signal processing - Optimal value of sampling frequency for guitar notes detection -

i running fft algorithm detect music note played on guitar.

the frequencies interested in range 65.41hz (c2) 1864.7hz (a#6).

if set sampling frequency of input 16khz, output of fft yield n points 0hz 16khz linearly. input interested in first n/8 points approximately. other n*7/8 points of no use me. decreasing resolution.

from nyquist's theory (https://en.wikipedia.org/wiki/nyquist_frequency), sampling frequency needed twice maximum frequency 1 desires. in case, 4khz.

is 4khz ideal sampling frequency guitar tuning app?

intuitively, 1 feel better sampling frequency give more accurate results. however, in case, seems having lesser sampling frequency better improving resolution. regards.

you confusing pitch of guitar note spectral frequency. guitar generates lots of overtones , harmonics @ higher frequency pitch of played note. higher harmonics , overtones, more possibly weak fundamental frequency in cases, human ear hears , interprets lower perceived pitch.

any of overtones , harmonics around or above 2 khz not low pass filtered out before sampling @ 4 khz cause aliasing , corruption of sampled data , spectrum.

if want create accurate tuner, use pitch estimation algorithm, not fft peak frequency bin estimator. , depending on pitch estimation method choose, higher density of samples per unit time might allow finer accuracy or greater reliability under background noise or more prompt responsiveness.