The pitch of a sound composed of multiple frequencies can be mathematically quantified.
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Reference materials and psychoacoustic studies confirm that the pitch of complex or multi-frequency sounds can be quantified in terms of component frequencies or temporal spike intervals.
1. The temporal discharge patterns of auditory nerve fibers in Dial-anesthetized cats were studied in response to periodic complex acoustic waveforms that evoke pitches at their fundamental frequencies. Single-formant vowels, amplitude-modulated (AM) and quasi-frequency-modulated tones. AM noise, click trains, and other complex tones were utilized. Distributions of intervals between successive spikes ("1st-order intervals") and between both successive and nonsuccessive spikes ("all-order intervals") were computed from spike trains. Intervals from many fibers were pooled to estimate interspike interval distributions for the entire auditory nerve. Properties of these "pooled interspike interval distributions," such as the positions of interval peaks and their relative heights, were examined for correspondence to the psychophysical data on pitch frequency and pitch salience. 2. For a diverse set of complex stimuli and levels, the most frequent all-order interspike interval present in the pooled distribution corresponded to the pitch heard in psychophysical experiments. Pitch estimates based on pooled interval distributions (30-85 fibers, 100 stimulus presentations per fiber) were highly accurate (within 1%) for harmonic stimuli that produce strong pitches at 60 dB SPL. 3. Although the most frequent intervals in pooled all-order interval distributions were very stable with respect to sound intensity level (40, 60, and 80 dB total SPL), this was not necessarily the case for first-order interval distributions. Because the low pitches of complex tones are largely invariant with respect to level, pitches estimated from all-order interval distributions correspond better to perception. 4. Spectrally diverse stimuli that evoke similar low pitches produce pooled interval distributions with similar most-frequent intervals. This suggests that the pitch equivalence of these different stimuli could result from central auditory processing mechanisms that analyze interspike interval patterns. 5. Complex stimuli that evoke strong or "salient" pitches produce pooled interval distributions with high peak-to-mean ratios. Those stimuli that evoke weak pitches produce pooled interval distributions with low peak-to-mean ratios. 6. Pooled interspike interval distributions for stimuli consisting of low-frequency components generally resembled the short-time auto-correlation function of stimulus waveforms. Pooled interval distributions for stimuli consisting of high-frequency components resembled the short-time autocorrelation function of the waveform envelope. 7. Interval distributions in populations of neurons constitute a general, distributed means of encoding, transmitting, and representing information. Existence of a central processor capable of analyzing these interval patterns could provide a unified explanation for many different aspects of pitch perception.
The spectrum of amplitude-modulated wide-band noise is invariant with changes in modulation frequency, and consequently such waveforms cannot convey melodic information by spectral changes. The results of several experiments indicate, however, that sinusoidally amplitude-modulated wide-band noise does have pitchlike properties. Simple melodies can be identified when the ’’notes’’ correspond to different modulation frequencies. More importantly, musically trained observers can immediately recognize melodic muscial intervals composed of such waveforms. The pitchlike properties of modulated noise are maintained when the modulated noise is bandpass filtered and when an unmodulated band-reject masker is added to the bandpass noise. Presumably the perception of pitch elicited by modulated noise is based upon temporal information in the envelope of the waveform. This ’’temporal pitch’’ is less salient than the pitch elicited by pure tones. Also, temporal pitch can be elicited only over a restricted range of modulation frequencies. The upper limit (approximately 850–1000 Hz) appears to reflect the inability of the auditory system to follow rapid temporal changes. Subject Classification: [43]65.54, [43]65.75.
Temporal models of pitch and harmonic segregation call for delays of up to 30ms to cover the full range of existence of musical pitch. To date there is little anatomical or physiological evidence for delays that long. We propose a mechanism by which delays may be synthesized from cross-channel phase interaction. Phases of adjacent cochlear filter channels are shifted by an amount proportional to frequency and then combined as a weighted sum to approximate a delay. Synthetic delays may be used by pitch perception models such as autocorrelation, segregation models such as harmonic cancellation, and binaural processing models to explain sensitivity to large interaural delays. The maximum duration of synthetic delays is limited by the duration of the impulse responses of cochlear filters, itself inversely proportional to cochlear filter bandwidth. Maximum delay is thus frequency dependent. This may explain the fact, puzzling for temporal pitch models such as autocorrelation, that pitch is more salient and easy to discriminate for complex tones that contain resolved partials.
The phenomenology of pitch has been difficult to rationalize and remains the subject of much debate. Here we test the hypothesis that audition generates pitch percepts by relating inherently ambiguous sound stimuli to their probable sources in the human auditory environment. A database of speech sounds, the principal source of periodic sound energy for human listeners, was compiled and the dominant periodicity of each speech sound determined. A set of synthetic test stimuli were used to assess whether the major pitch phenomena described in the literature could be explained by the probabilistic relationship between the stimuli and their probable sources (i.e., speech sounds). The phenomena tested included the perception of the missing fundamental, the pitch-shift of the residue, spectral dominance and the perception of pitch strength. In each case, the conditional probability distribution of speech sound periodicities accurately predicted the pitches normally heard in response to the test stimuli. We conclude from these findings that pitch entails an auditory process that relates inevitably ambiguous sound stimuli to their probable natural sources.
oscillations of sound waves can often be characterized in terms of frequency. Pitches are usually associated with, and thus quantified as, frequencies (in cycles
Pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a perceptual property that allows sounds to be ordered on a frequency-related scale.
Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.
Pitch may be quantified as a frequency, but pitch is not a purely objective p
Pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a perceptual property that allows sounds to be ordered on a frequency-related scale.
Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.
Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound. Historically, the study of pitch and pitch perception has been a central problem in psychoacoustics, and has been instrumental in forming and testing theories of sound representation, processing, and perception in the auditory system.
Since 1939 the A above middle C is usually set at 440 Hz (often written as A440 or sometimes "A = 440 Hz"), although other frequencies, such as 442 Hz, are also often used as variants. Another standard, the so-called 'baroque pitch', is now set at A = 415 Hz, a semitone lower than A440, so that period and modern instruments can be used together by transposing. 'Classical pitch' for fortepianos and other instruments for music of the Classical period can be tuned to either 427 Hz (about halfway between A415 and A440) or 430 Hz (also between A415 and A440 but slightly sharper than the quarter tone). And ensembles specializing in authentic performance of repertoire from the Romantic era set the A above middle C to 432 Hz or the French standard until the 1930s of 435 Hz.
Transposing instruments conventionally have their parts transposed and written in different keys from voices and non-transposing instruments, and indeed from different transposing instruments. As a result, musicians speak of "concert pitch" to avoid ambiguity when talking to each other. For example, the most common…
Constrict-Depart is a piece for string quartet in two movements that lasts approximately fourteen minutes. The title refers to an overarching sonic theme within and across both movements that consists of the constriction and subsequent expansion of a vacillating pitch band. In addition, the form of each movement is defined by the constriction and expansion of the string registers. The title also refers to a constant push and pull between a self-imposed binary categorization of sonic materials. The binary categories of sound being explored are defined as noise (aperiodic sounds) and pitch (periodic sounds). In this context, noise is classified best as a sound or collection of sounds that offer no perceivable pitch, or a cluster of pitches (either within the same register or multiple registers) so dense that individual pitches become imperceptible. By contrast, pitched sounds would be classified as sounds in which there is a definite and perceptible frequency, or group of frequencies. In the piece, these categories of sound are set as two extremes on a spectrum, with noise on one end and pitch on the other, and are juxtaposed as extremes, and also as collections of sounds that fall between the two extremes of the spectrum. The piece is composed with the use of time frames, and the graphic notation was created specifically to allow for a greater degree of performance freedom than is generally possible with standard notation, while still maintaining a fixed formal structure that
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