MAM Day 17: Music and Math

In trying to do a blog post on music and math, I very quickly got bogged down with very technical music knowledge that I don't have. Although it's incredible how linked music and math are, I don't have enough music theory under my belt to speak very intelligently about it. I hope you will understand if I explain just what I do know about the links between music and math.

As a child, my mother signed me up for after school math lessons from the nearby orchestra teacher. This is where I would meet some of my closest grade school friends and learn how to read and play violin for a few years.
Although I didn't stick through with violin, I later went on to dabble in piano and guitar. I also played taiko drums in college with Icho Daiko. I also enjoy whistling quite a bit, but that's the limit of my musical experience. I didn't study enough music to learn about music theory or anything more complex than learning how to read music.

Some basics:

• Music is made up of sound.
  
• Sound is made from repeating sound waves.
  
• The musical pitch of each note has a corresponding frequency measured physically in hz (hertz) or cycles per second.
  
• Check out this site if you don't know or recognize the terms pitch, frequency, or sound wavelength
  
• More explanation on wave patterns and note frequency ratios

Since thinking about frequency and wave patterns hertz my brain, we can talk about something much easier to grasp that is the fundamental background of music, rhythm - my favorite. Rhythm measures time in music, and time signatures tell musicians what speed they will be playing. Review this great introductory math and music site for children and non-musician math enthusiasts (like myself) if you're completely lost on these terms.


A different type of connection between math and music
If you've ever gotten a peek at sheet music, you'll notice the music is divided into "measures" that follow the "time signature." Time signature tells you what music unit to be playing, and how many music units make up a measure.

Musical pieces in 4/4 have four quarter notes to a measure, pieces in 3/4 have three quarter notes to a measure. Other time signatures include but aren't limited to: 2/2, 6/8, 3/8, 9/8, and 12/8. The difference in time signature typically changes the way a musical piece sounds.

Notes also have a certain math to them, whole notes, half notes, quarter notes, eighth notes, and sixteenth notes are the basic notes. They're all fractions! To add to the confusion, notes can also be dotted notes, or one and a half notes. Even rests or pauses in the flow of music are measured in musical time.


There's plenty more topics to talk about in terms of math and music, but I'm not an expert in either so I'll just leave you with these links below. Math patterns in great musical pieces, the math involved in making musical instruments, tuning, how math makes pieces sound good or bad, and lots of music theory are all at the intersection of math and music.

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Great introductory math and music site for children and non-musician math enthusiasts (like myself)

Make your own musical and mathematical instruments! I particularly liked the water xylophones. I had never thought of something so simple as water in glasses or glass bottles as being mathematical, but it weighs heavily on volume and getting the right pitch for a scale.

The math behind making musical instruments

An elementary lesson plan involving beats, measures, meter, and time signature.

More lesson plans on music and math

This email Q&A answers the question Why are harps shaped like they are?

More math and music connections. Some of these are very music theory heavy, but great resources for musicians who are interested in the connections between math and music.



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