I have written a number of programs to explore the connections between mathematics and music:
First, the program below (written as a shockwave movie - you'll need the shockwave plug-in) allows you to play combinations of pure sounds, choosing the pitch and amplitude of up to eight tones. To play a tone, enter a value in the pitch column, click the approriate check box, and click "Play" when you are ready. You can alter the amplitude (which corresponds roughly to volume) by dragging the appropriate slider. The graph of the linear combination of sine functions (that is, the mathematical model of the sound wave) is shown at the left.
Here are a few things you can try:
Another prrogram I have written allows you to explore scales and frequencies. Our current scale is even tempered, which means that a semitone is achieved by multiplying a frequency by 2 to the power 1/12th, which is about 1.059). The pythagorean scale has 7 notes of a "major" scale, and is based on multiplication by small fractions. A geometric scale is formed by multiplying frequencies in a scale with x semitones by 2x. An arithmetic scale is formed by taking a scale with x semitones and making the frequency of the ith tone to be the original base frequency times (1 + i/x). You can try out each of these scales below (the pythagorean scale is only available as a 7 semitone scale, but the others can have any number of semitones from 1 to 19).
Make sure after setting the number of semitones to play, click to create the keyboard. It is ready for you to play by clicking the mouse on each key. You can even move some notes up higher or back down again (as on a piano keyboard) by holding down the control key.
You can hear the difference between the scales, even with the same number of semitones. Try creating you own songs in standard and nonstandard scales!
Copyright©2012 Jason I. Brown