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Cents Deviation Calculation

By Roger Gable posted 12-16-2013 16:10

  

Today I had a customer ask me to tune his piano to "256 cps", but he didn't know which note he was referring to. I presumed he meant C4 because that is the closest note (when tuned to standard pitch) to his 256cps request. Because I tune aurally and only have a strobe tuner (with only a cents vernier scale) for pitch raises I don't have any way to determine how many cents C4 -256 is deviated from standard A-440. I don't do historical tunings. Does anybody know if this is a "standard" historical pitch?

Roger Gable

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Anthony Willey
02-08-2015 20:51

To find the cents difference between two frequencies you have to take the base 2 logarithm of the ratio of the frequencies and then multiply it by 1200. So the formula would be: 1200*Log2(f1/f2). The 1200 comes from the number of cents in an octave, and we use the base 2 log because the frequency doubles every octave.
You can do it in Excel with the following code: =1200*LOG((256/261.5),2). Here I plugged in the numbers of 256 (the desired frequency) and 261.5 (roughly what equal temperament would give you) and got a result of -36.8 cents.

Gregory Graham
06-20-2014 00:38

Middle C (C4) in a typical, equally tempered, stretched tuning based on A=440 hz would be 261.39 hz. C4 at 256 hz would be 36 cents flat. This would put A4 at 430.9 hz. Close to "Philosopher's pitch", I think? There was a debate about that a month or two ago on the Pianotech list. It is purported to be a fad, not generally accepted as a good idea.
I'm with Blaine. Talk him out of it. His piano was designed to sound best at A=440 hz. If he wants to play along with modern recordings, or nephew Johnny's accordion, A=430 will sound very sour.

Blaine Hebert
01-30-2014 02:09

Roger,
The "Physics Department" uses C 256; I have a set of C tuning forks from C 128 to C 1024. I have never figured out why this obscure standard is used but it is common on medical forks (for testing hearing) and in physics labs. The mid C is 512.
Since A440 C is 523 then 523 - 512 = 11, so you need to tune 11 beats per second flat.
I would try to talk him out of it!
Blaine Hebert