Equal Temperament
12-TET · cents · Werckmeister 1687
Physics: 12-TET: each semitone = 2^(1/12) ≈ 1.05946. 1 cent = 2^(1/1200). Interval errors vs just intonation: major third +13.7 cents (noticeable), perfect fifth −2 cents (barely audible), perfect fourth +2 cents. History: Zarlino (1558) theorized ET; Mersenne (1636) calculated; Werckmeister (1687) well-temperament (Bach's WTC exploits its characteristics); 12-TET became standard by ~1900. Alternative divisions: 7-TET (nearly perfect fifths), 19-TET (better thirds), 31-TET (very close to just intonation for most intervals).