Physics and music

All musical instruments rely on the vibration of air to produce a note. The air is usually set in vibration either by a moving string or by the oscillation of air enclosed in a pipe.

Stringed instruments are set in vibration either by a bow (as with a violin or cello), by a hammer (piano) or by plucking (guitar, harpsichord).

Wind instruments are all basically tubes in which the air is made to vibrate. Woodwind instruments are of two kinds:



(a) instruments with reeds such as the clarinet, saxophone and oboe.
(b) instruments where the passage of air across a hole causes the air in the tube to vibrate such as the flute, recorder and organ.





In brass instruments the air is vibrated by a mouthpiece, the tension of the player's lips or the length of the tube altering the pitch of the note.

An organ pipe in a cold church will be shorter than normal but the air molecules in it will be moving slowly and so the pitch of the note that comes from it will be lower than it should be – the note will be flat.

The Physics of musical sounds

What makes a pleasant musical sound is something that varies from person to person — some prefer pop and some jazz, while others only listen to Bach! All types of music are built up from basically the same set of notes, however. So an even more fundamental thing than the type of music we prefer are the actual frequencies of the notes that make up what we call a scale.

The situation is complicated by the fact that there are actually two different scales:
(a) the scientific scale based on middle C having a frequency of 256 Hz, also known as the diatonic scale, and
(b) the musicians' scale based on A having a frequency of exactly 440 Hz, also known as the equally tempered scale. On this scale middle C has a frequency of 261.6 Hz.

The frequency ratio for two notes one octave apart is 2:1 while for a fifth it is 1.5:1. On the equally tempered scale the frequency ratio for each semitone is 1.0595:1. The ratio for the tone interval is the sixth root of 2 and that for the semitone the twelfth root of 2.

The frequency of notes in music have a precise relationship with each other. It is these ratios between one note's frequency and the next that makes combinations of notes pleasant to listen to. Notice that if you increase the pitch by one octave the frequency doubles. Using a 'key note' we can build up the whole scale.

Note	C	D	F	F#	G	A	B	C'
Frequency (Hz)	256	288	320	341	384	427	480	512
Ratio of frequency to keynote	1	9/8	5/4	4/3	3/2	5/3	15/8	2