The Math Behind an Octave

There are so many things that are easy to take for granted as musicians. We are standing on the shoulders, as it were, of many who have gone before us, making observations and discoveries that have been instrumental (:-)) in the progress and development of music as we understand it today. Even this tidbit that Paulo Goncalves, of Do Re Mi Studios in Jannali, Australia, recently wrote regarding the relationship of math and music is fascinating!

Pythagoras, the Greek mathematician, discovered that notes that sound good together (i.e. are in harmony) are mathematically related. He also found that the sound of a note plucked on a string depends on its length and tension. In his experiments, he discovered that by halving the length of a string and plucking it again, you produce a sound that it is almost the same. However, this sound is higher in pitch. The interval between the original note and the note produced by halving the string is referred to as an octave. Mathematically, an octave is the distance between any given note with a set frequency, and another note with double that frequency. In music, both these notes have the same name but are written an octave apart on the staff.

Next semester, as part of our Classical Conversations homeschool program, we’re planning to go through a book called, Math in Motion: First Steps in Music Theory, so I’m excited to see what other interesting things we discover that go even beyond basic theory to a deeper understanding of the science and math of sound!

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One thought on “The Math Behind an Octave

  1. My own quote: “Music is the aural form of math. When you are hearing music, you are hearing math!”

    It blows students away when they hear it. I usually repeat it twice, and I have it posted right above the board. It’s not just rhythmical fractions of note durations, but also the math of the harmony. I play intervals on the piano and say, “Does the number 2 sound pretty?” No. “Does the number 3 sound pretty?” Yes. “What about 4.5?” NO!

    In the center of one of my walls, I have the word “MUSIC”. It is the center of a bubble map that connects music to just about everything: geography (the sound of countries and cultures), history (the sound of time periods), psychology (of the performer and the audience member), science (vibration/sound/pitch), math, language, etc….I love that wall. Music tells a lot more than people will ever realize.

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