Page 36 - Master Handbook of Acoustics

The only difference between Figs. 1-9E and 1-11E is that a phase shift has been introduced
between harmonics f and f , and the fundamental f . That is all that is needed to produce drastic
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changes in the resulting wave shape. Curiously, even though the shape of the waveform is
dramatically changed by shifting the time relationships of the components, the ear is relatively
insensitive to such changes. In other words, although waveforms E of Figs. 1-9 and 1-11 are visually
very different, they would sound very much alike.
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

Musicians may be 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 some 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 percussion instruments such as bells, cymbals, and chimes are in a
nonharmonic relationship to the fundamental.

Octaves

Audio engineers and acousticians frequently use the integral multiple concept of harmonics, closely

allied as it is to the physical aspect of sound. Musicians often refer to the octave, a logarithmic
concept that is firmly embedded in musical scales and terminology 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 various devices based on octaves.

Harmonics and octaves are compared in Fig. 1-12. Harmonics are linearly related; each next
harmonic is an integer multiple of the preceding one. An octave is defined as a 2:1 ratio of two
frequencies. For example, middle C (C4) has a frequency close to 261 Hz. The next highest C (C5)
has a frequency of about 522 Hz. Ratios of frequencies are very much a part of the musical scale. The
frequency ratio 2:1 is the octave; the ratio 3:2 is the fifth; 4:3 is the fourth; and so on.