Mezzo

Mezzo is a Haskell library and embedded domain-specific language for music description. Its novelty is in the fact that it can enforce various rules of music composition statically, that is, at compile-time. This effectively means that if you write "bad" music, your composition will not compile – think of it as a very strict spell-checker for music.

• Getting started
  • Prerequisites
  • Installation
  • First composition
• Composing in Mezzo
  • Basic concepts
  • Literal vs. builder style
  • Primitives
    • Notes
    • Rests
    • Chords
  • Composition
    • Harmonic composition
    • Melodic composition
  • Melodies
    • Examples:
  • Chord progressions
    • Harmonic regions
    • Phrases
• Scores
  • Score building
• Rendering and exporting
• Rule sets
  • The free rule set
  • The classical rule set
  • The strict rule set
  • Custom rule sets
  • Other constraints
• License
• Acknowledgments

Getting started

This section explains how to install Mezzo and start using the library.

Prerequisites

Mezzo is a Haskell library with only a few dependencies. The main requirement is GHC 8.0.2: the package uses the latest and greatest features of the Haskell type system so it needs the most up-to-date version of the compiler. If you're using stack, use the lts-8.5 resolver (or higher).

Installation

If using Cabal, run

cabal update
cabal install mezzo

If using Stack, you will need to add the package to your extra-deps in your stack.yaml (as Mezzo is not part of Stackage yet), and then add it normally to your .cabal file dependencies:

extra-deps: [ mezzo-0.3.1.0 ]

build-depends: base >= 4.7 && < 5
             , mezzo

Build the file, and you should be good to go.

First composition

Create a new project (e.g. with stack new) with a Main module. Type:

import Mezzo

comp = defScore $ start $ melody :| c :| d :| e :| f :>> g

main :: IO ()
main = renderScore "comp.mid" "First composition" comp

Save, build and execute (e.g. with stack exec <project_name>). You should get a .mid file in the project directory which looks something like this:

To test the correctness checking, change the d note in comp to a b. You should see the following when you save the file:

• Major sevenths are not permitted in melody: C and B
• In the first argument of ‘(:|)’, namely ‘melody :| c :| b’
  In the first argument of ‘(:|)’, namely ‘melody :| c :| b :| e’
  In the first argument of ‘(:>>)’, namely
    ‘melody :| c :| b :| e :| f_’

Composing in Mezzo

This section provides more detail on the syntax of Mezzo.

Basic concepts

Music description languages are textual representations of musical pieces, used for note input or transcription. Most MDLs provide ways of inputting notes, rests and ways to combine these into melodies or chords. Mezzo additionally lets users input chords in their symbolic representation, as well as chord progressions using a schematic description of functional harmony.

Literal vs. builder style

Mezzo provides two main ways of creating musical values:

• Literal style: create musical values with explicit constructors of literal values. For example a C natural in octave 4 is written as pitch _c _na _o4 and can be abbreviated to _cn. A quarter note (pitch with duration) is then written as noteP (pitch _c _na _o4) _qu or noteP _cn _qu. Literal values are prefixed with an underscore and can be combined using the constructors pitch and noteP.
• Builder style: create musical values by sequencing their attributes from left to right. This style is more concise, flexible and readable than literal style and is therefore preferred. Creating a middle C quarter note is c qn, an F sharp dotted sixteenth note in the 5th octave is fs sn' or f sharp sn'. Similarly, a C major chord would be c maj qc, a B flat diminished seventh in first inversion with dotted half duration would be b flat dim7 inv hc'.

The rest of this guide uses the builder style.

Primitives

Notes

Notes are given by their pitch and duration. In builder style, every pitch has an explicit value, consisting of three parts:

• Pitch class: one of c, d, e, f, g, a or b; determines the position of the note in the octave, a white key on the keyboard.
• Accidental: a suffix of the pitch class, one of f (flat, e.g. bf qn) or s (sharp, e.g. fs qn). Natural accidentals are not specified, so c means C natural. Accidentals can also be written out as a separate attribute (c sharp qn), or even repeated (for example, double sharps: c sharp sharp qn or cs sharp qn).
• Octave: the last component of the value. The default octave is 4, this is unmarked. Lower octaves are marked with _, __, _3, _4 and _5. Higher octaves are marked with ', '', '3 and '4. A C natural in octave 2 is therefore c__ qn, a B flat in octave 7 is bf'3 qn.

Durations are written after the pitch. For notes, the value is the first letter of the duration name (eighth, quarter, etc.) followed by n for note, e.g., qn for quarter note. A dotted duration is specified by following the name with a ' (single quote): hn' is a dotted half note, with the length of three quarters.

Rests

Rests are similar to notes, but with r instead of the pitch and an r instead of n in the duration. A quarter rest is r qr and a dotted whole rest is r wr'.

Chords

Chords are given by their root (a pitch), type, inversion and duration: a C major quarter triad in first inversion is c maj inv qc.

• Root: specified the same way as in a note (c, af'', etc.).
• Type: three classes of chords: dyads, triads and tetrads.
  • Dyads: A harmonic interval consisting of 2 notes. 5 types possible: minor thirds (min3), major thirds (maj3), fourths (fourth), fifths (fifth) and octaves (oct).
  • Triads: 3 pitches separated by thirds. 4 types possible: major (maj), minor (min), augmented (aug) and diminished (dim), based on the size of the intervals between the pitches.
  • Tetrads: 4 pitches separated by thirds (the top one is a seventh above the bottom one). 5 types possible: major seventh (maj7), major-minor/dominant seventh (dom7), minor seventh (min7), half-diminished seventh (hdim7), diminished seventh (dim7).
• Doubling: dyads and triads can be doubled to become a triad and tetrad respectively. This is done by repeating the bottommost note an octave higher, so a doubled C major third would consist of a C, an E, and another C an octave above. Doubling is specified by a D after the chord type, e.g. fifthD, majD or augD.
• Inversion: all of the types can be followed by a ' and then a separate attribute i0, i1, i2 or i3 to specify zeroth, first, second or third inversion: c maj' i2 qc. Alternatively, the inv attribute can be added (any number of times) to invert a chord once (or any number of times): c maj inv inv qc.

Chord durations end with a c and can be dotted, as before: c min7 qc, f sharp hdim inv wc'.

Composition

Mezzo has two ways of composing music, inspired by Haskore: sequential (melodic) and parallel (harmonic) composition. In addition, Mezzo provides a convenient shorthand input method for melodies.

Harmonic composition

Harmonic composition (:-:) plays two pieces of music at the same time:

g qn :-: e qn :-: c qn

For consistency, pieces should be composed from top voice to the bottom: the above example would therefore play a C major triad. The composed pieces can be any musical composition, as long as the durations of the pieces matches. If this is not the case, the shorter voice has to be padded by rests where necessary.

When using (:-:), both harmonic intervals and harmonic motion are checked for correctness, so it is mainly intended for contrapuntal compositions. For homophonic compositions (where the "voices" are not independent, the top one being the main melody and the bottom ones being the accompaniment), you can use the hom function which does not enforce rules of harmonic motion. For example,

(g qn :|: a qn) :-: (c qn :|: d qn)

would not compile due to a parallel fifth ((:|:) is melodic composition, described in the next section). However,

(g qn :|: a qn) `hom` (c qn :|: d qn)

compiles, as hom only checks for harmonic dissonance.

Melodic composition

Melodic composition (:|:) plays one piece of music after the other:

c qn :|: d qn :|: e qn

The pieces don't have to only be notes or single voices, but the number of voices in the two pieces must match. For example, the code

c qn :|: c maj qc

fails to compile (and unfortunately produces a very cryptic error message), as the first note is only one voice while the chord is three voices. We can remedy this either by explicitly adding rests, or padding the first piece with silent voices, using the functions pad, pad2, `