Class: HeadMusic::Rudiment::Tuning::Pythagorean

Inherits:
HeadMusic::Rudiment::Tuning show all
Defined in:
lib/head_music/rudiment/tuning/pythagorean.rb

Overview

Pythagorean tuning system based on stacking perfect fifths (3:2 ratio)

Constant Summary collapse

INTERVAL_RATIOS =

Frequency ratios for intervals in Pythagorean tuning (relative to tonic) Generated by stacking perfect fifths and reducing to within one octave

{
  unison: Rational(1, 1),
  minor_second: Rational(256, 243),        # Pythagorean minor second
  major_second: Rational(9, 8),            # Pythagorean major second
  minor_third: Rational(32, 27),           # Pythagorean minor third
  major_third: Rational(81, 64),           # Pythagorean major third (ditone)
  perfect_fourth: Rational(4, 3),          # Perfect fourth
  tritone: Rational(729, 512),             # Pythagorean tritone (augmented fourth)
  perfect_fifth: Rational(3, 2),           # Perfect fifth
  minor_sixth: Rational(128, 81),          # Pythagorean minor sixth
  major_sixth: Rational(27, 16),           # Pythagorean major sixth
  minor_seventh: Rational(16, 9),          # Pythagorean minor seventh
  major_seventh: Rational(243, 128),       # Pythagorean major seventh
  octave: Rational(2, 1)                   # Octave
}.freeze
CHROMATIC_RATIOS =

Additional chromatic intervals for enharmonic equivalents

{
  augmented_unison: Rational(2187, 2048),   # Pythagorean augmented unison (sharp)
  diminished_second: Rational(256, 243)     # Same as minor second in Pythagorean
}.freeze

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(reference_pitch: :a440, tonal_center: nil) ⇒ Pythagorean

Returns a new instance of Pythagorean.



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# File 'lib/head_music/rudiment/tuning/pythagorean.rb', line 32

def initialize(reference_pitch: :a440, tonal_center: nil)
  super
  @tonal_center = HeadMusic::Rudiment::Pitch.get(tonal_center || "C4")
end

Instance Attribute Details

#tonal_center ⇒ Object (readonly)

Returns the value of attribute tonal_center.



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# File 'lib/head_music/rudiment/tuning/pythagorean.rb', line 30

def tonal_center
  @tonal_center
end

Instance Method Details

#calculate_tonal_center_frequency ⇒ Object (private) 



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# File 'lib/head_music/rudiment/tuning/pythagorean.rb', line 55

def calculate_tonal_center_frequency
  # Use equal temperament to get the tonal center frequency from the reference pitch
  interval_to_tonal_center = (tonal_center - reference_pitch.pitch).semitones
  reference_pitch_frequency * (2**(interval_to_tonal_center / 12.0))
end

#frequency_for(pitch) ⇒ Object 



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# File 'lib/head_music/rudiment/tuning/pythagorean.rb', line 37

def frequency_for(pitch)
  pitch = HeadMusic::Rudiment::Pitch.get(pitch)

  # Calculate the frequency of the tonal center using equal temperament from reference pitch
  tonal_center_frequency = calculate_tonal_center_frequency

  # Calculate the interval from the tonal center to the requested pitch
  interval_from_tonal_center = (pitch - tonal_center).semitones

  # Get the Pythagorean ratio for this interval
  ratio = ratio_for_interval(interval_from_tonal_center)

  # Calculate the frequency
  tonal_center_frequency * ratio
end

#ratio_for_interval(semitones) ⇒ Object (private) 



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# File 'lib/head_music/rudiment/tuning/pythagorean.rb', line 61

def ratio_for_interval(semitones)
  # Handle octaves
  octaves = semitones / 12
  interval_within_octave = semitones % 12

  # Make sure we handle negative intervals
  if interval_within_octave < 0
    interval_within_octave += 12
    octaves -= 1
  end

  # Get the base ratio
  base_ratio = case interval_within_octave
  when 0 then INTERVAL_RATIOS[:unison]
  when 1 then INTERVAL_RATIOS[:minor_second]
  when 2 then INTERVAL_RATIOS[:major_second]
  when 3 then INTERVAL_RATIOS[:minor_third]
  when 4 then INTERVAL_RATIOS[:major_third]
  when 5 then INTERVAL_RATIOS[:perfect_fourth]
  when 6 then INTERVAL_RATIOS[:tritone]
  when 7 then INTERVAL_RATIOS[:perfect_fifth]
  when 8 then INTERVAL_RATIOS[:minor_sixth]
  when 9 then INTERVAL_RATIOS[:major_sixth]
  when 10 then INTERVAL_RATIOS[:minor_seventh]
  when 11 then INTERVAL_RATIOS[:major_seventh]
  end

  # Apply octave adjustments
  base_ratio * (2**octaves)
end