L 15s]]

| [[Liese]] / [[pycnic]] [[Triton]]

|}

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* 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 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 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

* [[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

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* [[Arto and Tendo Theory]]

* [[Lumatone mapping for 19edo]]

~~=== 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.

== Further reading ==

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* [[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 ===

* 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]]

@@ Line 13: / Line 13: @@
 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.
-In 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone|{{frac|1|3}}-comma meantone]], in which the fifth is 694.786 cents; the fifth of 19edo is 694.737, 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 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone|{{frac|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]).
@@ Line 20: / Line 20: @@
 edo's most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for [[meantone]]. It is also suitable for [[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 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. 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 major sixth, though [[46edo]] is a better sensi tuning.
-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 is in fact the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]]), and is the fifth [[zeta integral edo]], after 12edo. It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo 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 scale]]s in 19edo 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.
+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 is in fact the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]]), and is the fifth [[zeta integral edo]], after 12edo. It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo 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 scale]]s in 19edo 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.
 Being a zeta integral tuning, the no-11's 13-limit is represented relatively well and consistently. 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. 19edo's [[negri]], [[sensi]] and [[semaphore]] 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.)
-Another option would be to use [[octave stretching]]; the closest [[the Riemann zeta function and tuning #Optimal octave stretch|local zeta peak]] to 19 occurs at 18.9481, which makes the octaves 1203.29 cents, and a step size of between 63.2 and 63.4 cents would be preferable in theory. Pianos are frequently tuned with stretched octaves anyway due to the slight inharmonicity inherent in their strings, which makes 19edo a promising option for pianos 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 [[30ed3]] (which tune 6:1 and 3:1 just and have octaves stretched by 2.8 and 4.57 cents, 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-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. The most extreme of these options would be [[11edf]], which has octaves stretched by 12.47 cents.
+Another option would be to use [[octave stretching]]; the closest [[the Riemann zeta function and tuning #Optimal octave stretch|local zeta peak]] to 19 occurs at 18.9481, which makes the octaves 1203.29{{c}}, and a step size of between 63.2–63.4{{c}} would be preferable in theory. Pianos are frequently tuned with stretched octaves anyway due to the slight inharmonicity inherent in their strings, which makes 19edo a promising option for pianos 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 [[30ed3]] (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-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. The most extreme of these options would be [[11edf]], which has octaves stretched by 12.47{{c}}.
 === As a means of extending harmony ===
-Because 19edo allows for more blended, consonant harmonies than 12edo 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 12edo blend much better in 19edo.
+Because 19edo's 5-limit chords are more blended and consonant 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.
-edo's diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3 cents off [[23/16]].
+edo's 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 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.
@@ Line 47: / Line 47: @@
 == Intervals ==
 {| class="wikitable right-1 right-2 center-5 center-8"
+|-
 ! [[Degree]]
 ! [[Cent]]s
@@ Line 218: / Line 219: @@
 Using [[color notation]], qualities can be loosely associated with colors:
-{| class="wikitable" style="text-align: center"
+{| class="wikitable" style="text-align: center;"
+|-
 ! Quality
 ! [[Color name|Color Name]]
@@ Line 258: / Line 260: @@
 {| class="wikitable center-1 center-2 center-3 center-4"
+|-
 ! [[Kite's color notation|Color of the 3rd]]
 ! JI Chord
@@ Line 319: / Line 322: @@
 {| class="wikitable right-1 right-2 center-3 center-4"
-|+ style="font-size: 105%;" |Notation of 19edo
+|+ style="font-size: 105%;" | Notation of 19edo
 |-
-! rowspan="2" |[[Degree]]
+! rowspan="2" | [[Degree]]
-! rowspan="2" |[[Cent]]s
+! rowspan="2" | [[Cent]]s
-! colspan="2" |[[Chain-of-fifths notation|Standard Notation]]
+! colspan="2" | [[Chain-of-fifths notation|Standard Notation]]
 |-
-![[5L 2s|Diatonic Interval Names]]
+! [[5L 2s|Diatonic Interval Names]]
 ! Note Names<br />on D
 |-
 | 0
 | 0.00
-|'''Perfect unison (P1)'''
+| '''Perfect unison (P1)'''
-|'''D'''
+| '''D'''
 |-
 | 1
@@ Line 345: / Line 348: @@
 | 3
 | 189.47
-|'''Major second (M2)'''<br />Doubly diminished third (dd3)
+| '''Major second (M2)'''<br />Doubly diminished third (dd3)
-|'''E'''<br />Fbb
+| '''E'''<br />Fbb
 |-
 | 4
@@ Line 360: / Line 363: @@
 | 6
 | 378.95
-|'''Major third (M3)'''<br />Doubly diminished fourth (dd4)
+| '''Major third (M3)'''<br />Doubly diminished fourth (dd4)
-|'''F#'''<br />Gbb
+| '''F#'''<br />Gbb
 |-
 | 7
@@ Line 370: / Line 373: @@
 | 8
 | 505.26
-|'''Perfect fourth (P4)'''
+| '''Perfect fourth (P4)'''
-|'''G'''
+| '''G'''
 |-
 | 9
@@ Line 385: / Line 388: @@
 | 11
 | 694.74
-|'''Perfect fifth (P5)'''
+| '''Perfect fifth (P5)'''
-|'''A'''
+| '''A'''
 |-
 | 12
@@ Line 400: / Line 403: @@
 | 14
 | 884.21
-|'''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)
+| '''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)
-|'''B'''<br />Cbb
+| '''B'''<br />Cbb
 |-
 | 15
@@ Line 425: / Line 428: @@
 | 19
 | 1200.00
-|'''Perfect octave (P8)'''
+| '''Perfect octave (P8)'''
-|'''D'''
+| '''D'''
 |}
@@ Line 435: / Line 438: @@
 {{Sharpness-sharp1}}
-===Sagittal notation===
+=== 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====
+==== Evo flavor ====
 <imagemap>
 File:19-EDO_Evo_Sagittal.svg
@@ Line 448: / Line 451: @@
 Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.
-====Revo flavor====
+==== Revo flavor ====
 <imagemap>
 File:19-EDO_Revo_Sagittal.svg
@@ Line 643: / Line 646: @@
 |-
 ! [[Harmonic limit|Prime<br>limit]]
-! [[Ratio]]<ref group="note">{{rd|10}}</ref>
+! [[Ratio]]<ref group="note">{{rd}}</ref>
 ! [[Monzo]]
 ! [[Cents]]
@@ Line 990: / Line 993: @@
 | 126.32
 | m2
-| [[1L 8s]], [[9L 1s]]
+| [[1L&nbsp;8s]], [[9L&nbsp;1s]]
 | [[Negri]]
 |-
@@ Line 996: / Line 999: @@
 | 189.47
 | M2
-| [[1L 5s]], [[6L 1s]], [[6L 7s]]
+| [[1L&nbsp;5s]], [[6L&nbsp;1s]], [[6L&nbsp;7s]]
 | [[Deutone]]<br>[[Spell]]
 |-
@@ Line 1,002: / Line 1,005: @@
 | 252.63
 | A2, d3
-| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]
+| [[1L&nbsp;3s]], [[4L&nbsp;1s]], <br>[[5L&nbsp;4s]], [[5L&nbsp;9s]]
 | [[Godzilla]]
 |-
@@ Line 1,008: / Line 1,011: @@
 | 315.79
 | m3
-| [[3L 1s]], [[4L 3s]], <br>[[4L 7s]], [[4L 11s]]
+| [[3L&nbsp;1s]], [[4L&nbsp;3s]], <br>[[4L&nbsp;7s]], [[4L&nbsp;11s]]
 | [[Cata]] / [[keemun]]
 |-
@@ Line 1,014: / Line 1,017: @@
 | 378.95
 | M3
-| [[3L 1s]], [[3L 4s]], [[3L 7s]], <br>[[3L 10s]], [[3L 13s]]
+| [[3L&nbsp;1s]], [[3L&nbsp;4s]], [[3L&nbsp;7s]], <br>[[3L&nbsp;10s]], [[3L&nbsp;13s]]
 | [[Magic]] / [[muggles]]
 |-
@@ Line 1,020: / Line 1,023: @@
 | 442.11
 | A3, d4
-| [[3L 2s]], [[3L 5s]], [[8L 3s]]
+| [[3L&nbsp;2s]], [[3L&nbsp;5s]], [[8L&nbsp;3s]]
 | [[Sensi]]
 |-
@@ Line 1,026: / Line 1,029: @@
 | 505.26
 | P4
-| [[2L 3s]], [[5L 2s]], [[7L 5s]]
+| [[2L&nbsp;3s]], [[5L&nbsp;2s]], [[7L&nbsp;5s]]
 | [[Meantone]] / [[flattone]]
 |-
@@ Line 1,032: / Line 1,035: @@
 | 568.42
 | A4
-| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]
+| [[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]]
 |}
@@ Line 1,073: / Line 1,076: @@
 * 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 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 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
+* [[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
@@ Line 1,103: / Line 1,106: @@
 * [[Arto and Tendo Theory]]
 * [[Lumatone mapping for 19edo]]
-=== 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.
 == Further reading ==
@@ Line 1,125: / Line 1,121: @@
 * [[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]]