Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum How do you measure how many cents a pitch is off?

I'll preface my question by saying that, although I'm an Associate member of the PTG, I'm fairly new to the hands-on end of the art of tuning and am still wrapping my head around how some things interrelate. I have a question about cents.

In the PTG Tuning Examination Source Book, an article by Jim Coleman, Sr. states: "Those who have electronic aids may test unisons themselves by muting all but the left string, recording it's cents value, then doing the same for each of the other two strings, and then writing down the differences between left and center then center and right strings." (page 71)

My question is how do you determine/record the cents value of a string? Is there something on an ETD that specifically displays a numeric value relative to a frequency value to indicate how far off they are from each other? Can you only measure or determine cents with an ETD or is there also a way to tell aurally? Are cents related in some way to beats?

Thanks for any help on clarifying this for me.

Hi Jon,

On Tunelab97, you can use the letters K, I, L, and O to change the offset and read the cents from that, once the display stops.

The cents offset will be the cents difference between the string and what the ETD thinks it should be.

You can use this method to record cents offset of two different strings and take the difference of those numbers to give you a measurement of the difference in cents. Two unison strings, and before and after test blows, are two examples. This method does not require the ETD to be loaded with a stretch til since we are only using differences.

Each ETD has it's own way of displaying offset, which is usually in cents.

There is no way to aurally determine cents offset, but there are many aural techniques for improving tuning accuracy up to and beyond the PTG standard. I.e. by using these techniques and confirming aurally that the frequencies if the notes are good, you can be more or less sure that you are within the PTG tolerance.

I do not know the formula for converting cents to Hz and reverse.

Hope that helps.

There was an article in the PTG journal recently that describes how to test yourself against the RPT exam using different ETD's.

On your mobile phone, your pocket PC, your laptop, your specific ETD, cts are the most used unit.

Only in spectra analysis softwares most often only Hz are availeable.

Ha ha. I just beat you by miliseconds Isaac!

It is a simple formula, should be easy for you. You need a pitch reference first.There are a few web page with converters.

I will avoid writing maths as I will probably wrong, but it is not difficult, on a spreadsheet for instance.

Thank you, Mark and Olek. I have an SAT IV that I haven't learned how to use well yet...not the ETD's fault, but more due to my novice status. I'll check out the online and PTG references you suggested, though. Thanks again.

Hundred of second Mark, modesty

Jon,

Over the keyboard, frequency rises exponentially (doubles every octave), while the cents scale rises linearly. Cents represent one hundredth of a semitone, or 1/1200 of an octave. So cents have a logarithmic relationship with frequency (Hz).

At A440 (A4), a semitone up or down is about 25 Hz. So 1 Hz corresponds to about 4 cents. Conversely, an accuracy of 1 cent corresponds to one beat in 4 seconds.
At A220 (A3), a semitone is about 12 Hz, so 1Hz is about 8 cents. 1 cent corresponds to one beat in 8 seconds.
At A110 (A2), a semitone is only about 6 Hz, so 1 Hz is about 16 cents.
At A880 (A5), a semitone is about 50 Hz, so 1 Hz is about 2 cents, or 1 cent means one beat in 2 seconds.
And at A 1760 (A6), a semitone is bout 100 Hz, so Hz and cent correspond roughly 1:1.

If you tune, for example, the three strings of A4, you can check them against F2's 5th partial or B1's 7th partial. If one string beats at 4 beats per second, but the other at e.g. 4.5 bps (9 beats in 2 seconds), then they are de-tuned by 0.5 Hz, which at A4 corresponds to about 2 cents.

Similarly, in the 3rd to 4th octave, equally tempered P4s (2 cents wide of pure) beat at about 1 bps, while equally tempered P5s (2 cents narrow of pure) beat at about 1 beat per 2 or 3 seconds.

And equally tempered M3s (13.7 cents wide of pure) beat at about 7 bps at F3, and 14 bps at F4.

So, to my mind, just by listening to beat speeds, even a relative novice can actually estimate pitch to within 1 or 2 cents aurally, without any ETD.