Chapter 5: Musical Mathematics

5.1 Probability and Statistics in Music

Notes follow probabilities: tonic notes recur, chromatic tones appear less. Probability and statistics let us tally those choices, whether in a Bach chorale or a Coltrane solo. In Python we’ll call on random, NumPy, and Matplotlib to test musical data.

5.2 Generating Musical Sequences with Weighted Chance

Probability isn’t just analysis. It drives creativity. Assign a weight to each note, then let randomness pick pitches in proportion to those weights.

import random

notes   = ['C', 'D', 'E', 'F', 'G', 'A', 'B']
weights = [0.1, 0.15, 0.2, 0.15, 0.2, 0.1, 0.1]  # likelihood for each note

random_sequence = random.choices(notes, weights, k=10)
random_sequence

Vary the weights to tilt your melody toward major, minor, or modal flavors.