Text: So far, this division seems plain enough. But modern music requires that intervals shall be designated according to their scale value. Hence a perfect interval when accidentally flattened becomes imperfect and a major interval becomes minor. But the application of the word imperfect to a perfect interval made smaller led to serious confusion, because, an imperfect fifth came as a subdivision of perfect intervals, while imperfect intervals of themselves formed a separate class. To avoid this cross-division, theorists have in the last few years used the name diminished for perfect fifths reduced by one semitone. But it is important to note that by this change of a name a new difficulty arises, for diminished has almost by universal consent been applied to certain intervals when made less than minor, for example, C# to Bf is a diminished seventh, C# to B# a major seventh, C# to Bn a minor seventh, C# to Bf one semitone less than minor. The word diminished when applied by these authors to a fourth or fifth signifies that it is reduced from its normal state by one semitone, but the same word "diminished" when applied to a seventh signifies that it is reduced by two semitones. That utter confusion should result from such an undigested system is absolutely inevitable; and it will be found that professors and teachers of music to this day are unable to talk intelligibly to each other on the simple subject of Intervals. For many years a system has been taught in Germany which makes the whole matter perfectly plain. It is this: 1) Intervals are reckoned upwards, inclusively, and by the number of notes they contain. 2) Intervals are in their normal state when reckoned from the first note of the major scale. The lowest note of the interval being considered for the time as a tonic. 3) Normal intervals are major. Thus, D to F# is a major third, because F# is the third degree of the scale of D; F to Bf is a major fourth, because Bf is the fourth of the scale of F; B to F# is a major fifth, because F# is the fifth of the scale of B; and so on. In other words, all the intervals of any major scale reckoning up from the tonic respectively are major. 4) Intervals one semitone less than major are minor. Thus, C to Df is a minor second because it is one semitone less than the normal D in the scale of C; B to Fn is a minor fifth because one semitone less than the normal F# in the scale of B; and so on. 5) Intervals one semitone greater than major are augmented. Thus, C to D# is an aumented second, because it is one semitone greater than C to D, the normal interval; C to G# an augmented fifth; and so on. 6) Intervals one semitone less than minor are diminished. Thus, F# to Ef is a diminished seventh; C# to Gf, a diminished fifth; C# to Ef, a diminished third; and so on.

See Also: TEMPERAMENT; RATIO; SCALE

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