Page 111 - Master Handbook of Acoustics

Kuttruff and Applied Science Publishers Ltd., London.)

The horizontal directional effects shown in Fig. 5-7A demonstrate only a modest directional effect
of about 5 dB in the 125- to 250-Hz band. This is expected because the head is small compared to
wavelengths of 4.5 to 9 ft associated with this frequency band. However, there are significant
directional effects for the 1,400- to 2,000-Hz band. For this band, which contains important speech

frequencies, the front-to-back difference is about 12 dB.
In the vertical plane shown in Fig. 5-7B, the 125- to 250-Hz band shows about a 5-dB front-to-
back difference again. For the 1,400- to 2,000-Hz band, the front-to-back difference is also about the
same as the horizontal plane, except for the torso effect. The discrimination against high-speech
frequencies picked up on a lapel microphone is obvious (see Fig. 5-7B), although the measurements
were not carried to angles closer to 270°.

Music

Musical sounds are extremely variable in their complexity. Sounds can range from the near sine-wave

simplicity of a single instrument or voice to the highly intricate tonalities of a symphony orchestra
where each instrument has a different tonal texture for each note.

String Instruments

Musical instruments such as the violin, viola, cello, or bass produce their tones by vibration of
strings. On a stretched string, the overtones are all exact multiples of the fundamental, the lowest tone
produced. These overtones may thus be properly called harmonics. If the string is bowed in the
middle, odd harmonics are emphasized because the fundamental and odd harmonics have maximum

amplitude there. Because the even harmonics have nodes in the center of the string, they will be
subdued if bowed there. The usual place for bowing is near one end of the strings, which gives a
better blend of even and odd harmonics. The “unmusical” seventh harmonic is anathema in most
music (musically, it is a very flat minor seventh). By bowing (or striking or plucking) 1/7 or 2/7 of
the distance from one end, this harmonic is decreased. For this reason, the hammers in a piano are
located near a node of the seventh harmonic.

The harmonic content of the E and G notes of a violin are displayed in Fig. 5-8. Harmonic
multiples of the higher E tone are spaced wider and hence have a thinner timbre. The lower G tone,
on the other hand, has a closely spaced spectral distribution and a richer timbre. The small size of the
violin relative to the low frequency of the G string means that the resonating body cannot produce a
fundamental at as high a level as the higher harmonics. The harmonic content and spectral shape
depend on the shape and size of the resonating violin body, the type and condition of the wood, and

even the varnish. Why there are so few superb violins among the many good ones is a problem that
has not yet been solved completely.