Reply to Darren Burgess

I wrote,

>> The mathematically correct description of 12tET was found in China
shortly
>> before it was found in the West, and the theoretical idea of 12tET goes
back
>> to antiquity in both cultures

Darren Burgess wrote,

>Thanks for the clarification. I didn't know this. If you have a moment
>please take some time to explain more fully.

According to Manuel Op de Coul's careful research (thanks Manuel!), Prince
Tsai-y� published the first mathematically correct calculation of 12-tET in
1584, and Simon Stevin did so in 1585, though Partch credits Mersenne as
having been the first Westerner to do so. Aristoxenus described the division
of the octave into 12, 18, or 24 aurally equal parts in 330 B.C., and Ho
Tcheng-Tien apparantly had the idea of 12-tET around 400 A.D., though the
idea of a 12-tone Pythagorean scale is attributed by the Chinese to one Ling
Lun supposedly of the 27th century B.C. . . .