beat_frequencies

beat_frequency.py

from argparse import ArgumentParser
import sys
import math
import matplotlib.pyplot as plt
import numpy as np


# This variable holds the steps for a minor scale
MinorSteps = [
     0, # A
     2, # B
     3, # C
     5, # D
     7, # E
     8, # F
    10, # G
    12, # A
]

MinorStepNames = [
    'A', 'A#', 'B', 'C', 'C#', 'D', 'D#',
    'E', 'F', 'F#', 'G', 'G#'
]


Steps = [ 1,  3,  5,  6,  8, 10, 12,
         13, 15, 17, 18, 20, 22, 24]

def notestep_to_frequency(base_frequency, step):
    return base_frequency * (2 ** (step / 12))

def frequency_to_notestep(base_frequency, frequency):
    # This is a derivation of the above frequency to solve for notestep
    if frequency == 0:
        return 0
    else:
        return 17.3123404906676 * math.log(frequency / base_frequency)

def main():
    argp = ArgumentParser()
    argp.add_argument(
            '--base',
            type=int,
            default=220)
    args = argp.parse_args()

    # Generate the frequencies of a two octave list of the 12 tone scale.
    freq24 = []
    for i in range(24):
        freq24.append(notestep_to_frequency(args.base, i))

    # Generate the frequencies of a minor scale
    freq8 = []
    for step in MinorSteps:
        freq8.append(notestep_to_frequency(args.base, step))

    # For each note in the minor scale, compute its beat frequency with
    # each note in the 24 tone scale.
    beats = []
    for freq0 in freq24:
        row = []
        for freq1 in freq8:
            beat = abs(freq1 - freq0)
            row.append(beat)
        beats.append(row)

    #plt.imshow(np.array(beats), cmap='jet')

    # Now, derive the number of note steps from the frequency
    notes = []
    for row in beats:
        new_row = []
        for freq in row:
            note = frequency_to_notestep(args.base, freq)
            new_row.append(note)
        notes.append(new_row)

    #plt.imshow(np.array(beats), cmap='inferno')

    # The note numbers can be difficult to interpret, so let's convert them
    # into human readable notes.
    human = []
    for (i, row) in enumerate(notes):
        human_row = []
        for (j, step) in enumerate(row):
            ideal_step = int(step)
            ideal_freq = notestep_to_frequency(args.base, ideal_step)
            ideal_name = MinorStepNames[ideal_step % 12]
            actual_freq = notestep_to_frequency(args.base, step)
            octave = ideal_step // 12
            freq_shift = ideal_freq - actual_freq

            name = '{:+2d}{:2s}{:+6.2f}'.format(octave, ideal_name, freq_shift)
            human_row.append(name)
        human.append(human_row)

    # Print it into a CSV friendly format.
    for row in human:
        for value in row:
            sys.stdout.write('%s,' % value)
        sys.stdout.write('\n')

if __name__ == '__main__':
    main()