Description

This article is from the Acoustics FAQ, by Andrew Silverman with numerous contributions by others.

6.7 What are musical intervals ?

An interval is the ratio in frequency between musical notes. These intervals are sometimes called a second, third, fourth, fifth etc. which refers to the position on the scale that the note is to be found. In the scale of C major: C D E F G A B C, the note 'E' is the third note of the scale and the interval from C to E is therefore called a third. For the scale D major: D E F# G A B C# D, the third will be F#. The term 'interval' can also be used to indicate that the notes are sounded together, in which case there are consonant intervals and dissonant intervals.

The ratio of frequency intervals for Just Intonation is demonstrated below in the scale of C major, though the same ratios apply to all the major keys:

C
  (9:8)
D
  (10:9)
E
  (16:15)
F
  (9:8)
G
  (10:9)
A
  (9:8)
B
  (16:15)
C         <- Octave

The interval between E & F and between B & C is a semitone, whilst the other intervals are tones. The interval between any two notes above can be found by multiplying the intervening ratios; thus if all the above ratios are multiplied together the resultant is 2 because an octave is twice the original frequency.

The notes of minor scales differ from their major counterparts; one important difference being the flattened third. E flat is a minor third above the note C.

The use of Just Temperament causes serious problems of intonation when music modulates between keys. Equal Temperament is nearly always used as a compromise to the problem of tuning (see question 6.6).

Continue to:

• prev: 6.6 What is pitch ?
• Index
• next: 6.8 What causes "helium voice" ?