Tune with a Single Partial or Multiple Partials? An Example...

  • 1.  Tune with a Single Partial or Multiple Partials? An Example...

    Posted 02-14-2024 18:48

    We had a lively discussion last night at the South Bay PTG where I gave a class.

    One of the issues is whether we tune with a single partial or with multiple partials. If an app choses a single partial for tuning, we could be lucky to see virtually no difference where the mic was placed. But if we are unlucky we could get a 1 cent error range with a small mic placement movement. It is not that the movement creates a different frequency, but it creates a different resolution of that frequency. 

    Here is an example. Using the note C4 on a 7' grand piano, the mic was moved around to 9 different physical positions above the soundboard in reasonable locations that a tuner could place an iPhone. The .wav files were captured and analyzed in Matlab. The result was the following spread of errors with respect to placement. The data is below. Notice the sign of one relative to the other.

    Partial 2:     -0.88 cents

    Partial 3:     -0.10 cents

    Partial 4:     +0.93 cents

    Partial 5:     -0.47 cents

    Partial 6:     +0.79 cents

    Depending on the tuning app, if it tunes on one partial, it could either be lucky (-0.1 cents) or unlucky (+0.93 cents).

    Alternatively, if the app tunes by trying to fit the data statistically, it could use a mean, median, or standard deviation.

    mean             =   0.0540

    median          =   -0.1000

    std. dev.         =   0.7874

    range              =  1.8100

    A string sensor will not have these variances because small placement changes are inconsequential and produce one answer. Then it is up to the IH curve fitting in the app to make sure the measurements align with the IH initial calculations, thus ensuring we have extremely low variance and can trust the answer with more confidence.


    Steven Norsworthy

    Steven Norsworthy
    Cardiff By The Sea CA
    (619) 964-0101