A language for harmonic analysis and roman numerals

# Notating roman numeral analysis

## A quick reference

```# Using the default key (C Major)
V7          # G Dominant seventh chord

# Using a reference key
a:viio7     # G# Fully-diminished seventh chord

# Establishing a new key
V7/V        # D Dominant seventh chord
ii7         # A Minor seventh chord

# Use of special chords and inversions
viio7/ii    # F# Fully-diminished seventh chord
V43/V       # G Dominant seventh chord, second inversion
V6          # C Major triad, first inversion
V7          # C Dominant seventh chord
V6/N        # Db Major triad, first inversion (Dominant of the Neapolitan)
N           # Gb Major triad (Neapolitan of F Minor, root position)
```

## Guideline

A notation for roman numerals could be divided in three types of chords

• Tertian chords (e.g., `I`, `ii`, `V7`, etc.)
• Special chords (e.g., `Neapolitan`, `German augmented sixth`, etc.)
• Descriptive chords (e.g., `CM3D5`)

## Tertian chords

The syntax of a tertian chord is based mainly on the definition of a key, scale degree, added intervals, and an inversion.

Other features like missing intervals, tonicizations, modulations, and alternative notations also exist and will be covered later.

### Key

Keys in the notation are divided in three categories, depending on their function:

• Reference key: A key given by the user as the reference key for a particular annotation.

Example:

``````F:I
``````

A first degree major triad, `I`, in the context of `F Major`.

• Established key: Similar to a reference key, except that a established key becomes the new default key when no key is specified (default mechanism for annotating modulations).

Example:

``````F=>:I
IV
``````

A first degree major triad, `I`, in the context of `F Major`. The second annotation corresponds to a `IV` degree in `F Major`, namely, `Bb Major`.

• Applied key: The applied key is the key from which the roman numeral is interpreted

Example:

```C=>:V/V     # G Major is the applied key,
# roman numeral is V of G Major (D Major triad)

V/V/V       # D Major is the applied key,
# roman numeral is V of D Major (A Major triad)
```

### Scale degrees (or roman numerals)

• Scale degrees consist of the symbols `I-VII` and `i-vii`
• The notation for roman numerals is case sensitive
• The reason why it is case sensitive is because roman numerals provide two assets of information
• The root of the chord with respect to a key, given by the roman numeral itself, and,
• The quality of the third accompanying that root, given by the case of the roman numeral

For example:

`I` - The root is the first degree of the establshed key, and it is accompanied by a major third

`i` - The root is the first degree of the establshed key, and it is accompanied by a minor third

It might seem weird to denote the root of the chord and (only) its third with the scale degree.

## Behavior of the fifth

By default, the fifth of the chord is a perfect fifth, therefore, in major and minor triads, it is not necessary to add any additional symbol to denote the triad other than:

• The scale degree
• The case of the scale degree