Page 40 - The Master Handbook Of Acoustics

15
FUNDAMENTALS OF SOUND

tom of Fig. 1-12 falls in step with the top one, reaching positive peaks and
negative peaks simultaneously and producing the in-phase condition.
In Fig. 1-11, all three components of the complex wave of Fig. 1-11E
are in phase. That is, the f fundamental, the f second harmonic, and
1 2
the f third harmonic all start at zero at the same time. What happens if
3
the harmonics are out of phase with the fundamental? Figure 1-13 illus-
trates this case. The second harmonic f is now advanced 90°, and the
2
third harmonic f is retarded 90°. By combining f , f , and f for each
3 1 2 3
instant of time, with due regard to positive and negative signs, the con-
torted wave of Fig. 1-13E is obtained.
The only difference between Figs. 1-11E and 1-13E is that a phase
shift has been introduced between harmonics f and f , and the funda-
2 3
mental f . That is all that is needed to produce drastic changes in the
1
resulting waveshape. Curiously, even though the shape of the wave is
dramatically changed by shifting the time relationships of the compo-
nents, the ear is relatively insensitive to such changes. In other words,
waves E of Figs. 1-11 and 1-13 would sound very much alike to us.
A common error is confusing polarity with phase. Phase is the time
relationship between two signals while polarity is the / or the /
relationship of a given pair of signal leads.

Partials
A musician is inclined to use the term partial instead of harmonic, but
it is best that a distinction be made between the two terms because the
partials of many musical instruments are not harmonically related to
the fundamental. That is, partials might not be exact multiples of the
fundamental frequency, yet richness of tone can still be imparted by
such deviations from the true harmonic relationship. For example, the
partials of bells, chimes, and piano tones are often in a nonharmonic
relationship to the fundamental.

Octaves
Audio and electronics engineers and acousticians frequently use the
integral multiple concept of harmonics, closely allied as it is to the
physical aspect of sound. The musician often refers to the octave, a
logarithmic concept that is firmly embedded in musical scales and ter-
minology because of its relationship to the ear’s characteristics. Audio
people are also involved with the human ear, hence their common use
of logarithmic scales for frequency, logarithmic measuring units, and