Text: It will be seen from this that diminished intervals are produced in two ways - either by making the upper note of a minor interval flatter, or by making the lower note of some interval sharper. Hence it is that some intervals have to be calculated from notes not having a diatonic scale of their own; thus, B# to An. In such cases, the nature of the interval is readily found by temporarily reducing the lower note; thus, Bn to An is a minor seventh, therefore B# to An, being a semitone less than minor, must be a diminished seventh. The following is the simplest form of stating the rule for naming intervals according to this system: "When asked the nature of any interval, bear in mind the major scale of the lower note, then, if the upper note is higher by a semitone than it would be in the major scale of the lower note, it is augmented; if the upper note is actually a note of that major scale it is major; if it is less than major by one semitone it is minor; if it is less than minor by one semitone it is diminihed. When the lower note is a sharpened note, which has no scale of its own, consider it as one semitone lower, e.g., C## to G# is a minor fifth, because the interval is one semitone less than C# to G#, the normal fifth. When the lower note is a flattened note, which has no scale of its own, consider it as temporarily raised before determining the nature of the interval, thus Cff to Gf is an augmented fifth, because it is one semitone greater than the normal fifth Cf to Gf." The only obstacle to the general adoption of this excellent method of tabulating intervals is to be fund in the pertinacity with which professors adhere to the expression perfect fifth and perfect fourth, and abhor the term major fifth and major fourth. This absurd prejudice, which arguments drawn from the history and science of music seem to have no power to remove, must be allowed to die of old age. If there is any real distinction between the perfection of a fifth and the imperfection of a third, it might even then be allowed to students to call fourths and fifths majors, on the understanding that they also possessed a remarable perfection which no other intervals possess.

See Also: TEMPERAMENT; RATIO; SCALE

Source: 125