User:Vector/Vector's chord names

Goals:

• Make chord names entirely systematic and derivable from their intervals (no shorthands like Δ, + for augmented, or °)
• Support any interval quality system
• Avoid the use of accidentals wherever possible
• Do not place numbers directly after the note name (make chord quality always explicit)

Reserved symbols

Symbol	Function	Notes
- (hyphen-minus)	Removal indicator
+ (plus)	Addition indicator
, (comma)	Top note of tertian chain indicator	Using commas to separate chord names is unambiguous.
~ (tilde)	Reduced chord name indicator

This system uses spaces as an important syntactic element, use a . (period) or _ (underscore) when this is unviable.

Basic structure

Chords (in diatonic, separate schemas may be specified for other scale forms) are conceptualized as a chain of diatonic thirds with alterations, removals, and additions. Notating a chain of thirds that land on intervals with the same quality is simple:

P1 - M3 - P5 - M7 = "M7"

Perfect is considered to be simultaneously major and minor, and the first interval quality specified is assumed to apply to the third and "cascade" to all following notes of the chord. Thus, a minor chord looks like this:

P1 - m3 - P5 - m7 = "m7"

Interval qualities "cascade", meaning that they apply to all following intervals in the chain by default until a new quality is specified. For example,

P1 - M3 - P5 - m7 = "Mm7"

All interval qualities past the first must specify what interval they apply to. So for this example, M (major) applies to all intervals until the seventh, which is m (minor). If any more notes were in the chord, they would also be minor. To specify the highest note without having to specify its quality, you use a comma: a dominant chord with a minor ninth is

P1 - M3 - P5 - m7 - m9 = "Mm7,9"

By default, chords are assumed to have a root, third, and fifth.

To specify a specific root, place it before the rest of the chord name, separated by a space (or an underscore, dot, or other preferred separator where spaces are not supported. But not a dash, that has its own meaning). So, a major chord on C is always "C M" or "C.M" or "C_M", not "CM".

Additionally, "perfect" (P) is only specified to avoid ambiguity ("C d11" is always all intervals diminished including the 11th, and "C dP11" specifies that the 11 is meant to be perfect) and does *not* cascade, so the interval quality following a perfect interval must always be specified. That is, "C dP11,13" is not a valid chord name, but "C dP11d13" is.

To remove a note, place its degree after a minus sign:

P1 - M3 - m7 = "Mm7-5"

Note that although replacing a quality, it does not cascade, so that "-" by itself just means a chord without a 3rd, not a chord without a third or fifth. This applies also to a - that is followed by a degree that is not in the chord, such as 4, or 11 in chords with a ninth, seventh, or fifth as their highest note.

Other than removals, comma-affixed numbers, and the aforementioned case with perfect intervals specifying a degree without a quality is invalid. "7" is not a valid chord symbol, and a note name by itself cannot refer to a chord. These degrees are ALWAYS specified with interval qualities, NOT accidentals. "Mb9" is invalid (unless you have a magical interval quality named "bajor" in your system, or whatever). To specify the addition of a minor ninth, use "M+m9".

After this, any additions and alterations can be specified. They can be recognized by the breaking of the chain of thirds (for example, "M7d5" or "M7M10") or by following removals or comma-affixed numbers (Mm7-5M10, Mm7,9M10).

An interval in this section of the name is an addition if:

- it references a degree that does not exist in the chord, or

- it is prefixed by a "+"

Otherwise, it is an alteration. The first "+" in a chord name unambiguously signals that the chain of thirds section of the name does not continue to that point (and if a chord name begins with a "+" after the note, then there is no chain of thirds). So, C M+m9 is a tetrad, not a pentad, meanwhile "C M+m3" is a chord with both a major and a minor third and "C Mm3" is just a minor triad (but notated as if the minor third is replacing a default major third).

Specifying "3" is not necessary in the main interval chain or in removals, but it is always necessary in additions and alterations. Removals always lack a quality, so "-M7" is always the removal of the 3rd followed by the addition of a major seventh, not the removal of a major seventh. Additionally, -5 is always the removal of the perfect fifth, while -P5 is always the removal of the third followed by the alteration of the chord's fifth to the perfect fifth, or the addition of a perfect fifth to the chord.

Notes

"C d7" is taken to mean a chord that diminishes all intervals (including the third, so it has a diminished third) and stacks thirds up to the seventh (so C Ebb Gb Bbb). A chord that diminishes only the seventh should be C Md7 or C md7, depending on the quality of your third. The standard diminished seventh chord is C d7m3 or C m3d5,7. This system works with essentially any system of qualities, but for clarity multi-symbol qualities (i.e. "AA" for double-augmented, "sA" for semiaugmented, or even interval-size-based ones like "sM" for submajor) should be enclosed in parentheses.

Standard chords

Name	Notes	VCN
major triad	P1 - M3 - P5	M
minor triad	P1 - m3 - P5	m
augmented triad	P1 - M3 - A5	MA5
diminished triad	P1 - m3 - d5	md5
augmented 7th chord	P1 - M3 - A5 - m7	MA5m7
diminished 7th chord	P1 - m3 - d5 - d7	d7m3
half diminished 7th chord	P1 - m3 - d5 - m7	m7d5
major 7th chord	P1 - M3 - P5 - M7	M7
minor 7th chord	P1 - m3 - P5 - m7	m7
dominant 7th chord	P1 - M3 - P5 - m7	Mm7
minor major 7th chord	P1 - m3 - P5 - M7	mM7
sus2 chord	P1 - M2 - P5	-M2
sus4 chord	P1 - P4 - P5	-4
quartal chord	P1 - P4 - m7	+4m7

Inversions

Name	Notes
major	P1 - M3 - P5	M
major 1st inversion	P1 - m3 - m6	m-5m6
major 2nd inversion	P1 - P4 - M6	--5+4M6

Reduced chord names

Inversions are somewhat awkward to notate and change the apparent root of the chord (as per the chart above), but there is an inversion-agnostic way to write chords.

A tilde can be placed before the chord name and after the note name to specify that it is a reduced chord name, where the notes are octave-equivalent pitch classes. The chain of thirds works normally but the highest note that can be reached by it is 13 (equivalent to 6), meanwhile additions and alterations can only use 1 through 7. (2 is considered an alteration of a 9 if it exists in the chain by default, however, so ~m9M2 is considered to be altering the minor 2nd represented by the 9th in the third chain to a major 2nd. A major add9 chord is ~MM2.)

(This introduces a potential incompatibility with the "mid" symbol used by Kite's ups and downs notation, which is also a ~. N for neutral is preferred in this instance, and this use of a tilde cannot be mistaken for a tempered interval as diatonic scale degrees are already inherently tempered.)

Microtonal peculiarities

To generalize to any moment-of-symmetry scale in KISS notation, the scale degree to be used for the chain can be explicitly specified along with the MOS. Otherwise, consider the two generators within one period of the scale. If one of them is divisible into two parts that belong to the same interval category (for instance, a fifth divisible into two thirds, regardless of their quality), make that divided interval the base of the chain, so that the generator is found as the top note of a default triad. Otherwise, use the generator (that is less than half the period) itself. Ordinals are defined relative to the MOS in question, and reduced chord names generalize in the logical manner.

The application of subchromas to interval qualities cascades in the standard manner, but "skips" perfect intervals unless explicitly specified (in the chain or in alterations) to apply to them. This is to make notating, for instance, a pental major triad simple ((vM)); a wolf major triad is (vM)(vP)5.