A bit better modification of the argument: continue cycle of 5th. After 12 steps, you get (3/2)^12=129.7, which is really close to 128=2^7 (whole number of octaves). That's where 12 steps come from!
And from here, the natural idea follows: what if we take not exactly 3/2 for fifth, but value x such that x^12 is exactly equal to 128? This leads to equal temperament.
Yeah, that might be it! (Not sure that it's true historically though).
And from here, the natural idea follows: what if we take not exactly 3/2 for fifth, but value x such that x^12 is exactly equal to 128? This leads to equal temperament.
Yeah, that might be it! (Not sure that it's true historically though).