(See examples above.) The ‘distance’ between 2 notes is called an ‘interval’, i.e. the difference in pitch between any 2 notes. The ‘size’ of any interval is expressed numerically, e.g. C to G is a 5th, because if we proceed up the scale of C the 5th note in it is G. The somewhat hollow‐sounding 4th, 5th, and octave of the scale are all called perfect. They possess what we may perhaps call a ‘purity’ distinguishing them from other intervals. The other intervals, in the ascending major scale, are all called major (‘major 2nd’, ‘major 3rd’, ‘major 6th’, ‘major 7th’).
If any major interval be chromatically reduced by a semitone it becomes minor; if any perfect or minor interval be so reduced it becomes diminished; if any perfect or major interval be increased by a semitone it becomes augmented.
Enharmonic intervals are those which differ from each other in name but not in any other way (so far as modern kbd. instruments are concerned). As an example take C to G♯ (an augmented 5th) and C to A♭ (a minor 6th).
Compound intervals are those greater than an octave, e.g. C to the D an octave and a note higher, which may be spoken of either as a major 9th or as a compound major 2nd.
Inversion of intervals is the reversing of the relative position of the 2 notes defining them. It will be found that a 5th when inverted becomes a 4th, a 3rd becomes a 6th, and so on. It will also be found that perfect intervals remain perfect (C up to G a perfect 5th; G up to C a perfect 4th, etc.), while major ones become minor, minor become major, augmented become diminished, and diminished become augmented.
Every interval is either concordant or discordant. The concordant comprise all perfect intervals and all major and minor 3rds and 6ths; the discordant comprise all augmented and diminished intervals and all 2nds and 7ths. It therefore follows that all concordant intervals when inverted remain concordant and all discordant intervals remain discordant.