The way to measure chromatic tuners' precision I have a question about measuring precision of chromatic tuners.

I want to divide 2 cases.

CASE1:

link; Korg AW-2G's precision



If you check the link or this picture, it says that
Korg AW-2G has the precision of +/- 1 cent.

What's the way or measurement to get this result (+/- 1 cent)?

CASE2:

There are people using Arduino (ATMEL328 MCU) with microphone or piezoelectric diaphragm for the ADC input.

One blog introduced the autocorrelation method
for detecting the instrument's pitch.
After calculating autocorrelation, using parabolic interpolation gives
"accurate" results. (This is not sarcasm, don't get me wrong. :D)

Suppose I made a chromatic tuner using ATMEL328 and a piezoelectric diaphragm.
Also, suppose I chose sampling rate 9240 Hz, 512 samples, the autocorrelation method (with parabolic interpolation).

In this case, how should I define the precision of this chromatic tuner?
I can't buy tuning forks to compare the results.
Let's suppose I'm testing with electrical guitar, classical guitar, and violin.
So any ideas?


Best Regards~
Precision and accuracy are 2 different things. 

1 cent is 1/100th of the frequency difference between 2 adjacent semitone pitches in equal temperament tuning.  The frequency ratio is exp(ln(2)/1200) or roughly 1.00059  

Precision of 1 cent might mean the tuner reports frequency error from the nearest semitone in 1 cent units, whether accurate or not.

To test accuracy, you might want to synthesize test signals that "sound like" your desired instrument (in software, or using a calibrated programmable synthesizer).  Feed those test signal to your tuner (or your tuner's pitch estimation algorithm in a software environment as unit testing).  If the results matches the synthesized pitch to within 0.5 cents, then your accuracy is 1 cent at that frequency.  Vary the test signal (perhaps randomized) to different semitone notes and cent (or cent fraction) offsets over your tuners entire range to find the worst case to evaluate (get a statistical estimate of) your tuners accuracy.

You can add Gaussian random white noise or recorded typical background room noises to your generated test signals to test measurement precision (repeatability) at realistic S/N ratios as well.

One "gold standard" is to measure the WWV audio frequencies (500 and 600 Hz), and use those to calibrate your synth and test your tuner.