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Constant Spectrum Melody
A constant timbre at a constant pitch is characterized by a spectrum. Along a piece of music, the spectrum measured within a narrow time window varies with the melody and the possible effects of instruments. Therefore, it may seem paradoxical that a constant spectrum can be perceived as a melody rather than a stamp. The paradoxA. Chaigne (1988), “Psychoacoustique”, ENST, 114 pages. is that the ear is not an abstract spectrograph: it "calculates" the Fourier transform of the audio signal in a narrow time window, but the slower variations are seen as temporal evolution and not as pitch. However, the example of paradoxical melody above contains no infrasound (i.e. pure tone of period slower than the time window). The second paradox is that when two pitches are very close, they create a beat. If the period of this beat is longer than the integration window, it is seen as a sinusoidal variation in the average rating: sin(2π(f+ε)t) + sin(2π(f-ε)t) = sin(2πft)cos(2πεt), wh ...
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Timbre
In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both Woodwind instrument, woodwind instruments). In simple terms, timbre is what makes a particular musical instrument or human voice have a different sound from another, even when they play or sing the same note. For instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. Both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctively with its own unique tone color. Experienced musicians are able to distinguish between diff ...
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Frequency Spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would b ...
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Spectrogram
A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data are represented in a 3D plot they may be called ''waterfall displays''. Spectrograms are used extensively in the fields of music, linguistics, sonar, radar, speech processing, seismology, and others. Spectrograms of audio can be used to identify spoken words phonetically, and to analyse the various calls of animals. A spectrogram can be generated by an optical spectrometer, a bank of band-pass filters, by Fourier transform or by a wavelet transform (in which case it is also known as a scaleogram or scalogram). A spectrogram is usually depicted as a heat map, i.e., as an image with the intensity shown by varying the colour or brightness. Format A common format is a graph with two geometric dimensions: one axis represents time, and the other axis r ...
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Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ...
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Audio Signal
An audio signal is a representation of sound, typically using either a changing level of electrical voltage for analog signals, or a series of binary numbers for digital signals. Audio signals have frequencies in the audio frequency range of roughly 20 to 20,000 Hz, which corresponds to the lower and upper limits of human hearing. Audio signals may be synthesized directly, or may originate at a transducer such as a microphone, musical instrument pickup, phonograph cartridge, or tape head. Loudspeakers or headphones convert an electrical audio signal back into sound. Digital audio systems represent audio signals in a variety of digital formats.Hodgson, Jay (2010). ''Understanding Records'', p.1. . An audio channel or audio track is an audio signal communications channel in a storage device or mixing console, used in operations such as multi-track recording and sound reinforcement. Signal flow Signal flow is the path an audio signal will take from source to the sp ...
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Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, ''perceived'' as a periodic variation in volume whose rate is the difference of the two frequencies. With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, the beating starts to sound like a note, and a combination tone is produced. This combination tone can also be referred to as a missing fundamental, as the beat frequency of any two tones is equivalen ...
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Shepard Tone
A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the bass pitch of the tone moving upward or downward, it is referred to as the ''Shepard scale''. This creates the auditory illusion of a tone that seems to continually ascend or descend in pitch, yet which ultimately gets no higher or lower. Construction Each square in Figure 1 indicates a tone, with any set of squares in vertical alignment together making one Shepard tone. The color of each square indicates the loudness of the note, with purple being the quietest and green the loudest. Overlapping notes that play at the same time are exactly one octave apart, and each scale fades in and fades out so that hearing the beginning or end of any given scale is impossible. As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C4 ( middle C) and a loud C5 (an octave higher). The next would be a slight ...
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Spectral Music
Spectral music uses the acoustic properties of sound – or sound spectra – as a basis for composition. Definition Defined in technical language, spectral music is an acoustic musical practice where compositional decisions are often informed by sonographic representations and mathematical analysis of sound spectra, or by mathematically generated spectra. The spectral approach focuses on manipulating the spectral features, interconnecting them, and transforming them. In this formulation, computer-based sound analysis and representations of audio signals are treated as being analogous to a timbral representation of sound. The (acoustic-composition) spectral approach originated in France in the early 1970s, and techniques were developed, and later refined, primarily at IRCAM, Paris, with the Ensemble l'Itinéraire, by composers such as Gérard Grisey and Tristan Murail. Hugues Dufourt is commonly credited for introducing the term ''musique spectrale'' (spectral music) in an ar ...
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Auditory Illusion
Auditory illusions are false perceptions of a real sound or outside stimulus. These false perceptions are the equivalent of an optical illusion: the listener hears either sounds which are not present in the stimulus, or sounds that should not be possible given the circumstance on how they were created. Humans are fairly susceptible to illusions, despite an innate ability to process complex stimuli. Confirmation bias is believed to be largely responsible for the inaccurate judgments that people make when evaluating information, given that humans typically interpret and recall information that appeals to their own biases. Amongst these misinterpretations, known as illusions, falls the category of auditory illusions. The brain uses multiple senses simultaneously to process information, spatial information is processed with greater detail and accuracy in vision than in hearing. Auditory illusions highlight areas where the human ear and brain, as organic survival tools, differentiat ...
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Musical Acoustics
Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody, and in the clinical use of music in music therapy. The pioneer of music acoustics was Hermann von Helmholtz, a German polymath of the 19th century who was an influential physician, physicist, physiologist, musician, mathematician and philosopher. His book '' On the Sensations of Tone as a Physiological Basis for the Theory of Music'' is a revolutionary compendium of several studies and approaches that provided a complete n ...
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