Notes As Ratios

Notes are pitched sounds. A given note means little by itself. It could be the tonic of a key, or some member of a scale based on a different tonic. By itself, it generates no tension, resolution or sense of place on the harmonic map.

So when I name a note in this blog, I’ll usually be referring to a ratio, the relationship between the note and a reference note — the tonic, or the root of a chord, or another note in the harmony or melody.

Ratios are fractions. The first number is divided by the second number to give the value of the ratio.

If the tonic is, say, 100 Hz, then another 100 Hz note is related to the tonic by the ratio 1/1. This is the interval of a unison, two identical notes.

Each note name on the lattice represents a unique ratio, relative to the tonic. The 1, at the center, stands for 1/1.

Next: Octave Reduction