Perfect Fourths Calculator

fourthscalculator.py

#!/usr/bin/python3
# perfect fourths calculator for Geometric Elamite Musical Hypothesis
# 0xabad1dea (Melissa Elliott) May 5th 2022
import math

# reference pitch
a4 = 440.0

scalenames = ["A4", "Ab", "G", "Gb", "F", "E", "Eb", "D", "Db", "C", "B", "Bb", "A3"]
scale = [a4]
cents = [0]

# calculate a complete cycle of descending fourths
for i in range(0,12):
    # descend exactly one octave (double length of string)
    n = scale[i] / 2;
    # go back up by half of half (string is 1.5x length of original string)
    n = n + (n/2)
    # fold into one octave (cut string in half) if necessary
    if(n < a4/2):
        n = n*2
    scale.append(n)

# put them in order from highest pitch to lowest
scale.sort(reverse=True)

# calculate the cents distribution over our octave
for i in range(0,12):
    cents.append(1200 * math.log2(scale[i]/scale[i+1]))


# display
print("Note\tPitch\tStep c\tTotal cents")
for i in range(0,13):
    print("%s\t%.2f\t%.2f\t%.2f" % (scalenames[i], scale[i], cents[i], sum(cents[0:i+1])))
# the result will be very slightly off from equal temperament
# this is not an error. A3 should be exactly a pythagorean comma
# (23.46) short of a perfect 1200.