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Teaching the Mathematics Of Music

Music educator Chad Criswell offers easy cross-curricular teaching ideas for math or music teachers.Included: Links to more music resources and worksheets.

About the Author

Chad Criswell is a music educator and freelance education writer and runs the music education resource site

Music teachers are well aware of the very close link between math and music. Without mathematics, music simply would not exist.

The rhythms of a piece of music are based on a standard unit of time (known as a measure) that can be subdivided in many different ways. Drawing parallels between pop music and math concepts is a great way to reinforce those cross-curricular concepts while using a strong mental hook to keep students attention. Try these simple ideas to incorporate music or mathematics into your next lesson.


The beats in a piece of music are the pulses you tap your feet to while listening to it. Begin by proposing the notion that those beats are durations rather than instants in time. Draw a long horizontal rectangle on the board. That represents a full measure of music.

  • Cut a measure in half and each of the two chunks" becomes a "half note" that lasts for two beats.
  • Cut each half note into two parts and you get quarter notes. Quarter notes are the part of the music that is most often felt as the beat we tap our foot to. Each quarter note is equal to one beat of the music.
  • Each of these four beats can be cut in half again, leaving eight parts to the measure (known as eighth notes in music). Each eighth note lasts for one half of a beat.
  • Divide the eighth notes in half and you have sixteenth notes! Each sixteenth note lasts for one forth of a beat.
  • Remember that the names of the rhythms relate to a full measure rather than to the beats themselves. An eighth note is one eighth of a measure, not one eighth of a beat.


Once students understand the concept of beats and measures, the discussion can be taken to the next level and common musical symbols can be used as a way to do fractional math.

    Draw a diagram with four quarter notes in place of the four subdivided boxes mentioned previously. Put plus" signs between each quarter note and an equals" sign at the end. How many beats are in this math problem? Four!
  • Make things more challenging and get into fractions by adding eighth notes and sixteenth notes. Two eighth notes plus a sixteenth note equals one and one half beats (.5 +.5 +.25 = 1.25 beats)
  • Use the rectangle diagram to reinforce the math concepts at work here.

Music can be a lot more complicated than this, but the examples above relate to the most common time signature used in music (4/4 time) and the most commonly-heard time signature in popular music. Finding a piece of music to help demonstrate those concepts is as easy as listening to the radio or borrowing a student's iPod. Further, many great free music worksheets related to these and other musical concepts are available for use in the classroom. Try to incorporate these tricks into either a math or music class to show just how closely related these two subjects truly are.