HARMONIC RATIOS IN USE

The Harmonic Ratios1:1 – Unison2:1 – Octave3:2 – Perfect 5th

4:3 – Perfect 4th

5:4 – Major 3rd

6:5 – Minor 3rd

. . .9:8 – Major Second (Step)

What Can You Do With Them?

Calculate the length needed for pitches on:

String Instruments

Wind Instruments

The Monochord Monochords are ancient

instruments that appear in various forms in many cultures.

Pythagoras is said to have refined his theory of harmonic ratios by experimenting on it.

Students were expected to experiment with it when they studied music as part of the Quadrivium in medieval universities.

The Music of the Spheres

From One, Many When plucked, a string

doesn’t only vibrate as a whole, but also a half, third, fourth, etc...

These “overtones” harmonizes with the “fundamental” pitch and the other overtones.

All of the pleasing-sounding harmonies can be drawn from harmonic divisions of the fundamental.

Setting the Air in Motion

Like strings, air passing through tubes vibrate in relation to the length of the tube.

This includes all wind instruments: brass, woodwinds, didgeridoos, etc.

Name that Interval! Lengths: 180 and 90

Lengths: 180 and 135 (aka. 12 and 9)

Lengths: 180 and 120

Lengths: 180 and 144

Lengths: 180 and 150

Lengths: 180 and 160