Primer for 19edo
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 without new accidentals).
Music in what is essentially 19edo (1/3 comma meantone) dates back to the 16th century, contemporary with the initial proposals for 12edo. Major and minor thirds and sixths in 19edo sound sweeter (i.e. are closer to common just intervals) than they do in 12edo, 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
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)
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:
| Scale Degree | Interval | Alternative Interval | Name | In A | Enharmonic Equivalents |
|---|---|---|---|---|---|
| 1 | Unison | Tonic | A | ||
| bb2 | Diminished Second | A# | Bbb | ||
| b2 | Minor Second | Bb (*) | Ax | ||
| 2 | Major Second | Supertonic | B (*) | Cbb | |
| #2/bb3 | Augmented Second, Diminished Third | B# or Cb | |||
| b3 | Minor Third | C | Bx | ||
| 3 | Major Third | Mediant | C# | Dbb | |
| #3/b4 | Augmented Third, Diminished Fourth | Db | Cx | ||
| 4 | Perfect Fourth | Subdominant | D | ||
| #4 | Augmented Fourth | D# | Ebb | ||
| b5 | Diminished Fifth | Eb | Dx | ||
| 5 | Perfect Fifth | Dominant | E | Fbb | |
| #5 | Augmented Fifth | Diminished sixth | E# or Fb | ||
| b6 | Minor Sixth | F | Ex | ||
| 6 | Major Sixth | Submediant | F# | Gbb | |
| bb7/#6 | Diminished Seventh | Augmented Sixth | Gb | Fx | |
| b7 | Minor Seventh | G | |||
| 7 | Major Seventh | Subtonic | G# | Abb | |
| #7 | Augmented Seventh | Ab | Gx |
*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.
Key signatures are the same, but again, with the extra notes and different enharmonic equivalents, some key signatures can get messy. For example, the key of Bbb would have bb's on B and E, and b's on C, D, F, G, and A. Thinking of rewriting this key as A# might seem better, but then the key signature would contain x's on C, F, and G, and #'s on A, B, D, and E, which is actually worse.
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. One proposed modified solfege system is in the table below. See also List of uniform solfeges for EDOs -- 19edo (3 vowels).
| Scale Degree | Interval | Alternative Interval | Name | Solfege | Enharmonic Equivalents |
|---|---|---|---|---|---|
| 1 | Unison | Tonic | do | ||
| bb2 | Diminished Second | ro | (di) | ||
| 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 | Augmented Fifth | Diminished sixth | si | lo | |
| b6 | Minor Sixth | le | |||
| 6 | Major Sixth | Submediant | la | ||
| bb7/#6 | Diminished Seventh | Augmented Sixth | ta / li | ||
| b7 | Minor Seventh | te | |||
| 7 | Major Seventh | Subtonic | ti | ||
| #7 | Augmented Seventh | to | (da) |
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.
One approach is to maintain familiar spacing and tune open strings (low to high): E A D G B E.
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:
Major scale: 1 2 3 4 5 6 7
Natural minor: 1 2 b3 4 5 b6 b7
Mixolydian (a.k.a. "dominant"): 1 2 3 4 5 6 b7
Harmonic minor: 1 2 b3 4 5 b6 7
Dorian: 1 2 b3 4 5 6 b7
Lydian: 1 2 3 #4 5 6 7
Hungarian minor: 1 2 b3 #4 5 b6 7
Where it gets exciting is when you start to play with the extra notes when they no longer parse back into 12edo. For example, in 12edo, a diminished third is the same thing as a major second, so you can't play the notes C D Ebb in succession as distinct tones, but in 19edo, you can. So it will open up new tonal possibilities within the framework of classical western music theory, but without as many boundaries. You can make scales that wouldn't have made any sense in 12edo.
Saturated diminished: 1 bb2 bb3 b4 b5 bb6 bb7
Saturated augmented: 1 #2 #3 #4 #5 #6 #7
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
Just like how the most basic scales can be easily ported from 12edo into 19edo without too much thought about notation, the same applies for chords.
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 (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.
For example: in the key of A minor, a song might have the chords: Am - F - Dm - G, which could be represented as a movable structure as i - bVI - iv - bVII (typically the accidentals are used, even if the chords are in key with the tonic, being minor, since the context is not always clear). These chords would be spelled out as follows:
Am: A C E (tonic)
F: F A C (subdominant)
Dm: D F A (submediant)
G: G B D (subtonic)
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.
| 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
There are some tricks in 19edo a composer can use to make things sound not-so-familiar, even though 19edo generally sounds like "regular music."
Key changes
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.
For example:
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.
Another example from Schubert's op.9 D365
I - I - V - V7 - VII - #IV7 - VII
This is a tricky key change, with the tonic going VII=I and then the last three chords are I - V7 - I
Another method is by substituted chords, usually through a chain of ii - V - I or V - I changes, which, perhaps in itself isn't a key modulation, but can be used to that effect in a larger scope.
A simple example is
iii - VI7 - ii - V7 - I
iii is ii of ii, and VI7 is V7 of ii. You can chain a bunch of these together:
i - IV7 - #vi - bIII7 - #v - bII7 - #iv - VII7 - iii - VI7 - ii - V7 - I
Each two chords are ii and V7 of the root note of the following chord.
But more common in pop and rock music are simple, just shift the tonal center of the song up a semitone (e.g. "Man in the Mirror" by Michael Jackson), or a whole tone (e.g. "Got to Be Real" by Cheryl Lynn), or, if your singer is feeling confident, a minor third (e.g. "To Be with You" by Mr. Big), and proceed with exactly the same chord progression in that key with a higher root note.
In 19edo, though, you can subvert the listener's expectation by modulating around a pivot chord with the same enharmonic spelling in 12edo, but a different spelling in 19edo.
I'd like to revisit the Schubert example from above. For clarity's sake, let's say that the key is D major, so I - I - V - V7 - VII - #IV7 - VII is D - D - A - A7 - C# - G#7 - C#. This takes advantage of the spelling of A7 chord as A C# E G, and C# is C# E# G#, picking the third degree of the A major chord and increasing the others to slide into a major chord. A7 with a tonal perspective of C# looks like C# diminished with an altered seventh, so the change from A7 - C# gives a sense of cadence.
Try two ways:
I - I - V - V7 - VII - #IV7 - VII
and
I - I - V - V7 - bVII6 - IV7 - bVII
The second progression slips the C# down to a C natural and maintains the other notes of the A7 chord instead, which might be unexpected.
Or, in a pop or rock context, instead of stepping up the tonal center by a minor second or major second or major third, go in between, and step up a diminished third (or augmented second). If the chord progression of the song is simpler, this works well for shock value, bringing in a lot of musical tension for just a moment. Eventually, the listener will acclimate to the new tonal center.
Example:
I - IV - V - I - IV - V - #II - #V - #VI - #II -#V - #VI - #II
Or, in the key of C: C - F - G - C - F - G - D# - G# - A# - D# - G# - A# - D#
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 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 "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.