I recently posted in PTG Pianotech about why we absolutely cannot do multiple attacks within a relatively short time period and get a good accurate reading on frequency. The FFT processing of the ETD must measure 'one attack' within less than the FFT window time, 'delta T', or T2-T1. The ETD must 'hear' a period of silence briefly between attacks in order to start another FFT window analysis. If it does not, you have a mess and it violates the whole principle.
The 'Freeze Function (found in Pianoscope) is a concept I originated and Frank put it in the app. It is deterministic measure over a predetermined window of time to process an FFT off the attack and measure the frequencies of the harmonic series (partials) in a repeatable and reliable manner without a continuously running estimate (i.e., the 'red line indicator') as seen from having the ETD's needle. Without it, we see the line moving and not being able to 'remember' what the needle says at what time it says it. Why did I have this function put into the ETD? Because....
There is no such thing as an instantaneous measure of frequency. Think for a moment that time and frequency are inverses. Over zero time, the inverse of zero is infinity, so that would imply an infinitely high frequency, or put in another way, think about this. Delta-time is the interval from T1 to T2. The smaller the delta, T2-T1, the larger the inverse, F2-F1. So goes the idea that we can accurately measure frequency both accurately and in a short time interval. They trade off as inverses.
So, let's put this to a piano tuner's example. Let's say we want to watch our ETD needle and assuming we can 'catch and remember with our eye' in a few hundred milliseconds (we can't humanly do this even though we think we can!), we then process that few hundred milliseconds with an FFT (Fast Fourier Transform) in the ETD, and then see what the 'average frequency' of all the harmonics are during that time interval. The piano waveform is far from steady state during that interval.
First of all, the piano not only decays in amplitude exponentially from the attack, it also drifts in frequency at the same time. That frequency drift is usually to the flat side. Why does it drift in frequency? Because of the nonlinearity of the string and nonlinear hammer density. The attack is also typically sharper in frequency on the attack depending on the forcefulness of the hammer hitting the string, again due to the nonlinearities involved. A soft attack results in very little deviation in frequency because the motion of the string and hammer force-attack are more in the linear ranges.
I will be writing more about these important issues.
I created a YouTube video demo of how to tune with re-attack.
Professional Signal Processing Engineer, Inventor
Professional Musician / Pianist