HANDBOOK OF ACOUSTICS - online book

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

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218
HAND-BOOK OF ACOUSTICS.
In testing the results of this theoretical investigation, the student must be again reminded, that all the above intervals are supposed to be in just intonation. On a tempered instrument, the Combination Tones will be very different from those given above.
Consonant Tetrads.
If one of the tones of a consonant Triad be duplicated by adding its Octave, a consonant Tetrad or chord of four tones is obtained. A great variety of chords may be thus formed, and the method of investigating them, which we adopted in the case of the six original Triads, that is, by setting out the partials of each tone, would be somewhat laborious. Nevertheless this method is occasionally convenient, especially when two or three chords only have to be compared with one another. As an example, we will compare the following two Tetrads, the fundamentals being supposed to be of the same pitch, say D.
Fig 87 shows the full partials of each tone, up to the 6th in the Bass, 5th in the Tenor, 4th in the Contralto, and 3rd in the Soprano, tone dissonances being connected by a single, and semitone dissonances by a double line, as before; while below are given the Differentials generated by the four fundamentals of each chord. The following is a summary of the partial dissonances :