Composing Music with Grammars

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Composing Music with Grammars
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• grammar
• the whole system and structure of a language or
  of languages in general, usually taken as
  consisting of syntax and morphology (including
  inflections) and sometimes also phonology and
  semantics.
• a particular analysis of the system and
  structure of language or of a specific language.
• a set of actual or presumed prescriptive
  notions about correct use of a language
• Computing a set of rules governing what
  strings are valid or allowable in a language or
  text.

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• syntax - the arrangement of words and phrases to
  create well-formed sentences in a language.
• morphology - the study of the forms of things, in
  particular
• Linguistics the study of the forms of words.
• semantics - the branch of linguistics and logic
  concerned with meaning.
• the meaning of a word, phrase, sentence, or
  text

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• Definitions
• token - grammatical symbol
• root token root of parse tree
• vocabulary (V) all the tokens plus the null
  token
• alphabet of terminals (T) subset of vocabulary
• language (L) subset of finite concatenations of
  tokens of T
• alphabet of non-terminals (N) categories of
  macrostructures in V
• sentential form sequence of non-terminals
• production (rewrtiting) rule LHS ? RHS

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• Generative Grammar expressed as a quadruple
• G (N,T,?,P)
• G - generative grammar
• N - alphabet of non-terminals
• T - alphabet of terminals
• ? - root token
• P - collection of production rules of the form
• a ? ß, where a, ß ? (N ? T), and (N n T) Ø.
  (denotes the powerset or set of all subsets)

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• Chomskys four types of grammars
• Free (type 0) imposes no restrictions on the
  form of the production rule. Intermediate
  strings can expand and contract in length.
  Allows for infinite strings and null strings.
•  
• Context-sensitive (type 1) A a B ? A ß B.
  alpha produces beta in the context of A and B. a
  ? Ø is forbidden.
• Context-free (type 2) very useful with regards
  to natural language and programming. Good for
  representing multi-leveled syntactic formations
  of music. Any non-terminal (representing a
  macrostructural category like motive, phrase,
  sentence, section, movement, entire piece, etc.)
  may generate a string of tokens at a lower level.
•  
• Finite-state (type 3) no more than one
  non-terminal token may appear on each side of any
  production rule. Type 2 does not have this
  limitation.

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• Production/Rewrite Rules
• Random selection
• Serial selection Useful for musical purposes.
  No object is selected again until all the others
  are selected. (Compare to serialism)
• Finite-state transition matrix successive
  productions depend on previous productions. For
  example
• LHS-gt
• (A.1.0.1.0)
• (B.0.1.0.0)
• (C.1.1.0.0)
• (D.1.1.1.1)
• Selection functions higher level complex
  functions that return an integer value that
  corresponds to an object index.
• Meta-production rule a single generation by a
  rule is to be substituted for all occurrences of
  the LHS of the rule. An example of horizontal
  dependency.

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• The Bol Processor (Bel and Kippen)
• A tabla-oriented generative grammar based on
  machne learning. Acquires knowledge through
  parsing expert input, and attempted generation,
  followed by expert approval or disapproval.

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• EMI experiments in Musical Intelligence (David
  Cope, UC Santa Cruz)
• Arguably the most successful and developed
  automated grammar for music making. Analyzes the
  style of a composer through batch input of a
  multitude of pieces. Produces pieces of music
  that are highly faithful to the composers style.
• Developed in response to writers block occurring
  after the spending of a large commission for an
  opera. Composed in 10 days.

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• David Cope discusses EMI in a Radiolab interview

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• SenGen Production Rules
• Sentence -gt PrepositionalPhrase, NounPhrase1
  VerbPhrase
•  
• VerbPhrase1 -gt AdverbPhrase Verb1
  PrepositionalPhrase AdverbPhrase
•  
• VerbPhrase2 -gt AdverbPhrase Verb2
  NounPhrase PrepositionalPhrase
  AdverbPhrase
• NounPhrase -gt Determiner,90
  AdjectivePhrase Noun PrepositionalPhrase
•  
• NounPhrase1 -gt Determiner,90
  AdjectivePhrase agent
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• AdverbPhrase -gt AdverbPhrase,25 Adverb
•  
• AdjectivePhrase -gt AdverbPhrase,15 Adjective
  PrepositionalPhrase
• PrepositionalPhrase -gt Preposition NounPhrase
  , PrepositionalPhrase (last stacked
  PrepPhrase preceeded by and)

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• Note credit must be given to Curtis Roads and
  Paul Wieneke from whose paper Grammars as
  Representations for Music, I quote directly at
  times in this presentation as well as the New
  Oxford American Dictionary application bundled
  with Mac OS X. S.R. Holtzman deserves credit for
  the section on production rules taken from Using
  Generative Grammars for Music Composition. For a
  proper bibliography, see my accompanying paper,
  Composing Music with Grammars.