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Re: Understanding Chromatic Tuner Readings

Author: Dan Shusta
Date: 2018-10-23 01:49

Dibbs,

You stated that my comment:
> I believe it can be
> easily seen that a large negative reading on the low end
> actually equates to just a few hertz off the center tone
> frequency. However, a high, off center, positive reading on the
> high end means the actual tone frequency is quite far off from
> the true, center tone frequency.
>
> Hopefully, the above graph will help to put things into
> perspective for you and is useful in some way.
>

"This needs more explanation."

According to the formula found at http://www.sengpielaudio.com/calculator-centsratio.htm, a +20 cent deviation corresponds to an f2/f1 frequency ratio of 1.011619.

If f1 represents our known pitch or frequency, rearranging the formula of f2/f1=1.011619 yields f2=1.011619 x f1.

For a clarinet E3, the center frequency (f1) is 146.832 Hz. (Piano D3)
Therefore, f2=1.011619 x 146.832 = 148.538 Hz.
The +20 cent offset for clarinet E3 is the difference in the two frequencies or 148.538 - 146.832 = 1.7 Hz.

For a clarinet C7, the center frequency (f1) is 1864.66 Hz. (Piano Bb6)
Therefore, f2 = 1.011619 x 1864.66 = 1886.325 Hz.
The +20 cent offset for clarinet C7, again, is the difference in the two frequencies or 1886.325 - 1864.66 = 21.67 Hz.

To help clarify this non-linearity, the following represents a +5 cent reading from E3 to C7 in a non-chromatic fashion:

For a constant +5 reading, here’s how far off pitch (in hertz) the following clarinet notes are:

E3=0.372 Hz
F3=0.475 Hz
G3=0.503 Hz
A3=0.565 Hz
B3=0.634 Hz
C4=0.672 Hz
D4=0.754 Hz
E4=0.847 Hz
F4=0.897 Hz
G4=1.010 Hz
A4=1.134 Hz
B4=1.272 Hz
C5=1.348 Hz
D5=1.513 Hz
E5=1.698 Hz
F5=1.799 Hz
G5=2.019 Hz
A5=2.267 Hz
B5=2.545 Hz
C6=2.696 Hz
D6=3.026 Hz
E6=3.397 Hz
F6=3.599 Hz
G6=4.040 Hz
A6=4.535 Hz
B6=5.090 Hz
C7=5.393 Hz

Doing this mathematical exercise concerning the relationship of cents to hertz has been quite illuminating for me.

I hope this helps others.

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