Mason Green's New Common Practice Notation

This is Mason Green's proposed notation for chord progressions in scales related to:

• 19-edo itself (in which the octave is just but the fifth significantly flat).
• Carlos Beta (in which the just perfect fifth is divided into 11 equal parts, making the octave about 12 cents sharp.
• Phoenix (a compromise between the two in which the just 9:5 interval is divided into 16 equal parts. Thus the octaves and the fifths are both flat but less so than in Carlos beta and 19edo respectively. The octave here is about 9 cents sharp).

This notation is referred to as "New Common Practice" (NCP), in that it extends the Roman numeral analysis used for common practice to a 19-tone system. It should not be confused with standard Roman Numeral notation, which can also apply to 19-EDO and other tuning methods as well.

New intervals

19-EDO tempers out the large septimal diesis (49:48). Some tones can be seen as enharmonically equivalent to other tones.

Designating a particular pitch as the tonal center enables the other notes to be named relative to it. These names, which are independent of the notation used for the actual notes, are as follows:

Number of steps	Interval name	JI intervals represented	Scale degree
			Name	Symbol
				Number	Roman numeral
0	Unison	1/1	Tonic	1	I
1	Augmented unison	25/24, 21/20, 28/27, 26/25, 27/26	Upper bleeding tone	1♯	I♯
2	Minor second	15/14, 16/15, 13/12, 14/13	Upper leading tone	2♭	II♭
3	Major second	9/8, 10/9	Supertonic	2	II
4	Supermajor second; subminor third	7/6, 8/7, 15/13	Caesiant	2♯ ; 3♭	II♯ , III♭
5	Minor third	6/5, 25/21	Minor mediant	3	III
6	Major third	5/4, 16/13, 26/21	Major mediant	3	III
7	Supermajor third, subfourth	32/25, 9/7, 13/10	Rubric	3♯, 4♭	III♯ , IV♭
8	Perfect fourth	4/3	Subdominant	4	IV
9	Augmented fourth	25/18, 7/5, 18/13	Hygrant	4♯	IV♯
10	Diminished fifth	36/25, 10/7, 13/9	Subhygrant	5♭	V♭
11	Perfect fifth	3/2	Dominant	5	V
12	Augmented fifth, subminor sixth	25/16, 14/9, 20/13	Subrubric	5♯, 6♭	V♯, VI♭
13	Minor sixth	8/5, 13/8, 21/13	Minor submediant	6	VI
14	Major sixth	5/3	Major submediant	6	VI
15	Supermajor sixth, subminor seventh, harmonic seventh	7/4, 12/7, 26/15	Subcaesiant	6♯	VI♯
16	Minor seventh	9/5, 16/9	Subtonic	7♭	VII♭
17	Major seventh	15/8, 13/7, 28/15, 24/13	Lower leading tone	7	VII
18	Diminished octave	27/14, 25/13	Lower bleeding tone	1♭	I♭

The name "Caesiant" comes from the Latin word for blue (caesius), and is a reference to the relationship between septimal intervals and the "blue notes" used in African-American styles music such as blues and jazz. In 12edo, blue notes are typically described as inflections, but in enneadecimal scales they are promoted to a full scale degree. The tonic pentad (which is the closest NCP analogue to the major chord) contains the subcaesiant.

The rubric is named by analogy with the caesiant (it's a "red" third, instead of a "blue" one).

The name hygrant is a reference to Christiaan Huygens (the 7:5 interval is also known as Huygens' tritone) and is also a pun on the word "hydrant" and the prefix "hygro-" (meaning wet); this interval is one of the harder-to-distinguish "wet" intervals.

One noted feature of NCP (unlike standard common practice) is that compositions are not confined to the notes of the diatonic scale, or even to the "superdiatonic" (12-note subset of 19) extension. Both of these are fundamentally 5-limit systems, and modulation by 7-limit intervals will quickly take us outside of these confines.

As a result, the requirement of diatonicity is dropped and the whole 19-note gamut is accessible. There are therefore no "modes" in NCP, since all notes and chords are defined solely by their relationship to the tonic (the "home key"). This opens unusual possibilities, such as mixing major and minor tonality in the same composition.

Expanding beyond triads

Triads containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies. Occasionally tetrads (seventh chords) appear.

In NCP, triads may be considered incomplete depending on the context, and pentads, hexads, and even higher-order chords can appear and sound great. Also, there are many different possible chords, rather than just the major and minor. As a result, generalizing Roman numeral analysis presents problems.

The proposed solution is to add a string of subscripted lowercase letters to the Roman numeral.

For otonal chords, such as the common major triad and its variants, the first letter denotes the harmonic corresponding to the lowest (bass) note of the chord. The second letter denotes the harmonic corresponding to the highest (treble) note of the chord. The third and subsequent letters (if present) correspond to all the harmonics "skipped" (i. e., not present) between the root and the bass. If there are only two letters, it means that all the (sub)harmonics between the treble and bass (excepting those which are automatically skipped, see below) are present.

Utonal chords, such as the minor triad and its variants, are described similarly except they are "upside down" (so the letters denote subharmonics rather than harmonics, and the first letter corresponds to the treble and the second to the bass).

The lowercase letters used are:

a=4

b=5

c=6

d=7

e=8

f=9

g=10

h=12

i=13

j=14

k=15

l=16

m=18

n=20

o=21

p=24

q=25

r=26

s=27

t=28

u=30

v=32

The 11th, 17th, 19th, 23rd, and 29th harmonics have no letters assigned to them and are automatically assumed to be skipped since enneadecimal scales do not approximate them easily. The 13th is not skipped because it is approximated fairly well, particularly if the octave is stretched a bit.

Whether or not the chord is otonal or utonal is indicated by the Roman numerals being uppercase (for otonal chords) or lowercase (for utonal chords); this is a generalization of common practice notation where uppercase Roman numerals correspond to major chords and lowercase Roman numerals correspond to minor chords.

This system can be used to describe a very large number of chords, although not every possible chord (there are some "mixed" chords, which are not purely utonal or otonal, that cannot be described using this system; alternative symbols will need to be developed for them). Nevertheless, the most commonly used and harmonically strong chords all all describable using this notation.

Some important examples include:

Symbol	Name	Just approximation
I(ae)	Major pentad	Otonal 4:5:6:7:8
i(ae)	Minor pentad	Utonal 4:5:6:7:8
I(ch)	Major hexad	Otonal 6:7:8:9:10:12
i(ch)	Minor hexad	Otonal 6:7:8:9:10:12

Due to tempering, some chords may be notated in more than one way. For example, the chord I_(gkhj) , which corresponds to the otonal 10:13:15, is tempered to be the same as i_(cfe)(the utonal 6:7:9).

Chord progressions

Porting is the process of translating chord progressions from one tuning system to another. Most chord progressions can be ported in some way, although it's important to note that some commas are not tempered out anymore, and there are chord progressions that close in one tuning (for example: 12-edo) that don't close in another (for example: 19-edo) (so that you will end up one semitone higher or lower than where you started). Most of the time, however, this can easily be remedied. For instance, the Coltrane changes no longer work as before because three major thirds do not make an octave. However, a variant can be constructed in which one of the major thirds is replaced with a supermajor third; this version does close.

Porting the following progressions is trivial:

• All progressions using only I, IV, and V.
• The circle progression (vi - ii- V - I).
• The 50s progression (I – vi - IV - V)
• "Axis of Awesome" (I - V - vi - IV).
• Pachelbel's Canon (I - V - vi - iii - IV - I - IV - V)

There are also many new possibilities that don't have any close analogues in 12edo. In general, enneadecimal scales offer more flexibility as well as orders of magnitude more possibilities for chord progressions, due to the greater diversity of both chords and scale degrees.