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This week’s question was asked by: a friend.

QUESTION: How is music like math?

ANSWER: Yes, there’s math in music, art, architecture and almost every human endeavor. It started with that Greek, Pythagoras, born in the sixth century BC. He is credited with developing our understanding of the harmonic or overtone series. A plucked two-foot string will vibrate at a certain tone or frequency, but a string that is one foot long will have twice the frequency. The two frequencies create an octave, a combination of notes whose frequencies are in a ratio of two to one.

Music is constructed around intervals, the frequency ratio between two different tones. The ratio is found by dividing one tone’s frequency by another. Our hearing is very sensitive to intervals, especially the ratio of three to two, which is also called a fifth. The fifth is the interval between the two “twinkles” at the beginning of Twinkle, Twinkle Little Star.

The octave is divided into 12 equal half steps. Pythagoras loved the number 12. The frequency ratio for a half step is the 12 root of two, which turns out to be about 1.06.

What is meant by the 12 root of two? We are familiar with the square root of 16, which is four, because four times four is 16. The cube root of 27, is three, since three times three times three yields 27. What number, multiplied by itself 12 times, with give you two? That number, carried out to the fourth decimal digit is 1.0595. If we go with 1.06; that would be close enough.

If you take the note A above middle C which is 440 Hz, and multiply it by 1.06, you get the next note, 466, which is the note B flat. Multiply 466 by 1.06 and you get a frequency of 493, which is note B. All music is based on the 12 root of two. This 12 root of 2 rule is often referred to as the equal temperament system in which the frequency interval between every pair of adjacent notes has the same ratio.

Whether you are listening to Ricky Martin or Dean Martin, there is math in music.

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Larry Scheckel is a retired Tomah High School physics teacher.


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