[Lecturer's Summary.]

Interval is a characteristic quality which distinguishes the sound of all pairs of tones, the ratio of whose vibration numbers is the same. This quality is in most cases disagreeable, the few agreeable or consonant intervals having vibration ratios which can be expressed by the first five integers. Helmholtz has sought to explain this remarkable fact by the use of the same principle of the disagreeableness of the strong and rapid pulsations of sound formed by very near tones, which in his theory of Timbre accounts for the aesthetic superiority of notes with a few integral overtones to all others. He has shown that in all of the intervals called dissonant, some of the partial tones of one note must fall near enough to some of those of the other to produce this disagreeable interferference; while in all those called consonant the roughness from this source is insignificant in amount and the beauty of the tones involved can produce its full effect upon the ear. But later criticism has demanded a positive reason for the beauty of a concord and questions whether the character of an Interval depends to the extent asserted by Helmholtz upon the timbre of the notes comprising it. A view which may be ascribed to Von Oettingen points to the fact that the consonant intervals are those which are given in the partial tones of the most pleasing musical note. In accordance with this suggestion we may suppose that habituation to this note has impressed upon the auditory sense a norm for the combination of tone, and that this expresses itself in our satisfaction in those combinations of notes which present the intervals between its partials.

A like hypothesis would throw light upon the remarkable distinction in emotional character between the two forms of consonant chord, the Major and the Minor Triad. The former presents, through its fundamental tones, and their difference tones an approximately complete musical note; the Minor on the other hand gives fragments of three different notes. The Minor Triad is thus equivocal and unsatisfying, and to this fact may be due its tinge of melancholy.

In the next lecture we have the study of simultaneous note-combination to take up the discussion of notes in sequence.