The final topic that arose during the discussion of scales was intervals. We noted how major scales are constructed from two intervals, the semitone and the tone, and how the harmonic form of the minor scale includes another interval, the tone plus semitone, i.e. three semitones. There is no reason why you couldn’t, in theory, count up larger and larger intervals in semitones. However, as the size of intervals increases, identifying them by counting semitones becomes impractical.
To make things easier, intervals are identified by labels that consist of two determinants, quality and number. You can calculate the number of an interval by regarding the lower note as the tonic and then counting up the degrees of the scale. Thus, as shown in Example 60, the interval C–E would be a third, C–G a fifth and C–B a seventh. C to the same C is a unison; C to the C eight notes higher, an octave. Note that the two notes in the interval can be sounded together as a harmonic interval, or in succession as a melodic interval.
The quality of an interval can be perfect, major,minor, augmented or diminished.
So, for instance, you can have a perfect fourth, a major third, an augmented sixth.
However, for our purposes, here I comment only on the perfect fifth, which consists of seven semitones, e.g. C–G in the C major scale, and the minor third, which consists of three semitones, e.g. A–C in the A minor scale (see Example 61).