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{{Breadcrumb|19edo}}
== Background ==
== Background ==
[[19edo]] can be an easy tuning for those with a little music theory background, but no xenharmonic experience.  Standard notation can be used (just be vigilant with spelling and watch enharmonic equivalents), and there are only 7 more notes than 12edo (making it the edo with the fewest notes more than 12 where standard notation can be used).
[[19edo]] can be an easy tuning for those with a little music theory background, but no xenharmonic experience.  Standard notation can be used (just be vigilant with spelling and watch enharmonic equivalents), and there are only 7 more notes than 12edo (making it the edo with the fewest notes more than 12 where standard notation can be used without new accidentals).
 
Music in what is essentially 19edo ({{frac|1|3}}-[[81/80|comma]] [[meantone]]) dates back to the 16th century, contemporary with the initial proposals for [[12edo]]. Major and minor thirds and sixths in 19edo are more concordant than in 12edo, due to being closer to common just intervals, and the perfect fourth and fifth are only slightly less clear than 12edo. 
 
Longer scale fretted instruments like guitar and bass guitar have fret placements that don't require major modification of playing techniques, and isometric keyboard instruments can represent this tuning ergonomically with three rows of keys or buttons.  Due to the close relationship with other classical temperaments, some wind instruments can be played with alternative fingerings to approximate 19edo. 
 
Because of its history, advantages, and playability, it is a strong choice for many players eager to experience music outside of 12edo.


== Notation ==
== Notation ==
Looking at 19edo as an extension of 12edo, standard notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam. Notes with enharmonic equivalents are different than they are in 12edo, though.
Looking at 19edo as an extension of 12edo, standard notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam. Notes with enharmonic equivalents are different than they are in 12edo, though.


=== Letter Notation (anglophonic standard) ===
=== Letter notation (anglophonic standard) ===
Using the letters A-G and "accidentals" b to lower a tone and # to raise a tone, with also bb to lower a tone two degrees and x to raise a tone two degrees, the notes and enharmonic equivalents are shown in the table below:
Using the letters A–G and accidentals b to lower a tone and # to raise a tone, with also bb to lower a tone two degrees and x to raise a tone two degrees, the notes and enharmonic equivalents are shown in the table below:
 
{| class="wikitable"
{| class="wikitable"
|+A Basic Look at Letter Notation in 19edo
|+ style="font-size: 105%;" | A basic look at letter notation in 19edo
!Scale Degree
!Interval
!Alternative Interval
!Name
!In A
!Enharmonic Equivalents
|-
|-
|1
! Scale degree
|Unison
! Interval
|
! Function
|Tonic
! In A
|A
! Equivalents
|
|-
|-
|bb2
| 1
|
| Unison
|Diminished Second
| Tonic
|
| A
|A#
|  
|Bbb
|-
|-
|b2
| #1/bb2
|Minor Second
| Augmented unison, diminished second
|
|  
|
| A#
|Bb (*)
| Bbb
|Ax
|-
|-
|2
| b2
|Major Second
| Minor second
|
|  
|Supertonic
| Bb (*)
|B (*)
| Ax
|Cbb
|-
|-
|#2/bb3
| 2
|
| Major second
|Augmented Second, Diminished Third
| Supertonic
|
| B (*)
|B# or Cb
| Cbb
|
|-
|-
|b3
| #2/bb3
|Minor Third
| Augmented second, diminished third
|
|  
|
| B# or Cb
|C
|  
|Bx
|-
|-
|3
| b3
|Major Third
| Minor third
|
|  
|Mediant
| C
|C#
| Bx
|Dbb
|-
|-
|#3/b4
| 3
|
| Major third
|Augmented Third, Diminished Fourth
| Mediant
|
| C#
|Db
| Dbb
|Cx
|-
|-
|4
| #3/b4
|Perfect Fourth
| Augmented third, diminished fourth
|
|  
|Subdominant
| Db
|D
| Cx
|
|-
|-
|#4
| 4
|Augmented Fourth
| Perfect fourth
|
| Subdominant
|
| D
|D#
|  
|Ebb
|-
|-
|b5
| #4
|Diminished Fifth
| Augmented fourth
|
|  
|
| D#
|Eb
| Ebb
|Dx
|-
|-
|5
| b5
|Perfect Fifth
| Diminished fifth
|
|  
|Dominant
| Eb
|E
| Dx
|Fbb
|-
|-
|#5
| 5
|Augmented Fifth
| Perfect fifth
|Diminished sixth
| Dominant
|
| E
|E# or Fb
| Fbb
|
|-
|-
|b6
| #5/bb6
|Minor Sixth
| Augmented fifth, diminished sixth
|
|  
|
| E# or Fb
|F
|  
|Ex
|-
|-
|6
| b6
|Major Sixth
| Minor sixth
|
|  
|Submediant
| F
|F#
| Ex
|Gbb
|-
|-
|bb7/#6
| 6
|Diminished Seventh
| Major sixth
|Augmented Sixth
| Submediant
|
| F#
|Gb
| Gbb
|Fx
|-
|-
|b7
| #6/bb7
|Minor Seventh
| Augmented sixth, diminished seventh
|
|  
|
| Gb
|G
| Fx
|
|-
|-
|7
| b7
|Major Seventh
| Minor seventh
|
|  
|Subtonic
| G
|G#
|  
|Abb
|-
|-
|#7
| 7
|
| Major seventh
|Augmented Seventh
| Subtonic
|
| G#
|Ab
| Abb
|Gx
|-
| #7/b8
| Augmented seventh, diminished octave
|  
| Ab
| Gx
|}
|}
<nowiki>*</nowiki>Some cultures use letter notation, but there is a common variation to replace Bb from the table with B and then replace B from the table with H.
<nowiki />* Some cultures use letter notation, but there is a common variation to replace Bb from the table with B and then replace B from the table with H.


Chords would follow the same spelling as with standard 12edo notation, just be careful with spelling. For example, Bb chord would be spelled Bb D F, and A# chord would be A# Cx E#; but the two are different chords, one degree apart from each other.
Chords would follow the same spelling as with standard 12edo notation, just be careful with spelling. For example, Bb chord would be spelled Bb D F, and A# chord would be A# Cx E#; but the two are different chords, one degree apart from each other.
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=== Solfege ===
=== Solfege ===
There are a lot of variants of solfege, depending on culture and tradition. Some traditions use moveable "do," and others use fixed "do."  Typically, moveable "do" systems employ varying vowel sounds to note accidentals, whereas fixed "do" systems usually use sharp and flat accidentals as letter notation does.
There are a lot of variants of solfege, depending on culture and tradition. Some traditions use moveable "do", and others use fixed "do". Typically, moveable "do" systems employ varying vowel sounds to note accidentals, whereas fixed "do" systems usually use sharp and flat accidentals as letter notation does. One proposed modified solfege system is in the table below. See also [[List of uniform solfeges for EDOs#19edo_.283_vowels.29|List of uniform solfeges for EDOs—19edo (3 vowels)]].


== Major Scale ==
{| class="wikitable"
The major scale in 19edo is the same as it is in 12edo, with the notation above in mind.  So, C major scale is spelled C D E F G A B C.  G major scale is G A B C D E F# G.  D major scale is D E F# G A B C D, and so forth.  The difference, again, is in the number of accidentals necessary to account for the extra keys possible and all of the additional notes.  In 12edo, the key of F# is the same as the key of Gb, but in 19edo, F# and Gb are not even the same tone.
|-
! Scale degree
! Interval
! Function
! Solfege
|-
| 1
| Unison
| Tonic
| do
|-
| #1/bb2
| Augmented unison, diminished second
|
| di, ro
|-
| b2
| Minor second
|
| ra
|-
| 2
| Major second
| Supertonic
| re
|-
| #2/bb3
| Augmented second, diminished third
|
| ri, ma
|-
| b3
| Minor third
|
| me
|-
| 3
| Major third
| Mediant
| mi
|-
| #3/b4
| Augmented third, diminished fourth
|
| mo, fe
|-
| 4
| Perfect fourth
| Subdominant
| fa
|-
| #4
| Augmented fourth
|
| fi
|-
| b5
| Diminished fifth
|
| se
|-
| 5
| Perfect fifth
| Dominant
| sol
|-
| #5/bb6
| Augmented fifth, diminished sixth
|
| si, lo
|-
| b6
| Minor sixth
|
| le
|-
| 6
| Major sixth
| Submediant
| la
|-
| #6/bb7
| Augmented Sixth, diminished seventh
|
| li, ta
|-
| b7
| Minor seventh
|
| te
|-
| 7
| Major seventh
| Subtonic
| ti
|-
| #7/b8
| Augmented seventh, diminished octave
|
| to, da
|}


Often times in music theory, a scale will be spelled out by its degrees instead of by letters.  For example, the major scale is "1 2 3 4 5 6 7."  Now 1 is whichever note you use as a root or "tonic" note, and the rest of the scale follows a formula.  This is useful for communicating musical ideas without having to specify the key of the song.  So, C major is 1 2 3 4 5 6 7, or Gb major is 1 2 3 4 5 6 7, or any major scale is 1 2 3 4 5 6 7.
== Tuning (a stringed instrument) ==
There are many approaches to tuning (if you are reading this, then that statement should seem ironic here), so tuning something like a guitar in 19edo might seem like a daunting task.


== Other Scales ==
One approach is to maintain familiar spacing and tune open strings (low to high): E A D G B E.
The minor scales all work exactly the same as they do in 12edo.  So, the A minor scale is the same as the C major scale, just starting and ending on A instead of on C.  In fact, all of the "church modes" also known as the "classical modes," are the same.  All of the altered scales are the same, too.  Just account for the spellings of notes with accidentals carefully and you are all set.


Spelling scales out with degrees works the same way as it does in 12edo, too. The natural minor scale (in the key of A minor) is A B C D E F G, and is spelled with degrees (in any key) as 1 2 b3 4 5 b6 b7.
But make sure to use 19edo E A D G and B.  If you use a [[reference tone]] A=440 Hz, then you can use an electronic chromatic tuner with a needle or digital display.
 
E - flat 5 cents (5.263 to be more precise)
 
A  - right on the money
 
D - sharp 5 cents (again 5.263)
 
G - sharp 11 cents (10.526 to be more precise)
 
B - flat 11 cents (again 10.526)
 
E - same as the other E, flat 5 cents
 
Keep in mind that not everyone uses A=440 Hz, especially in xenharmonic tunings like 19edo, though.  If the other musicians playing with you use a C standard instead of an A standard, you'll have to tune everything flatter to keep up.  In that case:
 
E - 23 cents flat
 
A - 18 cents flat
 
D - 12 cents flat
 
G - 7 cents flat
 
B - 28 cents flat
 
E - 23 cents flat
 
Since electric bass usually has the same strings as a guitar, use the same scheme, but ignore the unused notes.  If you have a low B, use the same offset (in cents) as listed for the guitar's high B.  Since the tuning is based on the octave, it doesn't matter which octave.  Likewise, if you play guitar in drop D or DADGAD, just use the offsets for the notes you use to tune.
 
For violin or mandolin, just use the same offsets for G, D, A, and E.
 
For viola or 'cello, or mandola or mandocello, you will need to offset the C string only if the reference tone is not C standard.  For A standard, tune C 16 cents sharp.
 
== Major scale ==
The major scale in 19edo is the same as it is in 12edo, with the notation above in mind. So, C major scale is spelled C D E F G A B C. G major scale is G A B C D E F# G. D major scale is D E F# G A B C# D, and so forth. The difference, again, is in the number of accidentals necessary to account for the extra keys possible and all of the additional notes.  In 12edo, the key of F# is the same as the key of Gb, but in 19edo, F# and Gb are not even the same tone.
 
Often times in music theory, a scale will be spelled out by its degrees instead of by letters. For example, the major scale is "1 2 3 4 5 6 7."  Now 1 is whichever note you use as a root or "tonic" note, and the rest of the scale follows a formula. This is useful for communicating musical ideas without having to specify the key of the song. So, C major is 1 2 3 4 5 6 7, or Gb major is 1 2 3 4 5 6 7, or any major scale is 1 2 3 4 5 6 7.
 
The major scale can be mapped out mentally as whole and half steps: WWHWWWH. In 12edo H is one quantum (the minimum distance between tones) and W is two. In 19edo, H is two quanta and W is three. In more complex tuning systems, one has to be more careful to account for the fact that the whole steps and half steps can vary in size between intervals, but not in 19edo; a half step is always two minimum steps (keys or buttons or frets, etc.), and a whole step is three.
 
== Other scales ==
The minor scales all work exactly the same as they do in 12edo. So, the A minor scale is the same as the C major scale, just starting and ending on A instead of on C. In fact, all of the "church modes", also known as the "classical modes", are the same. All of the altered scales are the same, too. Just account for the spellings of notes with accidentals carefully and you are all set.
 
Spelling scales out with degrees works the same way as it does in 12edo, too. The natural minor scale (in the key of A minor) is A B C D E F G, and is spelled with degrees (in any key) as 1 2 b3 4 5 b6 b7.


To review some scale formulas (in degrees) from regular old 12edo:
To review some scale formulas (in degrees) from regular old 12edo:
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Saturated augmented: 1 #2 #3 #4 #5 #6 #7
Saturated augmented: 1 #2 #3 #4 #5 #6 #7


The two examples above could not be spelled out in 12edo with distinct notes as they can in 19edo.
Lydian Whole Diminished: 1 2 b3 #4 b5 b6 bb7
 
The three examples above could not be spelled out in 12edo with distinct notes as they can in 19edo.


== Chords ==
== Chords ==
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C major chord is spelled C E G (letters) or 1 3 5 (degrees), in either 12edo or 19edo.  C minor chord is spelled C Eb G or 1 b3 5.  But again, some new chords are possible in 19edo that would be problematic in 12edo, because 19edo has some new intervals.
C major chord is spelled C E G (letters) or 1 3 5 (degrees), in either 12edo or 19edo.  C minor chord is spelled C Eb G or 1 b3 5.  But again, some new chords are possible in 19edo that would be problematic in 12edo, because 19edo has some new intervals.


The strongest example of this is the third.  In 12edo, there are major thirds and minor thirds.  A diminished third sounds exactly the same as a suspended second in 12edo, so that sort of chord is never going to define its own sound.  But in 19edo, you can play a diminished third chord 1 bb3 5.  You can also use augmented thirds in 19edo.
The strongest example of this is the third.  In 12edo, there are major thirds and minor thirds.  A diminished third sounds exactly the same as a suspended second in 12edo, so that sort of chord is never going to define its own sound.  But in 19edo, you can play a diminished third chord 1 bb3 5 (notated as Cdim3).  You can also use augmented thirds in 19edo (for example C E# G, would be Caug3).  You could diminish or augment the third and the fifth: Caugaug3 = C E# G# (1 #3 #5), C°dim3 = C Ebb Gb Bbb (1 bb3 b5 bb7).  These spellings would be nonsense in 12edo, although they are certainly not the most consonant-sounding chords, even as an extended set, so they should be used sparingly.


Following in the tradition of 12edo, chord names and roman numeral notation can be exactly the same as it is in classical musical analysis.
Following in the tradition of 12edo, chord names and roman numeral notation can be exactly the same as it is in classical musical analysis.
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This chord structure is pleasant and consonant in 19edo, as it is in 12edo.
This chord structure is pleasant and consonant in 19edo, as it is in 12edo.
=== Roman numeral notation ===
Just how the staff and letter names of notes from 12edo can carry over into 19edo with a simple shift in mindset, roman numeral chord notation can be used in pretty much the same way it was used in 12edo.  Only the relationships between enharmonic equivalent chords are changed.
{| class="wikitable"
|-
! Scale degree
! Name
! Major chord
! Minor chord
|-
| 1
| Tonic
| I
| i
|-
| bb2
| Supertonic
| bbII
| bbii
|-
| b2
| Supertonic
| bII
| bii
|-
| 2
| Supertonic
| II
| ii
|-
| #2/bb3
|
| #II / bbIII
| #ii / bbiii
|-
| b3
| Mediant
| bIII
| biii
|-
| 3
| Mediant
| III
| iii
|-
| #3/b4
|
| #III / bIV
| #iii / biv
|-
| 4
| Subdominant
| IV
| iv
|-
| #4
| Subdominant
| #IV
| #iv
|-
| b5
| Dominant
| bV
| bv
|-
| 5
| Dominant
| V
| v
|-
| #5
| Dominant
| #V
| #v
|-
| b6
| Submediant
| bVI
| bvi
|-
| 6
| Submediant
| VI
| vi
|-
| bb7/#6
|
| bbVII / #VI
| bbvii / #vi
|-
| b7
| Subtonic
| bVII
| bvii
|-
| 7
| Subtonic
| VII
| vii
|-
| #7
| Subtonic
| #VII
| #vii
|}
Again, there are sometimes, confusingly, other notation conventions.  For example, in common practice, the chords in the natural minor scale are i - ii° - bIII - iv - v - bVI - bVII, but since the minor scale is sometimes assumed, some people use the notation "i - ii° - III - iv - v - VI - VII" without the accidentals.  This is not expressly incorrect, but many consider it confusing.  In the case of xenharmonic music, it is recommended to use the accidental marks whenever possible to avoid the confusion introduced by notation that doesn't specify them, compounded by the complication of having more accidentals for which to account.
Another competing form of notation is [[Mason Green's New Common Practice Notation]].


=== Tricks in 19edo ===
=== Tricks in 19edo ===
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In 12edo, there are some key changes that may be subtle, while others can be a little jarring to the listener.
In 12edo, there are some key changes that may be subtle, while others can be a little jarring to the listener.


One method of key change that is subtle is the common chord or pivot chord method. This usually happens on a ii or IV chord, but any chord in two overlapping keys can be used.
One method of key change that is subtle is the common chord or pivot chord method. This usually happens on a ii or IV chord, but any chord in two overlapping keys can be used.


For example:
For example:
Line 225: Line 471:
I - IV - V - I - vi - II - II7 - V
I - IV - V - I - vi - II - II7 - V


It seems like a weird progression, based on numerals, but, this is an example in which the key is pivoting. It's really I - IV - V - I, and then I=IV with the dominant becoming the new tonic, so the second half of the progression is ii - V - V7 I, one of the most common progressions.
It seems like a weird progression, based on numerals, but, this is an example in which the key is pivoting. It's really I - IV - V - I, and then I=IV with the dominant becoming the new tonic, so the second half of the progression is ii - V - V7 I, one of the most common progressions.


Another example from Schubert's op.9 D365
Another example from Schubert's op.9 D365
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== Harmonies ==
== Harmonies ==
The biggest strength of 19edo is its major and minor thirds (or sixths, if you look at inversions) being closer to just intonation than 12edo.  Simple melodies in the major and minor scales with harmonies in thirds or sixths should sound fantastic to anyone able to notice the slight sourness of harmonies in 12edo.
The biggest strength of 19edo is its major and minor thirds (or sixths, if you look at inversions) being closer to just intonation than 12edo.  Simple melodies in the major and minor scales with harmonies in thirds or sixths should sound fantastic to anyone able to notice the slight sourness of harmonies in 12edo.
The fifth is a little flatter in 19edo than it is in 12edo, which is audible to the trained ear and perhaps, even if the beats are not audible to the untrained ear, the loss of consonance might still be "felt" or perceived on a level of lower consciousness by casual listeners.  De-emphasizing the fifth and relying more on harmonies of thirds and sixths is advisable in composition, but laying heavily into less-consonant intervals can also be used for effect to intentionally unsettle the listener.
Add9 chords can be both strong and weak.  An add9 chord, such as Cmajadd9 ("C major add nine"), spelled 1 3 5 9 or, in this case C E G D, benefits from a more consonant third, but also contains a flatter fifth and an over-corrected (sharper) ninth, so the chord, although it sounds generally consonant, can sound very foreign to listeners fully conditioned to 12edo tonalities.
More complex harmonies are possible in 19edo than are available in 12edo, by the nature of the extended option palette of intervals, but most are quite difficult for a beginner to use.  It would be recommended to start out looking at 19edo as an alternative version of 12edo, at first, and then add some experimentation as the composer begins to get comfortable with the nuances of the tuning system.  Although any rule of thumb in music, generally speaking, is just begging to be dashed apart by a good counter-example.
== Serialism ==
One of the more advanced compositional tools in 12edo is "12-tone serialism."  In order to avoid an obvious tonal center in a piece, each of the twelve tones are used once per series. A phrase could consist of one or more series of twelve notes. These notes do not need to appear in the same octave or adjacent octaves, but each note (i.e., Ab A A# B C C#, etc) is to only appear once per series.
This tool can be used in any tuning system with a set number of discrete tones per defined interval.  For example, in Bohlen-Pierce, there are 13 tones per perfect twelfth.  The technique can still be used.  In a continuous tuning system, the technique cannot be used.  But in 19edo, the technique can be used similarly to how it is used in 12edo.
Each of the nineteen notes (i.e., Ab A A# Bb B Cb C C# Db D D# etc.) is to be used once per 19-note series.  The octave of the note and the duration can be whatever the composer chooses.
An example of 19-tone serialism is given in "[https://www.youtube.com/watch?v=JTpF2MifP5Y Brain for Breakfast]" by Bostjan Zupancic.
== Onward ==
19edo can be used as an alternative to 12edo temperament and played un-xenharmonically, but, with the added tonal palette, there is much to discover xenharmonically as well. As a player develops broader skills by performing in 19edo as opposed to a 12-tone system, it should become easier to conceptualize the ideas that go into more complex tuning temperaments. 19edo is a fantastic stepping stone with that regard. But, just as 12edo offers near limitless possibilities with melody and harmony, 19edo offers even more, so it is possible to spend a lifetime with that temperament and still find new concepts.
[[Category:Method]]
[[Category:Approaches to tuning systems]]
[[Category:19edo]]
[[Category:Notation]]
[[Category:Tuning]]
[[Category:Guides]]
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