Reckoning from the tonic of the major scale to each degree of the scale produces the following intervals:—
8th or prime. 2nd 3rd 4th 5th 6th 7th octave 9th
The interval of the ninth is often called a second, the octave not being considered.
These intervals are the normal intervals of the major scale. These normal intervals are qualified in two ways. The prime, fourth, fifth and octave are called perfect. The second, third, sixth and seventh are called major; thus:—
All intervals should be reckoned from the lower note, which is considered a major key-note. If the upper note is in the major scale of the lower note, the interval is normal; that is, either perfect or major. If the upper note is not in the major scale of the lower note, the interval is a derivative interval. The derivative intervals are called minor, diminished and augmented.
A minor interval is derived from a major interval and is one semi-tone smaller. By lowering the upper tone of any major interval one half step or by raising the lower tone of any major interval one half step (not altering the letter name in either case) a minor interval is formed, thus:—
