Codex Harmonicus I — De Proportione Sonorum

Folio I of the Codex Harmonicus, a recovered-manuscript-style plate on the divided string and the ratios of consonance — the single string, the wheel of fifths, and why some numbers please the ear.

What's inside

• The monochord and its division into consonances, with a diagram of the canon divided at the octave, fifth, fourth and third
• The Pythagorean comma — why twelve fifths overshoot the octave, and where the surplus must hide
• How one plucked string sounds many voices at once, shown on a diagram of the first four harmonic modes
• A table of the intervals on a 1200 mm canon, with their ratios given both as whole numbers and in thousandths of the octave
• The twelfth root of two and the equal semitone, and a table comparing Pythagorean, just, mesotonic and equal temperament
• A table of which small-number ratios the ear accepts as consonant, and which it refuses