How Many Micro tones you think are like A limit

  1. You mean in an octave? Mathematically there is no limit but there is a point where frequencies will be so close to each other that humans can't distinguish them anymore. If I remember correctly, that point would be around 5 cents (5% or 1/20 of a semitone), so the absolute maximum judging from that should be 240 notes per octave.

  2. Nice, you beat me to it, though to be fair, there's a difference between the melodic JND at around 5 cents and the harmonic JND at around 3.5 cents.

  3. In terms of mathematics, you can have infinite amount of notes between any two arbitrary notes. If you have a note at 20.921934hz, then you could have another at 20.921935hz and million notes between them.

  4. It's not so much an innate or early learning thing like absolute pitch is, but learning what to listen for when hearing an interval (and then having the interval occur for long enough to hear it). Fairly fine distinctions can result in noticeably different speeds of beating in the harmonics. For example, the best approximation to the 3/2 perfect fifth in 31edo, which is 218/31, is only about 5 cents flat which is very tolerable. If you put it up against one that is in tune though, there is quite a noticeable difference in beating. Starting with a note of frequency f, the second harmonic of 218/31 f will beat against the third harmonic of f at the rate of |3*f - 2*218/31 f| ~= 0.009 f. So, when f = 440Hz for example, that'll be about 4 times per second, which is not offensive, but anyone can hear it, especially with something nicely sustained like an electric piano sound. It sounds like a gentle chorus effect "wawawawa" that gets faster for higher notes. When the fifths become closer to justly tuned, that beating gets slower until it gets so long that it's longer than you hear the notes for, and then it's effectively gone. If you wanted it to beat 3 times per second instead, you'd need to make it 1.2 cents sharper. If you wanted it to be 5 times per second, about 1.3 cents flatter. So while a difference of one cent isn't normally something you'd care about, it's still something that's within the limits of any human with normal hearing to hear under the right conditions (whether they understand it or not).

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