Cents and Musical Intervals

While the western musical scale is broken into twelve notes, we often need more specific ways of describing the pitch of a sound, especially during the tuning process. For example, let's say that you are tuning one of your guitar's strings to the E note played by a piano. As you twist your tuning peg and strike the corresponding string, you get closer the frequency of the E and eventually reach the point where the frequency of your string is lower than F but higher than E. How can we quantify this difference? The piano player may tell you that you are 50 cents sharp of E, but what does this mean?

The chromatic scale is broken into twelve notes, but the cents system allows us to further break this up. The basic definition of this is that the interval between two semitones consists of 100 cents, evenly spaced frequency values between the two notes. Since an octave consists of twelve notes in a chromatic scale, we also know that an octave is made up of 1200 cents. Given this understanding, we now know when the pianist tells us that we are 50 cents sharp of E when tuning, our note is tuned exactly in between E and F. Though this frequency does not have a specific letter name, it can easily be quantified by using the cents system.

Many electronic tuning devices (or tuning apps) can help you tune your instrument to standard pitches. With remarkable precision, these devices are often able to show how many cents sharp or flat your detuned note is in order to help you reach the ideal frequency.

Works Cited:

1.  Gunther, Leon. The Physics of Music and Color. New York, New York: Springer, 2012.