Math and music
Harmony Fractions
Every musical interval is a fraction. Choose one, listen to it, and see the string lengths and cycle counts that make it sound the way it does.
Sound is off until you tap a play button.
String lengths
Cycles that line up
Build a ratio
The upper note vibrates n times while the base note vibrates d times. Move the sliders and listen for which fractions sound smooth and which sound tense.
3
2
Notes outside a comfortable range are played in a different octave. The ratio stays the same.
Adding intervals means multiplying fractions
Going up a fifth and then up a fourth multiplies the ratios. The cents, a unit where an octave is 1200, simply add.
Stacking perfect fifths
Stack fifths (3/2 each time) and fold the result back into one octave by dividing by 2. After twelve fifths you might expect to land on the starting note.