10 100 1,000 10,000

Comparison Frequency - Hz

Figure 13 Equal loudness contours showing the level of a comparison tone required to match the perceived loudness of a 1000-Hz standard tone presented at different levels (20, 40, 60, 80, and 100 dB SPL). Each curve is an equal loudness contour. Based on International Standards Organization Standard ISO, R-532 (1981).

phons loud is judged to be equally loud to an x dB SPL, 1000-Hz tone.

Pitch is measured in hertz, and the most often used scales of pitch are musical scales. Musical scales are based on octaves, where an octave is a doubling of frequency (e.g., 440 to 880 Hz is one octave). The octave is divided into 12 equal logarithmic steps (semitones), with each semitone containing 100 cents. Thus, in a musical scale an octave is divided into 1200 logarithmic steps called cents. The musical note scale (A, B, C, D, E, F, G with or without sharps and flats) is also used as a pitch scale.

The perception of pitch exists even when there is no energy in a sound's spectrum at frequencies that correspond to the perceived pitch. These pitches are often referred to as complex, virtual, or missing fundamental pitches. The latter name is derived from the following type of stimulus conditions: a complex sound consisting of six tones added together with equal levels and with frequencies of 400, 500, 600, 700, 800, 900, and 1000 Hz. Independent of the phases of the individual tones, this complex sound has a salient perceived pitch of 100 Hz. Note that all the tones are harmonics of 100 Hz (integer multiples of 100 Hz), but 100 Hz is "missing" (hence the term missing fundamental pitch). Also note that there is no energy in this sound's spectrum in the region of the reported pitch (100 Hz). The temporal waveform of this stimulus can produce an amplitude modulation of 100 Hz, but neither simple measures of the periodicity of the amplitude modulation nor those of the spectral structure of these complex sounds are able to predict complex pitch, suggesting that pitch processing involves more complex operations than simple temporal or spectral mechanisms.

Due to the nonlinear properties of the transduction of sound by the auditory periphery, pitches associated with nonlinear distortion products are often perceived. For instance, a complex sound consisting of 700- and 1000-Hz, equal-amplitude tones may produce pitches in addition to those of 700 and 1000 Hz. In many conditions, listeners also report pitches of 400, 1400, and 2000 Hz for primary stimuli with frequencies of 700 and 1000 Hz. The pitches of 400, 1400, and 2000 Hz are nonlinear distortion products caused by nonlinear peripheral transduction. The 1400- and 2000-Hz pitches are aural harmonics (the second harmonics of 700 and 1000 Hz). The 400-Hz pitch results from the cubic difference tone, which is twice the lower frequency minus the higher frequency (2f1 — f2 = 2 x 700 — 1000 = 400). The cubic difference tone is often the most salient distortion product.

Sounds can have many other subjective attributes. The spectral complexity of sound is often correlated with a sound's timbre. Sounds differ in timbre if the sounds are perceived as different even though they have the same perceived loudness, pitch, and duration. Thus, the perceptual difference between a violin and viola playing the same musical note, with the same loudness and duration, is a timbre difference.

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