The straight and narrow

Just to keep the record straight, it should be noted that the first equal-tempered tuning systems were not actually developed in ancient Greece, but rather in China. Although there is little evidence that Han dynasty Taoist philosophers Liu An (劉安) and Jing Fang (京房) did more than articulate what is essentially a mathematical problem of how to divide the octave into twelve equal portions around the first and second centuries BCE, an ingenious solution to the puzzle was at last published in 1584 in a treatise written by Zhu Zai-yü (朱載堉) called A New Account of the Science of Pitch Pipes. 

Zai-yü's method was elegantly simple: Multiply the ratio corresponding to the musical interval of a perfect fifth (3:2) to obtain a new equivalent ratio, 750:500. Then, subtract 1 from the numerator, shrinking the harmonic ratio ever so slightly. When these "imperfect" intervals are stacked in a series, one on top of the next (along what musicians today call the "circle of fifths") the result is reasonably close to every degree of the 12-note equal-tempered scale, with the 13th note matching very closely with the octave; something that isn't at all possible if you stack 12 fifths having a "perfect" ratio of 3:2. (The modern derivation, incidentally, is based on roots: namely, the 12th root of 2, but such mathematical conveniences were barely understood in antiquity).    

It appears that the problem of equal temperament was for the Chinese primarily one of theoretical rather than practical importance, emerging over many centuries by way of ancient Taoist ritual rather than arising out of the demands newly encountered in the construction of workable keyboard instruments capable of being played in any key without excessive dissonance, as was the case in 17th century Europe. Chinese scholars had already established a tradition of commentary on the proper tuning of bamboo pitch pipes going back as far as 2700 BCE. These ancient scholars were mainly interested in the psycho-spiritual aspects of sound and musical pitch in relation to their unique strand of theosophical cosmology which, among other things, commemorated the passing of a year with a series of monthly ceremonies associated with specific customs, modes of behavior, colors, foods and dress, along with musical pitches which were said to represent a kind of "balance of energies" for each calendar month. The question, then, of what the correct pitches were became one of extreme importance. Consequently, although Zhu Zai-yü is now credited as the earliest inventor of twelve-tone equal temperament, Chinese music overall doesn't seem to have had very much traffic with it except in this rather scholarly, rarified context prior to the modern era.   
      
For further reading and general information on the historical development of equal-tempered tuning, see Isacoff, 2001: Temperament (Vintage Books). See also Needham & Ronan, 1978: The Shorter Science and Civilisation in China, Volume 4 - Part 1 (Cambridge University Press). A more recent Chinese treatment by Hui Yu (喻輝) can also be found here.