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282                     HAND-BOOK OF ACOUSTICS.
4.    On keyboard instruments, four minor thirds are taken as equal to an octave, (a) Is this correct ? (b) If not, state as a vibration ratio the interval by which one exceeds the other, and show clearly which is the greater.
Ant. (a) No.
(») fxfxfxf='«iW
x          —           OJLP
1             ----              6 45
therefore the former is the greater by the interval j||| = |^§-
5.   (a) State precisely what you understand by " Simple Tone," "Compound Tone," "Partial," "Overtone," and "Fundamental," and
(b) Explain how you would demonstrate to anyone the existence of each.
Ant. (a) See Summary, pp. 83 and 84.
{b) Simple Tone. See p. 84.
Compound Tones are obtained from any ordinary musical instrument. Partials, overtones, and fundamentals may easily be discriminated by resonators (see pp. 69 and 70.)
6.  (a) Explain clearly and Illustrate what is meant by resonance.
(b) What are the relations between the length of an air column and the pitch of its note of maximum resonance ? Ant. (a) See pp. 67 and 62, or 63 or 64. (b) The length of air column must be J or ^ the wave-length (that is
1100 — vibration number) according as the air column is in an open or stopped, tube.
Second Stage.
1.    Wherabouts are the hammers made to strike the middle strings of a pianoforte ? Why is this ?
Ant —See p. 95.
2.    Show clearly why -. is a dissonant interval, and 5, a consonant
Ant.—See p. 168 for former and pp. 188 and 191 for latter, which is a major third.
3.  Show clearly how it comes about that the major third is too sharp in equal temperament.
Ant.— See p. 240.
4.    Explain as fully as you can why a primary dissonance is worse than a secondary, and a secondary worse than a tertiary.