Equal Temperament

i ching symbolInteresting how Zhu Zaiyu, in China in 1584, was creating music based on mathematical ideas (Zhu Zaiyu was the first person to solve the equal temperament problem mathematically), while in Italy, Jacopo Brocardo (Anglicised as James Brocard(e), Latin: Jacobus Brocardus Pedemontanus) (c.1518 – 1594?), who was an Italian Protestant convert and biblical interpreter, had prophesied the year 1584 as the inauguration of a major new cycle.

The two figures frequently credited with the achievement of equal temperament are Zhu Zaiyu or Chu-Tsaiyu in 1584 and Simon Stevin in 1585. According to Fritz A. Kuttner, a critic of the theory,[1] it is known that “Chu-Tsaiyu presented a highly precise, simple and ingenious method for arithmetic calculation of equal temperament mono-chords in 1584” and that “Simon Stevin offered a mathematical definition of equal temperament plus a somewhat less precise computation of the corresponding numerical values in 1585 or later.” Both developments occurred independently.[2]

Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu[3] and provides textual quotations as evidence.[4] Zhu Zaiyu is quoted as saying that, in a text dating from 1584, “I have founded a new system. I establish one foot as the number from which the others are to be extracted, and using proportions I extract them. Altogether one has to find the exact figures for the pitch-pipers in twelve operations.”[4]