A language for harmonic analysis and roman numerals.
A language for encoding roman numeral analysis
The easiest way to test the language is to download the pip package
pip install harmalysis
and try the harmalysis interpreter
python -m harmalysis
Try some entries in the interpreter. Here is a quick reference of possible annotations.
# Using the default key (C Major) I # C Major triad IV # F Major triad V7 # G Dominant seventh chord
# Using a reference key a:i # A Minor triad a:viio7 # G# Fully-diminished seventh chord a:VI # F Major triad
# Establishing a new key I # C Major triad iii # E Minor triad V7/V # D Dominant seventh chord G=>:I # G Major triad IV # C Major triad ii7 # A Minor seventh chord V # D Major triad
# Use of special chords and inversions f=>:i # F Minor triad viio7/ii # F# Fully-diminished seventh chord iio # G Diminished triad V43/V # G Dominant seventh chord, second inversion V6 # C Major triad, first inversion V7 # C Dominant seventh chord i # F Minor triad V6/N # Db Major triad, first inversion (Dominant of the Neapolitan) N # Gb Major triad (Neapolitan of F Minor, root position) i # F Minor triad
The chord annotations in harmalysis can be divided in three types of chords:
- Tertian chords (e.g.,
- Special chords (e.g.,
German augmented sixth, etc.)
- Descriptive chords (e.g.,
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 and alternative notations are also available.
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.
A first degree major triad,
I, in the context of
- Established key: Similar to a reference key, except that a established key becomes the new default key when no key is specified.
This is the suggested notation for establishing a key at the beginning of the piece, or after a modulation.
F=>:I IV # <-- The IV degree of F major (Bb major triad)
The first annotation corresponds to a first degree major triad,
I, in the context of
The second annotation corresponds to a
IV degree in
F Major, namely,
- Tonicized key: The tonicized key is the key from which the roman numeral is interpreted
C=>:V/V # G Major is the tonicized key, # roman numeral is V of G Major (D Major triad) V/V/V # D Major is the tonicized key, # roman numeral is V of D Major (A Major triad)
In the case of multiple levels of tonicization (e.g., the
V/V/V annotation), the sequence of tonicized keys are resolved recursively from right to left until a resulting key is found. This key will be the tonicized key.
harmalysiskeeps track of all the intermediate tonicizations and they can be retrieved from the returned object.
Scale degrees (or roman numerals)
- Scale degrees consist of the symbols
- The notation for roman numerals is case sensitive
- They are case sensitive because they 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
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.
What about the fifth of the triad?
By default, the fifth of the chord is a perfect fifth.
Major and minor triads
Therefore, major and minor triads can be described with only a case-sensitive scale degree (lower-case for minor, and upper-case for major triads))
I # C major i # c minor
Augmented triads are denoted by the
+ symbol after the scale degree.
c:III+ # Eb augmented triad
Augmented triads are only accepted when the scale degree is upper cased. That is, it implies a major triad. In this context, the
+ can be interpreted as an augmented fifth instead of a perfect fifth.
Diminished triads are denoted by the
o symbol after the scale degree.
c:viio # B diminished triad
Diminished triads are only accepted when the scale degree is lower cased. That is, it implies a minor triad. In this context, the
o can be interpreted as a diminished fifth instead of a perfect fifth.
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