Class: HeadMusic::Analysis::PitchCollection

Inherits:
Object
  • Object
show all
Defined in:
lib/head_music/analysis/pitch_collection.rb

Overview

A PitchCollection is a collection of one or more pitches with specific registers. In music theory, "pitch collection" refers to an ordered or unordered group of actual pitches, as distinct from a "pitch-class set" which abstracts away register and octave equivalence. See also: PitchClassSet

Constant Summary collapse

TERTIAN_SONORITIES = 
{
  implied_triad: [3],
  triad: [3, 5],
  seventh_chord: [3, 5, 7],
  ninth_chord: [2, 3, 5, 7],
  eleventh_chord: [2, 3, 4, 5, 7],
  thirteenth_chord: [2, 3, 4, 5, 6, 7] # a.k.a. diatonic scale
}.freeze
TRIAD_PATTERNS = 
{
  major: [%w[M3 m3], %w[m3 P4], %w[P4 M3]],
  minor: [%w[m3 M3], %w[M3 P4], %w[P4 m3]],
  diminished: [%w[m3 m3], %w[m3 A4], %w[A4 m3]],
  augmented: [%w[M3 M3], %w[M3 d4], %w[d4 M3]]
}.freeze

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(pitches) ⇒ PitchCollection

Returns a new instance of PitchCollection.



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# File 'lib/head_music/analysis/pitch_collection.rb', line 27

def initialize(pitches)
  @pitches = pitches.map { |pitch| HeadMusic::Rudiment::Pitch.get(pitch) }.sort.uniq
end

Instance Attribute Details

#pitches ⇒ Object (readonly)

Returns the value of attribute pitches.



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# File 'lib/head_music/analysis/pitch_collection.rb', line 18

def pitches
  @pitches
end

Instance Method Details

#==(other) ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 93

def ==(other)
  pitches.sort == other.pitches.sort
end

#augmented_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 132

def augmented_triad?
  triad_type?(:augmented)
end

#bass_pitch ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 81

def bass_pitch
  @bass_pitch ||= pitches.first
end

#consonant_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 109

def consonant_triad?
  major_triad? || minor_triad?
end

#diatonic_intervals ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 43

def diatonic_intervals
  @diatonic_intervals ||= pitches.each_cons(2).map do |pitch_pair|
    HeadMusic::Analysis::DiatonicInterval.new(*pitch_pair)
  end
end

#diatonic_intervals_above_bass_pitch ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 49

def diatonic_intervals_above_bass_pitch
  @diatonic_intervals_above_bass_pitch ||= pitches_above_bass_pitch.map do |pitch|
    HeadMusic::Analysis::DiatonicInterval.new(bass_pitch, pitch)
  end
end

#diminished_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 128

def diminished_triad?
  triad_type?(:diminished)
end

#eleventh_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 172

def eleventh_chord?
  hexachord? && tertian?
end

#equivalent?(other) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 97

def equivalent?(other)
  pitch_classes.sort == other.pitch_classes.sort
end

#first_inversion_seventh_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 156

def first_inversion_seventh_chord?
  tetrachord? && reduction.uninvert.diatonic_intervals.all?(&:third?)
end

#first_inversion_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 140

def first_inversion_triad?
  trichord? && reduction.uninvert.diatonic_intervals.all?(&:third?)
end

#inspect ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 85

def inspect
  pitches.map(&:to_s).join(" ")
end

#integer_notation ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 59

def integer_notation
  # questions:
  # - should this be absolute? 0 = C?
  # - should there be both absolute and relative versions?
  @integer_notation ||= begin
    return [] if pitches.empty?
    diatonic_intervals_above_bass_pitch.map { |interval| interval.semitones % 12 }.flatten.sort.unshift(0).uniq
  end
end

#invert ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 69

def invert
  inverted_pitch = pitches[0] + HeadMusic::Analysis::DiatonicInterval.get("perfect octave")
  new_pitches = pitches.drop(1) + [inverted_pitch]
  HeadMusic::Analysis::PitchCollection.new(new_pitches)
end

#major_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 120

def major_triad?
  triad_type?(:major)
end

#minor_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 124

def minor_triad?
  triad_type?(:minor)
end

#ninth_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 168

def ninth_chord?
  pentachord? && tertian?
end

#pitch_class_set ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 35

def pitch_class_set
  @pitch_class_set ||= HeadMusic::Analysis::PitchClassSet.new(pitch_classes)
end

#pitch_classes ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 31

def pitch_classes
  @pitch_classes ||= reduction_pitches.map(&:pitch_class).uniq
end

#pitches_above_bass_pitch ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 55

def pitches_above_bass_pitch
  @pitches_above_bass_pitch ||= pitches.drop(1)
end

#reduction ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 39

def reduction
  @reduction ||= HeadMusic::Analysis::PitchCollection.new(reduction_pitches)
end

#reduction_pitches ⇒ Object (private) 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 209

def reduction_pitches
  pitches.map do |pitch|
    pitch = HeadMusic::Rudiment::Pitch.fetch_or_create(pitch.spelling, pitch.register - 1) while pitch > bass_pitch + 12
    pitch
  end.sort
end

#root_position_seventh_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 152

def root_position_seventh_chord?
  tetrachord? && reduction_diatonic_intervals.all?(&:third?)
end

#root_position_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 136

def root_position_triad?
  trichord? && reduction_diatonic_intervals.all?(&:third?)
end

#scale_degrees ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 191

def scale_degrees
  @scale_degrees ||= pitches.empty? ? [] : scale_degrees_above_bass_pitch.unshift(1)
end

#scale_degrees_above_bass_pitch ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 195

def scale_degrees_above_bass_pitch
  @scale_degrees_above_bass_pitch ||= diatonic_intervals_above_bass_pitch.map(&:simple_number).sort - [8]
end

#second_inversion_seventh_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 160

def second_inversion_seventh_chord?
  tetrachord? && reduction.uninvert.uninvert.diatonic_intervals.all?(&:third?)
end

#second_inversion_triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 144

def second_inversion_triad?
  trichord? && reduction.invert.diatonic_intervals.all?(&:third?)
end

#seventh_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 148

def seventh_chord?
  tetrachord? && tertian?
end

#size ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 101

def size
  pitches.length
end

#sonority ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 199

def sonority
  @sonority ||= HeadMusic::Analysis::Sonority.new(self)
end

#tertian? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 180

def tertian?
  return false unless diatonic_intervals.any?

  inversion = reduction
  pitches.length.times do
    return true if TERTIAN_SONORITIES.value?(inversion.scale_degrees_above_bass_pitch)
    inversion = inversion.invert
  end
  false
end

#third_inversion_seventh_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 164

def third_inversion_seventh_chord?
  tetrachord? && reduction.invert.diatonic_intervals.all?(&:third?)
end

#thirteenth_chord? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 176

def thirteenth_chord?
  heptachord? && tertian?
end

#to_s ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 89

def to_s
  pitches.map(&:to_s).join(" ")
end

#triad? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 105

def triad?
  trichord? && tertian?
end

#triad_type?(type) ⇒ Boolean (private)

Returns:

  • (Boolean) 


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# File 'lib/head_music/analysis/pitch_collection.rb', line 205

def triad_type?(type)
  TRIAD_PATTERNS[type].include?(reduction_diatonic_intervals.map(&:shorthand))
end

#uninvert ⇒ Object 



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# File 'lib/head_music/analysis/pitch_collection.rb', line 75

def uninvert
  inverted_pitch = pitches[-1] - HeadMusic::Analysis::DiatonicInterval.get("perfect octave")
  new_pitches = [inverted_pitch] + pitches[0..-2]
  HeadMusic::Analysis::PitchCollection.new(new_pitches)
end