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)

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. 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 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.