File Name: simultaneous estimation of chords and musical context from audio .zip
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- Reassigned spectrum-based feature extraction for GMM-based automatic chord recognition
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- Simultaneous Estimation of Chords and Musical Context From Audio
- Simultaneous Consonance in Music Perception and Composition
Reassigned spectrum-based feature extraction for GMM-based automatic chord recognition
The authors are very grateful to Daniel Bowling for contributing helpful advice and for sharing research materials. They would also like to thank Manuel Anglada-Tort, Emmanouil Benetos, and Matthew Purver for useful feedback and advice regarding this project.
Peter M. Simultaneous consonance is a salient perceptual phenomenon corresponding to the perceived pleasantness of simultaneously sounding musical tones. Various competing theories of consonance have been proposed over the centuries, but recently a consensus has developed that simultaneous consonance is primarily driven by harmonicity perception.
Here we question this view, substantiating our argument by critically reviewing historic consonance research from a broad variety of disciplines, reanalyzing consonance perception data from 4 previous behavioral studies representing more than participants, and modeling three Western musical corpora representing more than , compositions. We hope that this package will facilitate further psychological and musicological research into simultaneous consonance.
Simultaneous consonance is a salient perceptual phenomenon that arises from simultaneously sounding musical tones. Consonant tone combinations tend to be perceived as pleasant, stable, and positively valenced; dissonant combinations tend conversely to be perceived as unpleasant, unstable, and negatively valenced. The opposition between consonance and dissonance underlies much of Western music e. Here we question whether harmonicity is truly sufficient to explain simultaneous consonance perception.
First, we critically review historic consonance research from a broad variety of disciplines, including psychoacoustics, cognitive psychology, animal behavior, computational musicology, and ethnomusicology. Second, we reanalyze consonance perception data from four previous studies representing more than participants Bowling et al. On the basis of these analyses, we estimate the degree to which different psychological mechanisms contribute to consonance perception in Western listeners. Computational modeling is a critical part of our approach.
We review the state of the art in consonance modeling, empirically evaluate 20 of these models, and use these models to test competing theories of consonance. Our work results in two new consonance models: a corpus-based cultural familiarity model, and a composite model of consonance perception that captures interference between partials, harmonicity, and cultural familiarity.
We release these new models in an accompanying R package, incon , alongside new implementations of 14 other models from the literature see Software for details. In doing so, we hope to facilitate future consonance research in both psychology and empirical musicology. Western music is traditionally notated as collections of atomic musical elements termed notes , which are organized along two dimensions: pitch and time. In performance, these notes are translated into physical sounds termed tones , whose pitch and timing reflect the specifications in the musical score.
Western listeners are particularly sensitive to pitch intervals , the perceptual correlate of frequency ratios. Correspondingly, a key principle in Western music is transposition invariance , the idea that a musical object e. A particularly important interval is the octave , which approximates a frequency ratio. Correspondingly, a pitch class is defined as an equivalence class of pitches under octave transposition. The pitch-class interval between two pitch classes is then defined as the smallest possible ascending interval between two pitches belonging to the respective pitch classes.
In Western music theory, a chord may be defined as a collection of notes that are sounded simultaneously as tones. The lowest of these notes is termed the bass note. Chords may be termed based on their size: For example, the terms dyad , triad , and tetrad denote chords comprising two, three, and four notes respectively. Chords may also be termed according to the representations of their constituent notes: a Pitch sets represent notes as absolute pitches; b Pitch-class sets represent notes as pitch classes; and c Chord types represent notes as intervals from the bass note.
This paper is about the simultaneous consonance of musical chords. For psychological studies, however, it is often useful to provide a stricter operationalization of consonance, and so researchers commonly define consonance to their participants as the pleasantness , beauty , or attractiveness of a chord e. Consonance and dissonance are often treated as two ends of a continuous scale, but some researchers treat the two as distinct phenomena e.
Under such formulations, consonance is typically treated as the perceptual correlate of harmonicity, and dissonance as the perceptual correlate of roughness see Consonance Theories. Here we avoid this approach, and instead treat consonance and dissonance as antonyms.
Here we review current theories of consonance perception. We also discuss several related theories, including vocal similarity, fusion, and combination tones. Human vocalizations are characterized by repetitive structure termed periodicity.
This periodicity has several perceptual correlates, of which the most prominent is pitch. Sound can be represented either in the time domain or in the frequency domain.
In the time domain, periodicity manifests as repetitive waveform structure. Each periodic sound constitutes a possibly incomplete harmonic series rooted on its fundamental frequency; conversely, every harmonic series incomplete or complete is periodic in its fundamental frequency.
For example, octaves are typically performed as complex tones that approximate frequency ratios, where every cycle of the lower-frequency waveform approximately coincides with a cycle of the higher-frequency waveform. The combined waveform therefore repeats approximately with a fundamental frequency equal to that of the lowest tone, which is as high a fundamental frequency as we could expect when combining two complex tones; we can therefore say that the octave has maximal periodicity.
In contrast, the dissonant tritone cannot be easily approximated by a simple frequency ratio, and so its fundamental frequency approximate or otherwise must be much lower than that of the lowest tone.
We therefore say that the tritone has relatively low periodicity. So far these models have only received limited empirical comparison e. One possibility is that long-term exposure to vocal sounds Schwartz et al. A second possibility is that the ecological importance of interpreting human vocalizations creates a selective pressure to perceive these vocalizations as attractive Bowling et al.
Musical chords can typically be modeled as complex tones , superpositions of finite numbers of sinusoidal pure tones termed partials. Each partial is characterized by a frequency and an amplitude. Pure-tone interference has two potential sources: beating and masking. Beating develops from the following mathematical identity for the addition of two equal-amplitude sinusoids:. For sufficiently large frequency differences, listeners perceive the left hand side of Equation 1 , corresponding to two separate pure tones at frequencies f 1 , f 2.
Slow amplitude fluctuation c. This roughness is thought to contribute to dissonance perception. Masking describes situations where one sound obstructs the perception of another sound e. These models embody long-established principles that masking increases with smaller frequency differences and with higher sound pressure level. Beating and masking are both closely linked with the notion of critical bands. The mutual masking of pure tones approximates a linear function of the number of critical bands separating them termed critical-band distance , with additional masking occurring from pure tones within the same critical band that are unresolved by the auditory system Terhardt et al.
This indicates that these phenomena depend, in large part, on physical interactions in the inner ear. In contrast, the literature linking masking to consonance is relatively sparse. Huron , suggests that masking induces dissonance because it reflects a compromised sensitivity to the auditory environment, with analogies in visual processing such as occlusion or glare. Unfortunately, these ideas have yet to receive much empirical validation; a difficulty is that beating and masking tend to happen in similar situations, making them difficult to disambiguate Huron, The kind of beating that elicits dissonance is achieved by small, but not too small, frequency differences between partials.
The kind of masking that elicits dissonance is presumably also maximized by small, but not too small, frequency differences between partials. For moderately small frequency differences, the auditory system tries to resolve two partials, but finds it difficult on account of mutual masking, with this difficulty eliciting negative valence Huron, , For very small frequency differences, the auditory system only perceives one partial, which becomes purer as the two acoustic partials converge on the same frequency.
Musical sonorities can often be treated as combinations of harmonic complex tones , complex tones whose spectral frequencies follow a harmonic series. The interference experienced by a combination of harmonic complex tones depends on the fundamental frequencies of the complex tones. A particularly important factor is the ratio of these fundamental frequencies.
Certain ratios, in particular the simple-integer ratios approximated by prototypically consonant musical chords, tend to produce partials that either completely coincide or are widely spaced, hence minimizing interference.
Interference between partials also depends on pitch height. A given frequency ratio occupies less critical-band distance as absolute frequency decreases, typically resulting in increased interference. This mechanism potentially explains why the same musical interval e. It is currently unusual to distinguish beating and masking theories of consonance, as we have done above.
Most previous work solely discusses beating and its psychological correlate, roughness e. However, we contend that the existing evidence does little to differentiate beating and masking theories, and that it would be premature to discard the latter in favor of the former.
Moreover, we show later in this paper that computational models that address beating explicitly e. For now, therefore, it seems wise to contemplate both beating and masking as potential contributors to consonance.
Several mechanisms for this effect are possible. Through the mere exposure effect Zajonc, , exposure to common chords in a musical style might induce familiarity and hence liking.
Through classical conditioning, the co-occurrence of certain musical features e. It remains unclear which musical features might become consonant through familiarity. A second possibility is that listeners internalize Western tonal structures such as diatonic scales Johnson-Laird et al.
Alternatively, listeners might develop a granular familiarity with specific musical chords McLachlan et al. Vocal similarity theories hold that consonance derives from acoustic similarity to human vocalizations e. However, Bowling et al. Indeed, such intervals are negatively associated with consonance; however, this phenomenon can also be explained by interference minimization. Stumpf , proposed that consonance derives from fusion , the perceptual merging of multiple harmonic complex tones.
The substance of this hypothesis depends on the precise definition of fusion. Subsequently, however, Stumpf wrote that fusion should not be interpreted as indiscriminability but rather as the formation of a coherent whole, with the sophisticated listener being able to attend to individual chord components at will Schneider, Following Stumpf, several subsequent studies have investigated the relationship between fusion and consonance, but with mixed findings.
Guernsey and DeWitt and Crowder tested fusion by playing participants different dyads and asking how many tones these chords contained. In both studies, prototypically consonant musical intervals octaves, perfect fifths were most likely to be confused for single tones, supporting a link between consonance and fusion.
McLachlan et al. Combination tones were also argued to have important implications for music perception, explaining phenomena such as chord roots and perceptual consonance Hindemith, ; Krueger, ; Tartini, , cited in Parncutt, However, subsequent research showed that the missing fundamental persisted even when the difference tone was removed by acoustic cancellation Schouten, , described in Plomp, , and that, in any case, difference tones are usually too quiet to be audible for typical speech and music listening Plomp, We therefore do not consider combination tones further.
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Simultaneous Estimation of Chords and Musical Context From Audio
Metrics details. Most existing automatic chord recognition systems use a chromagram in front-end processing and some sort of classifier e. The vast majority of front-end algorithms derive acoustic features based on a standard short-time Fourier analysis and on mapping energy from the power spectrum, or from a constant-Q spectrum, to chroma bins.
Music Perception 1 April ; 36 4 : — W e investigated perception of virtual pitches at missing fundamentals MFs in musical chords of three chromas simultaneous trichords. Tone profiles for major, minor, diminished, augmented, suspended, and four other trichords of octave-complex tones were determined.
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Simultaneous Consonance in Music Perception and Composition
In music , the term chroma feature or chromagram closely relates to the twelve different pitch classes. Chroma-based features, which are also referred to as " pitch class profiles ", are a powerful tool for analyzing music whose pitches can be meaningfully categorized often into twelve categories and whose tuning approximates to the equal-tempered scale. One main property of chroma features is that they capture harmonic and melodic characteristics of music, while being robust to changes in timbre and instrumentation. The underlying observation is that humans perceive two musical pitches as similar in color if they differ by an octave.
Computer Science [cs]. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. Je remercie M. Geoffroy Peeters pour avoir su partager son dynamisme et son excellence scientifique avec une grande attention, rendant nos discussions toujours enrichissantes. Most of the previous works that address the problem of estimating musical attributes from the audio signal have dealt with these elements independently. However, musical elements are deeply related to each other and should be analyzed considering the global musical context, as a musician does when he or she analyzes a piece of music.
Fundamentals of Music Processing pp Cite as. In music, harmony refers to the simultaneous sound of different notes that form a cohesive entity in the mind of the listener. The main constituent components of harmony, at least in the Western music tradition, are chords , which are musical constructs that typically consist of three or more notes. Harmony analysis may be thought of as the study of the construction, interaction, and progression of chords. The progression of chords over time closely relates to what is often referred to as the harmonic content of a piece of music. These progressions are of musical importance for composing, describing, and understanding Western tonal music including popular, jazz, and classical music.
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