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).

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:

A Basic Look at Letter Notation in 19edo

Degree	Interval with A	Alternative Interval with A	Name in the key of A	Letter(s)	Enharmonic Equivalents
1	Unison		Tonic	A
2		Diminished Second		A#	Bbb
3	Minor Second			Bb (*)	Ax
4	Major Second		Supertonic	B (*)	Cbb
5		Augmented Second, Diminished Third		B# or Cb
6	Minor Third			C	Bx
7	Major Third		Mediant	C#	Dbb
8		Augmented Third, Diminished Fourth		Db	Cx
9	Perfect Fourth		Subdominant	D
10	Augmented Fourth			D#	Ebb
11	Diminished Fifth			Eb	Dx
12	Perfect Fifth		Dominant	E	Fbb
13	Augmented Fifth			E# or Fb
14	Minor Sixth			F	Ex
15	Major Sixth		Submediant	F#	Gbb
16	Diminished Seventh	Augmented Sixth		Gb	Fx
17	Minor Seventh			G
18	Major Seventh		Subtonic	G#	Abb
19		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.

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.

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

The two 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. You can also use augmented thirds in 19edo.