Just Intonation

Physics: Just major scale ratios: 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2. Equal temperament: 2^(n/12). Syntonic comma: 81/80 ≈ 21.5 cents (difference between Pythagorean major third 81/64 and just major third 5/4). Pythagorean comma: (3/2)^12/2^7 ≈ 23.46 cents (12 perfect fifths vs 7 octaves). Wolf fifth: 40/27 ≈ 680 cents (vs 702 for perfect fifth). Harpsichords were retuned between pieces to favor different key centers.