Author: Dan Shusta
Date: 2018-10-20 04:44
Attachment: Chromatic Tuner Scale.jpg (659k)
I recently bought a CA-50 Chromatic Tuner and noticed that the scale read in “cents”. I was curious as to whether any relationship existed between “cents” and “hertz or cycles per second” and found out that there is no direct relationship. I then began to wonder… “Well, if I’m 5 cents high or low, how many hertz am I off of the center tone note frequency?”
Upon further investigation, I found 2 websites that helped me understand this non-linear relationship. First of all, I had to know the piano frequencies corresponding to various notes on the clarinet and then I found a website that converted frequency ratios into cents.
So, with the use of these two websites, I wanted to determine what the tuner would read at 1 and 2 hertz low of the actual clarinet tone frequency.
Here are the two websites I used:
To find out piano frequencies: https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Piano_key_frequencies.html
To determine the non-linear relationship between “cents” and “hertz”, I found the following website to be absolutely essential: http://www.sengpielaudio.com/calculator-centsratio.htm
To determine the frequency ratio of f2 / f1, I simply divided the center frequency (f2) by the frequency which was 1, then 2 hertz lower (f1).
Utilizing the information obtained by using the above two websites, I formulated the following graph:
tone….......frequency…..meter reading in cents
……………………………….......…….1 hertz low…..2 hertz low
E3 (D3-P)…………146.832…………-11.83………………-23.74
G3 (F3-P)…………195.997……………-8.85………………-17.75
C4 (Bb3-P)..…261.626……………-6.63………………-13.29
G4 (F4-P)……….349.228……………-4.96……………..-9.94
C5 (Bb4-P)…..466.164……………-3.72……………….-7.44
G5 (F5-P)……….698.456……………-2.48……………….-4.96
C6 (Bb5-P)………932.328……………-1.86……………..-3.72
G6 (F6-P)…………1396.91……………-1.24……………..-2.48
C7 (Bb6-P)………1864.66……………-0.93……………….-1.86
Generally speaking, I’ve read where many clarinets go very flat at the extreme low end and quite sharp at the very high end. Using this generalized information, 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.
Would somebody please tell me what the hollowed out, downward arrows represent? Nothing was said about them in the directions. Thanks.
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The Clarinet BBoard
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