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Please verify my understanding that pitch detection precision is dynamic across a pitch range, whereas relatively higher pitches can be measured to increasingly higher precision, and vice versa. Based on this, I would like to conclude that pitch detection precision described as ± x cents is a technical simplification.

Given the logarithmic nature of pitch, the linear distance (in Hz frequency) between two adjacent semitones increases as you go up in pitch, and decreases as you go down. In other words, the resolution between notes is dynamic.

The logarithmic unit cent is used to cut the semitone into one hundred smaller pieces, which are "logarithmically equally spaced," but again take on different linear resolution based on the actual pitch.

The linear span between cents at lower pitches becomes smaller, and therefore relatively more difficult to measure. Likewise, the resolution of 1 cent at higher pitches is higher. As a rough visualization, it's like watching your lowest octave at 144P video quality and seeing it progess up the octaves to 4k video quality.

As the range of applicable pitches being measured by the hardware increases, so does this difference in precision across the range.

Is my understanding correct that hardware pitch detection precision is dynamic according to the pitch being detected, and that statements of precision as ± x cents are a simplification?

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In my sorta meatball experience with pitch detection for audio and musical purpose was that I was using autocorrelation of some form which returns the estimated period length in terms of samples (to a fractional precision) of period length.

So, in terms of cents, longer periods (lower pitch) had better precision than shorter periods (higher pitch) because, ostensibly they both have the same precision in terms of samples in the period.

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  • $\begingroup$ Interpreting your writing, I see how the constant sample rate equates to higher precision of the longer period. However, in a tuning sense also consider the gap in cycles per second between adjacent semitones. The gap, or room for error, is smaller at lower pitches. This seems it would offset the increased precision for lower periods, right? And vice versa at higher pitches (less precision, but a bigger room for error). At the very least, your observations support my understanding that precision is dynamic according to the pitch. Thank you $\endgroup$
    – bazz
    Oct 27, 2023 at 3:23
  • $\begingroup$ after some ruminating, I now think tuning precision specified in cents is constant across octaves. My confusion arised from traversing between linear and logarithmic space. semitone ratios are constant despite octave, and I ruminated on that. So measuring with a precision of .01hz at some low octave would be the same as measuring every 20hz at some high octave (these are made up numbers just to make the point). Depending on the pitch range and samplerate selected, perhaps there might be notable negative effects on precision for increasingly higher pitches, as you mentioned. $\endgroup$
    – bazz
    Oct 27, 2023 at 4:07
  • $\begingroup$ //"So measuring with a precision of .01hz at some low octave would be the same as measuring every 20hz at some high octave"// So the low octave could be around 10 Hz and the high octave could be around 20 kHz and it would be about 1.73 cents in either case ----- //"(these are made up numbers just to make the point)"// My point is that however you describe pitch, there can be integer+fractional values of samples in the period length, or there can be integer+fractional cycles completed in a second. So pitch can have high precision in an expression. $\endgroup$ Oct 27, 2023 at 6:12

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