A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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In the arrangement of the subject, the reader should observe that up to and including the 7th Chapter, the sounds treated of are supposed to be simple; the next four chapters treat of soundsóboth simple and compoundósingly, that is to say, only one tone is supposed to be produced at a time ; the phenomena accompanying the simultaneous production of two or more sounds are reserved for the remaining chapters.
The movable Sol-fa names for the notes of the scale have been used throughout, as they are so much better adapted to scientific treatment than the fixed Staff Notation symbols. It may be useful to readers not acquainted with the Tonic Sol-fa Notation to mention that in this system, the symbol d is taken to represent a sound of any assumed pitch, and the letters, r, m, f, S, 1, t, represent the other tones of the diatonic scale in ascending order. The sharp of any one of these tones is denoted by placing the letter e after its symbol: thus, the sharp of s is se; of r, re: and so on. The flat of any tone is denoted by placing the letter a after its symbol: thus the flat of t is ta; of nij ma; and so on. The upper or lower octaves of these notes are expressed by marks above or below their symbols : thus d1 is one octave, d2 two octaves above d; Si is one octave, Sa two octaves below s- Absolute pitch has been denoted throughout by the ordinary symbols, C representing the note on the ledger line below the treble staff. Its successive higher octaves are denoted by placing the figures 1, 2, 3, &c, above it, and its lower octaves by writing the same figures beneath it; thus, CJ, Ca, C8, &c.; Ca, C2, C3, &c.
It is perhaps as well to observe, that although Helmholtz'e theory as to the origin of Combination Tones given in Chap. XII is at present the received one, it is possible that in the future it may require modification, in view of the recent researches of Preyer, Koenig, and Bosanquet.