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For the mel frequency spectrum, which is used extensively in audio-processing, the technique uses subjects to identify pitches of uniform distance from one another. Isn't this distance just the 12-th root of two in the regular frequency scale. why must we incorporate subjective listening?

thanks a.s.

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    $\begingroup$ 12 tone equal temperament is a historically recent invention in Western music, and quite unnatural. Humans most likely evolved relative pitch identification capability many many millennia before this artificial tuning system was ever invented. $\endgroup$ – hotpaw2 Aug 21 '15 at 5:20
  • $\begingroup$ 12th root of 2 has nothing to do with anything. uniform pitch distance = uniform frequency ratio. 100 Hz is the same pitch distance from 200 Hz as 1000 Hz is from 2000 Hz. $\endgroup$ – endolith Aug 21 '15 at 20:34
  • $\begingroup$ @hotpaw2 thanks, so the idea of the half step is pretty arbitrary except maybe experimental testing that humans can only discern half tones, but equal temperament in essence has the same goal as uniform pitch distance since the twelth-root of 2 is applied as the same ratio. i.e. a = 440Hz, one octave higher a has freq = 880, two octave higher a has freq 1760 etc $\endgroup$ – Austin Shin Aug 24 '15 at 2:56
  • $\begingroup$ Humans vary in their pitch discernment capabilities, but most musicians can detect an instrument about 6 cents (or about 1/16th of a semitone ) "out of tune" relative to other notes in the mid-range, but are worse at tuning very high or low notes (the octaves at the far ends of an 88-key piano keyboard). $\endgroup$ – hotpaw2 Aug 24 '15 at 3:11

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