Representation of musical notation in Haskell Edward Lilley - - PowerPoint PPT Presentation

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Representation of musical notation in Haskell Edward Lilley Institute of Astronomy, University of Cambridge September 9, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Representation of musical notation in Haskell

Edward Lilley

Institute of Astronomy, University of Cambridge

September 9, 2017

Edward Lilley Representation of musical notation in Haskell

SLIDE 2

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Motivation

Edward Lilley Representation of musical notation in Haskell

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Theory

(Notated) musical pitches are the points on a lattice (Notated) musical intervals connect the points, forming a ‘ee Abelian group’ with two generators

Edward Lilley Representation of musical notation in Haskell

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Theory

a♮ b♮ c♯ d♯ e♯ f𝄫 g𝄫 a♭ b♭ c♮ d♮ e♮ f♯ g♯ A♯ B♯ a♯ b♯ c𝄫 d𝄫 b𝄬 c♭ d♭ e♭ f♮ g♮ A♮ B♮ d𝄬 e𝄬 f♭ g♭ A♭ B♭

Edward Lilley Representation of musical notation in Haskell

SLIDE 5

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Theory

a♮ b♮ c♯ d♯ e♯ f𝄫 g𝄫 a♭ b♭ c♮ d♮ e♮ f♯ g♯ A♯ B♯ a♯ b♯ c𝄫 d𝄫 b𝄬 c♭ d♭ e♭ f♮ g♮ A♮ B♮ d𝄬 e𝄬 f♭ g♭ A♭ B♭

M2 m2

Edward Lilley Representation of musical notation in Haskell

SLIDE 6

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Theory

a♮ b♮ c♯ d♯ e♯ f𝄫 g𝄫 a♭ b♭ c♮ d♮ e♮ f♯ g♯ A♯ B♯ a♯ b♯ c𝄫 d𝄫 b𝄬 c♭ d♭ e♭ f♮ g♮ A♮ B♮ d𝄬 e𝄬 f♭ g♭ A♭ B♭

P5 P8

Edward Lilley Representation of musical notation in Haskell

SLIDE 7

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Theory

a♮ b♮ c♯ d♯ e♯ f𝄫 g𝄫 a♭ b♭ c♮ d♮ e♮ f♯ g♯ A♯ B♯ a♯ b♯ c𝄫 d𝄫 b𝄬 c♭ d♭ e♭ f♮ g♮ A♮ B♮ d𝄬 e𝄬 f♭ g♭ A♭ B♭

A1 d2

Edward Lilley Representation of musical notation in Haskell

SLIDE 8

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Theory

‘Syntonic’ temperaments assign two equency ratios to the two generators ‘Equal’ temperaments project the two dimensions down to one

Edward Lilley Representation of musical notation in Haskell

SLIDE 9

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Theory

Pythagorean P5 → 3/2, P8 → 2 ‘Quarter-comma meantone’ M3 → 5/4, P8 → 2 12-equal temperament d2 → 1, P8 → 2 19-equal temperament dd2 → 1, P8 → 2 31-equal temperament dddd3 → 1, P8 → 2

Edward Lilley Representation of musical notation in Haskell

SLIDE 10

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Theory

Pythagorean P5 → 3/2, P8 → 2 ‘Quarter-comma meantone’ M3 → 5/4, P8 → 2 12-equal temperament d2 → 1, P8 → 2 19-equal temperament dd2 → 1, P8 → 2 31-equal temperament dddd3 → 1, P8 → 2

Edward Lilley Representation of musical notation in Haskell

SLIDE 11

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Implementation

Flexibility (via typeclasses) in what counts as a Pitch, Interval

r Duration

A Note is an ordered pair (Pitch, Duration) A Phrase is just a linked list, [Note] A piece of music consists of a Rose tree of musical phrases Internally the preferred lattice basis is (A1, d2) Have to invert a 2 ∗ 2 matrix to calculate tuning map

Edward Lilley Representation of musical notation in Haskell