Logical Representation of Musical Concepts

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Logical Representation of Musical Concepts

• By Somnuk Phon-Amnuaisuk
• Presented by Shane Hoversten
• USC ISE 575, February 22, 2007

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What are we trying to do?

• Were interested in some domain. (Music.)
• We want to talk about the entities (concepts)
  that exist in that domain.
• To do so, we need to agree on what the concepts
  are, and have some way to map them into language
  ( a symbol system) s.t. they can be reasoned
  with (manipulated).
• The nature of the manipulation, and the nature of
  the domain, will determine the concepts and their
  representations.

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A motivating example

• Were in LA. Lets take an example from another
  domain.

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(No Transcript)
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Producer to writer

• Make me a show like Prison Break, only w/ a mad
  scientist as the lead and with his virginal
  sister as the felon. Except not stupid, and with
  lots of flashbacks, like Lost.

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Make me a show like Prison Break, only w/ a
mad scientist as the lead and with his virginal
sister as the felon. Except not stupid, and with
lots of flashbacks, like Lost.

• Whats a show, and what does it mean for a show
  to be like another show?

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Make me a show like Prison Break, only w/ a
mad scientist as the lead and with his virginal
sister as the felon. Except not stupid, and with
lots of flashbacks, like Lost.

• To understand this, we need to know the concept
  of lead, mad scientist, virginal sister,
  and felon. We also need to know how to replace
  one entity with another.

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Make me a show like Prison Break, only w/ a
mad scientist as the lead and with his virginal
sister as the felon. Except not stupid, and with
lots of flashbacks, like Lost.

• Whats stupid, in this context? How can we make
  something not stupid while still complying with
  the rules of the domain? These rules are
  themselves concepts, or at least operators on
  concepts.

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Make me a show like Prison Break, only w/ a
mad scientist as the lead and with his virginal
sister as the felon. Except not stupid, and with
lots of flashbacks, like Lost.

• To understand the concept flashback we first
  need concepts for time, the flow of time,
  causality

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Concepts

• What are they, exactly?
• Opinions vary
• Necessary and sufficient vs. exemplar vs.
  prototype vs
• How do you find them?
• Domain analysis.
• although this begs the question. More on this
  later.

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Concept discovery
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What makes these things concepts?

• Statistical regularity
• subject to cognitive limitations
• Some regularities cannot be perceived due to
  working memory constraints
• Concepts and information are intimately connected
• One persons concept is another persons noise

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For instance

• I have no idea what this means.

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Concepts and representations

• A single concept can have many representations.
  (the paper calls these views)
• A representation is a convenience, and is good
  inasmuch as it facilitates what you want to do
  with the concept.
• Nitpick this is NOT unstructured knowledge

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A perfectly good structure

• This particular model seems to use hidden units
  1, 4, and 6 to activate nouns (word units
  1-16).   Verbs are activated by hidden unit 5 and
  2 (word units 17-28).  And articles are activated
  by hidden units 9 and 2.   Different models will
  have different units that represent these
  distinctions.

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Anyway.
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Select representations

• Notation (notes)
• Sequencers (notes in time)
• Synthesizers (note production)
• Inferrers (symbolic manipulation)
• Different aspects of a concept are emphasized in
  different representations (views.)

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What we want to do with these representations

• (according to the paper)

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1 Narrative and description

• Prison Break is, at this point, a show thats
  lost its way. The characterization is shallow
  and the situations are absurd. The plot moves
  with all the subtlety of a cast-iron skillet
  applied to the face.

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2 Analyze structural patterns

• Michael and Lincoln narrowly escape the
  governments clutches. Then Maroney finds a
  source of inside information that reveals the
  fugitives next move.
• (ARGH!!)

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3 Analyze extra-musical contents

• Prison Break, with its muddy view of morality,
  is a show that could not have existed a decade
  ago. A charming but evil president, good guys
  who are bad guys - the confused ethics of the
  modern era have marked irrevocably televisions
  attitude toward its audience.

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Abstraction again

• We abstract the domain so that it is expressive
  enough for us to say things we want to say and
  abstract enough to be computationally feasible.
• (Remember the Borges map example?)

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This looks a lot like OOP
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Class instances have name, type (concept) and
attributes
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Operators are overloaded to work with different
objects.
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Classes (concepts) can model hierarchies by
containing other objects (classes)
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Classes can export different views to offer
clients different key abstractions.
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Theres even OOP programming

• Score(musical materials, interpretations)
• Imagine
• sOrig new Score(Blue Suede Shoes, Perkins)
• sFunky new Score(Blue Suede Shoes, Elvis)

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This is no surprise

• OOP was born out of work in category and concept
  theory
• Any good conceptual decomposition will lend
  itself to programmatic manipulation
• There is a general science of abstraction
• The hard work is in figuring out what the
  concepts are, and how they relate to each other

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Summary

• To discuss a domain, we need to have identified
  and agreed upon the key abstractions of that
  domain.
• How, precisely, the key abstractions can be
  identified is a huuuuuge topic. For the musical
  domain, theres five hundred years of prior work
  to guide us.
• Representing these abstractions in some regular,
  logical form allows them to be manipulated and
  reasoned with by humans and by machines.
• I hate Prison Break, but I cant stop.