note_frequency.rb

class Note

  class MalformedNotationError < StandardError
  end

  A4_FREQUENCY = 440
  STEP_FREQUENCY_FACTOR = 1.059463094359

  INTERVALS = {'C'  => 0, 'C#' => 1, 'Db' => 1, 'D'  => 2,
               'D#' => 3, 'Eb' => 3, 'E'  => 4, 'F'  => 5,
               'F#' => 6, 'Gb' => 6, 'G'  => 7, 'G#' => 8,
               'Ab' => 8, 'A'  => 9, 'A#' => 10,'Bb' => 10,
               'B'  => 11}

  STEPS_PER_OCTAVE = 12

  attr_reader :cypher, :octave

  def initialize(notation)
    @cypher, @octave = parse_notation(notation)
    @octave = @octave.to_i
  end

  def freq
    A4_FREQUENCY * (STEP_FREQUENCY_FACTOR ** distance_from_a4)
  end

  def distance_from(another)
    self.distance_from_c0 - another.distance_from_c0
  end

  protected

  def distance_from_a4
    distance_from(Note.new('A4'))
  end
  
  def distance_from_c0
    (STEPS_PER_OCTAVE * octave) + distance_in_same_octave
  end

  def distance_in_same_octave
    INTERVALS[cypher]
  end

  def parse_notation(notation)
    match = notation.match /\A([A-G][b#]?)(\d)\z/
    if match.nil?
      raise MalformedNotationError.new("Malformed notation `#{notation}`")
    end      
    match.captures
  end
end

class NoteTest < MiniTest::Test

  def frequencies
    [['C0',  16.35],   ['C#0', 17.32],   ['Db0', 17.32],
     ['D0',  18.35],   ['D#0', 19.45],   ['Eb0', 19.45],
     ['E0',  20.60],   ['F0',  21.83],   ['F#0', 23.12],
     ['Gb0', 23.12],   ['G0',  24.50],   ['G#0', 25.96],
     ['Ab0', 25.96],   ['A0',  27.50],   ['A#0', 29.14],
     ['Bb0', 29.14],   ['B0',  30.87],   ['C1',  32.70],
     ['C#1', 34.65],   ['Db1', 34.65],   ['D1',  36.71],
     ['D#1', 38.89],   ['Eb1', 38.89],   ['E1',  41.20],
     ['F1',  43.65],   ['F#1', 46.25],   ['Gb1', 46.25],
     ['G1',  49.00],   ['G#1', 51.91],   ['Ab1', 51.91],
     ['A1',  55.00],   ['A#1', 58.27],   ['Bb1', 58.27],
     ['B1',  61.74],   ['C2',  65.41],   ['C#2', 69.30],
     ['Db2', 69.30],   ['D2',  73.42],   ['D#2', 77.78],
     ['Eb2', 77.78],   ['E2',  82.41],   ['F2',  87.31],
     ['F#2', 92.50],   ['Gb2', 92.50],   ['G2',  98.00],
     ['G#2', 103.83],  ['Ab2', 103.83],  ['A2',  110.00],
     ['A#2', 116.54],  ['Bb2', 116.54],  ['B2',  123.47],
     ['C3',  130.81],  ['C#3', 138.59],  ['Db3', 138.59],
     ['D3',  146.83],  ['D#3', 155.56],  ['Eb3', 155.56],
     ['E3',  164.81],  ['F3',  174.61],  ['F#3', 185.00],
     ['Gb3', 185.00],  ['G3',  196.00],  ['G#3', 207.65],
     ['Ab3', 207.65],  ['A3',  220.00],  ['A#3', 233.08],
     ['Bb3', 233.08],  ['B3',  246.94],  ['C4',  261.63],
     ['C#4', 277.18],  ['Db4', 277.18],  ['D4',  293.66],
     ['D#4', 311.13],  ['Eb4', 311.13],  ['E4',  329.63],
     ['F4',  349.23],  ['F#4', 369.99],  ['Gb4', 369.99],
     ['G4',  392.00],  ['G#4', 415.30],  ['Ab4', 415.30],
     ['A4',  440.00],  ['A#4', 466.16],  ['Bb4', 466.16],
     ['B4',  493.88],  ['C5',  523.25],  ['C#5', 554.37],
     ['Db5', 554.37],  ['D5',  587.33],  ['D#5', 622.25],
     ['Eb5', 622.25],  ['E5',  659.25],  ['F5',  698.46],
     ['F#5', 739.99],  ['Gb5', 739.99],  ['G5',  783.99],
     ['G#5', 830.61],  ['Ab5', 830.61],  ['A5',  880.00],
     ['A#5', 932.33],  ['Bb5', 932.33],  ['B5',  987.77],
     ['C6',  1046.50], ['C#6', 1108.73], ['Db6', 1108.73],
     ['D6',  1174.66], ['D#6', 1244.51], ['Eb6', 1244.51],
     ['E6',  1318.51], ['F6',  1396.91], ['F#6', 1479.98],
     ['Gb6', 1479.98], ['G6',  1567.98], ['G#6', 1661.22],
     ['Ab6', 1661.22], ['A6',  1760.00], ['A#6', 1864.66],
     ['Bb6', 1864.66], ['B6',  1975.53], ['C7',  2093.00],
     ['C#7', 2217.46], ['Db7', 2217.46], ['D7',  2349.32],
     ['D#7', 2489.02], ['Eb7', 2489.02], ['E7',  2637.02],
     ['F7',  2793.83], ['F#7', 2959.96], ['Gb7', 2959.96],
     ['G7',  3135.96], ['G#7', 3322.44], ['Ab7', 3322.44],
     ['A7',  3520.00], ['A#7', 3729.31], ['Bb7', 3729.31],
     ['B7',  3951.07], ['C8',  4186.01], ['C#8', 4434.92],
     ['Db8', 4434.92], ['D8',  4698.63], ['D#8', 4978.03],
     ['Eb8', 4978.03], ['E8',  5274.04], ['F8',  5587.65],
     ['F#8', 5919.91], ['Gb8', 5919.91], ['G8',  6271.93],
     ['G#8', 6644.88], ['Ab8', 6644.88], ['A8',  7040.00],
     ['A#8', 7458.62], ['Bb8', 7458.62], ['B8',  7902.13]]
  end

  def test_frequencies
    frequencies.each do |f|
      assert_in_delta f[1], Note.new(f[0]).freq, 0.01
    end
  end

  def test_distance_from
    note = Note.new('A4')
    assert_equal -1,  note.distance_from(Note.new('A#4'))
    assert_equal 1,   note.distance_from(Note.new('Ab4'))
    assert_equal 57,  note.distance_from(Note.new('C0'))
    assert_equal -39, note.distance_from(Note.new('C8'))
    assert_equal 0,   note.distance_from(Note.new('A4'))
  end

  def test_raises_malformed_notation_error
    assert_raises(Note::MalformedNotationError) do
        Note.new('4A')
    end
  end
end