Musical pitch is defined as follows:
“Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as “higher” and “lower” in the sense associated with musical melodies”
Pitch is a perception of sounds as being higher and lower, or better put, the ‘human’ perception of frequency. The pitch of a note is how high or low the note is based on a specific frequency. Today’s mini-math lesson explores the relationships between the pitch of a note and the frequency of the note, based on the notes relationship to middle C on a piano. There are 12 notes in music, played with 7 white and 5 black keys (see image). The black keys show two different notes, but because they are the same sound/note they only count once. On a regular piano, with 88 keys, the same 12 notes repeat but at different pitch. Guitars also have the same 12 notes, as do most musical instruments, and understanding their relationship helps understand how to create different pitch (or play in a different key, as another way to think about this).
In the activity I explore today, Pitching the Right Note (adapted from Fostering Mathematical Thinking with Music, Casio 2015), the 12 notes are looked at by octaves (group of 12), with three octaves explored (the octave below middle C, the octave at middle C and then octave above middle C). Students are given the frequency, in Hertz (Hz), of each note, and then explore through looking at graphs and numerical calculations, the relationships between the same notes at different octaves. They discover how the frequencies change (increase, decrease) over the octaves, and proportional relationships between the octaves and corresponding notes. Through this exploration, they learn how mathematics plays a huge part in musical pitch.
This activity is a graphing calculator activity that I created a ClassPad.net version of so that now you have options no matter which technology tool you might have access to. Below I have provided the ClassPad.net activity link for use online (great for remote learning!) and also the PDF version (for use with a hand held graphing calculator). I have also included a video overview that walks through the ClassPad.net version of the activity. The PDF contains possible solutions and some teacher guidance that could be used for both the ClassPad.net or calculator, again, depending on your resources.
- ClassPad.net – Musical Frequencies and Pitch Relationships
- Pitching the Right Note – Fostering Mathematical Thinking through Music (PDF)
- Video Overview: Musical Frequencies and Pitch Relationships – Data Tables, Proportions & Regressions
The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.
Remember – if you want to save and/or modify any of these activities, create a free account. Some useful links below:
- How to create a free ClassPad.net account (for anyone – students, parents, teachers)
- How to organize activities & share activities
- Some Ready-to-use activities that are already out there
- ClassPad.net YouTube Channel