Pitch Transitions Research Articles

Musical stylistic analysis: a study of intervallic transition graphs via persistent homology

We develop a novel method to represent a weighted directed graph as a finite metric space and then use persistent homology to extract useful features. We apply this method to weighted directed graphs obtained from pitch transitions information of a given musical fragment and use these techniques to the quantitative study of stylistic trends. As a first illustration, we analyse a selection of string quartets by Haydn, Mozart and Beethoven and discuss possible implications of our results in terms of different approaches by these composers to stylistic exploration and variety. We observe that Haydn is stylistically the most conservative, followed by Mozart, while Beethoven is the most innovative. Finally we also compare the variability of different genres, namely minuets, allegros, prestos, and adagios, by a given composer and conclude that the minuet is the most stable form of the string quartet movements.

Linked auditory and motor patterns in the improvisation vocabulary of an artist-level jazz pianist

Improvising musicians possess a stored library of musical patterns forming the basis for their improvisations. According to a prominent theoretical framework by Pressing (1988), this library includes linked auditory and motor information. Though examples of libraries of melodic patterns have been shown in extant recordings by some improvising musicians, the underlying motor component has not been experimentally investigated nor related to its auditory counterparts. Here we analyzed a large corpus of ∼100,000 notes from improvisations by one artist-level jazz pianist recorded during 11 live performances with audience. We compared the library identified from these recordings to a control corpus consisting of improvisations by 24 different advanced jazz pianists. In addition to pitch, our recordings included accurate micro-timing and key velocity (i.e., force) data. Following a previously validated procedure, this information was used to identify the underlying motor patterns through correlations between relative timing and velocity between notes in different iterations of the same pitch pattern. A computational model was, furthermore, used to estimate the information content and generated entropy exhibited by recurring pitch patterns with high and low timing and velocity correlations as perceived by a stylistically enculturated expert listener. Though both corpora contained a large number of recurring patterns, the single-player corpus showed stronger evidence that pitch patterns were linked to motor programs in that within-pattern timing and velocity correlations were significantly higher compared to the control corpus. Even when controlling for potentially greater baseline levels of motor self-consistency in the single-player corpus, this effect remained significant for velocity correlations. Amongst recurring 5-tone pitch patterns, those exhibiting more consistent motor schema also used less idiomatic pitch transitions that were both more unexpected and generated more uncertain expectations in enculturated experts than less consistently repeated patterns. Interestingly, we only found partial evidence for fixed pattern boundaries as predicted by the Pressing model and therefore suggest an expanded view in which the beginning and ends of idiomatic audio-motor patterns are not always clear-cut. Our results indicate that the library of melodic patterns may be idiosyncratic to the individual improviser and relies both on motor programming and predictive processing to promote stylistic distinctiveness.

An Automatic Synthesis of Musical Phrases from Multi-Pitch Samples

Abstract Sound synthesizers are a natural element of a musician’s toolset. In music arrangement, samplers can often produce satisfactory results, but it requires a combination of manual and automatic methods that may be arduous at times. Concatenative Sound Synthesis reproduces many of natural performance- and expression-related nuances but at a cost of high demand for processing power. Here, another method of musical phrase synthesis aimed at music arrangement is presented that addresses these and other related issues. Contrary to common practice, we propose to record and utilize sound samples containing not one,but short sequences of pitches. In effect, natural pitch transitions are preserved and phrases appear to be much smoother, despite using very limited set of performance rules. The proof-of-concept implementation of the proposed method is discussed in detail along with attempts at optimizing the final sound effects, based on auditory tests. The limitations and future applications of the synthesizer are also discussed.

Ear Advantage for Musical Location and Relative Pitch: Effects of Musical Training and Attention.

Trained musicians have been found to exhibit a right-ear advantage for high tones and a left-ear advantage for low tones. We investigated whether this right/high, left/low pattern of musical processing advantage exists in listeners who had varying levels of musical experience, and whether such a pattern might be modulated by attentional strategy. A dichotic listening paradigm was used in which different melodic sequences were presented to each ear, and listeners attended to (a) the left ear or the right ear or (b) the higher pitched tones or the lower pitched tones. Listeners judged whether tone-to-tone transitions within each melodic sequence moved upward or downward in pitch. Only musically experienced listeners could adequately judge the direction of successive pitch transitions when attending to a specific ear; however, all listeners could judge the direction of successive pitch transitions within a high-tone stream or a low-tone stream. Overall, listeners exhibited greater accuracy when attending to relatively higher pitches, but there was no evidence to support a right/high, left/low bias. Results were consistent with effects of attentional strategy rather than an ear advantage for high or low tones. Implications for a potential performer/audience paradox in listening space are considered.

Transitional Probabilities Are Prioritized over Stimulus/Pattern Probabilities in Auditory Deviance Detection: Memory Basis for Predictive Sound Processing.

Representations encoding the probabilities of auditory events do not directly support predictive processing. In contrast, information about the probability with which a given sound follows another (transitional probability) allows predictions of upcoming sounds. We tested whether behavioral and cortical auditory deviance detection (the latter indexed by the mismatch negativity event-related potential) relies on probabilities of sound patterns or on transitional probabilities. We presented healthy adult volunteers with three types of rare tone-triplets among frequent standard triplets of high-low-high (H-L-H) or L-H-L pitch structure: proximity deviant (H-H-H/L-L-L), reversal deviant (L-H-L/H-L-H), and first-tone deviant (L-L-H/H-H-L). If deviance detection was based on pattern probability, reversal and first-tone deviants should be detected with similar latency because both differ from the standard at the first pattern position. If deviance detection was based on transitional probabilities, then reversal deviants should be the most difficult to detect because, unlike the other two deviants, they contain no low-probability pitch transitions. The data clearly showed that both behavioral and cortical auditory deviance detection uses transitional probabilities. Thus, the memory traces underlying cortical deviance detection may provide a link between stimulus probability-based change/novelty detectors operating at lower levels of the auditory system and higher auditory cognitive functions that involve predictive processing. Our research presents the first definite evidence for the auditory system prioritizing transitional probabilities over probabilities of individual sensory events. Forming representations for transitional probabilities paves the way for predictions of upcoming sounds. Several recent theories suggest that predictive processing provides the general basis of human perception, including important auditory functions, such as auditory scene analysis. Our results demonstrate that the memory traces underlying cortical deviance detection form a link between stimulus probability-based change/novelty detectors operating at lower levels of the auditory system and higher auditory cognitive functions that involve predictive processing.

Expectations Evoked on Hearing a Piece of Music for the First Time: Evidence from a Musical Savant

This study investigates expectations in music evoked during the course of hearing a piece for the first time, particularly those which stem from recently appearing groups of notes (Ockelford, 2006). A prodigious musical savant (Derek Paravicini) attempted to reproduce a novel composition on the piano at the same time as hearing it. The piece was designed to minimise the impact of the more general expectations that arise from tonality, whereby different pitch transitions are felt to occur with different probabilities according to their level of past exposure. The design of the study was informed by ‘zygonic’ theory (Ockelford, 2009, 2012b), which holds that structural regularities in music suggest future continuations, whose perceived likelihood of occurrence is proportional to the number of ways in which their existence is implied in what has gone before. Using this principle, a ‘strength of implication’ factor was calculated for each note of the stimulus piece (following the first). It was hypothesised that the higher the implication factor, the more likely Derek would predict its occurrence (and therefore play it correctly at the appropriate point in time). Data gathered from Derek’s performance support the principles of the zygonic model, although they also suggest certain refinements.

Light-induced pitch transitions in photosensitive cholesteric liquid crystals: Effects of anchoring energy

We experimentally study how the cholesteric pitch P depends on the equilibrium pitch P0 in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC of the right-handed chiral dopant 7-dehydrocholesterol (7-DHC, provitamin D3) which transforms to left-handed tachysterol under the action of uv irradiation at the wavelength of 254nm. By using the model of photoreaction kinetics we obtain the dependencies of isomer concentrations and, therefore, of the equilibrium pitch on the uv irradiation dose. The cholesteric pitch was measured as a function of irradiation time using the polarimetry method. In this method, the pitch is estimated from the experimental data on the irradiation time dependence of the ellipticity of light transmitted through the LC cells. It is found that the resulting dependence of the twist parameter 2D/P (D is the cell thickness) on the free twisting number parameter 2D/P0 shows jumplike behavior and agrees well with the known theoretical results for the anchoring potential of Rapini-Papoular form.

Brain dynamics encode the spectrotemporal boundaries of auditory objects

Perception of objects in the scene around us is effortless and intuitive, yet entails profound computational challenges. Progress has been made in understanding some mechanisms by which the brain encodes the boundaries and surfaces of visual objects. However, in the auditory domain, these mechanisms are poorly understood. We investigated differences between neural responses to spectrotemporal boundaries in the auditory scene. We used iterated rippled noise to create perceptual boundaries with and without energy transients. In contrast to boundaries marked by energy transients, second-order boundaries were characterized by an absence of early components in the event-related potential. First-order energy boundaries triggered a transient evoked gamma-band response and a well-defined P90 component of the event-related potential, whereas second-order boundaries evoked only the later N1 component. Furthermore, the N1 component was delayed when evoked by second-order boundaries and theta-band electroencephalography activity at this latency exhibited significant phase lag for second-order compared to first-order boundaries. We speculate that boundaries defined by sharp energy transients can be registered by early feed-forward mechanisms. By contrast, boundaries defined only by discontinuities at discrete frequency bands require integration across the tonotopic representation of the frequency spectrum and require time-consuming interaction between auditory areas.

Cholesteric pitch transitions induced by mechanical strain

We investigate thickness and surface anchoring strength influence on pitch transitions in a planar cholesteric liquid crystal layer. The cholesteric-nematic transition is also investigated. We assume planar boundary conditions, with strong anchoring strength at one interface and weak anchoring strength at the other. The surface anchoring energy we consider to describe the deviation of the surface twist angle from the easy axis induced by a bulk deformation is a parabolic potential or Rapini and Papoular periodic potential, respectively. We show that under strain, all pitch transitions take place at a critical thickness that is equal to the quarter of the natural cholesteric pitch. The latter result does not depend on the anchoring strength, the particular surface potential, or material properties. The twist angle on the limiting surface characterized by weak anchoring varies with strain either by slipping and or in a discontinuous manner according to the thickness of the sample. The position of the bifurcation point depends only on the ratio of the extrapolation length over the layer thickness, but its value is model dependent. Multistability and multiplicity of the transition are discussed.

Effects of musical training on the early auditory cortical representation of pitch transitions as indexed by change‐N1

The effects of musical training on the early auditory cortical response to pitch transitions in music were investigated by use of the change-N1 component of auditory event-related potentials. Musicians and non-musicians were presented with music stimuli comprising a melody and a harmony under various listening conditions. First, when the subjects played a video game and were instructed to ignore the auditory stimuli, the onset of stimuli elicited a typical, fronto-central onset-N1, whereas melodic and harmonic pitch transitions within the stimuli elicited so-called change-N1s that were more posterior in scalp distribution. The pitch transition change-N1s, but not onset-N1, were enhanced in musicians. Second, when the listeners attended to the same stimuli as above to detect infrequently occurring target stimuli, the change-N1 elicited by pitch changes (in non-target stimuli) was augmented, in non-musicians only when the target was easily detectable, and in both musicians and non-musicians when it was difficult to detect. Thus, the early, obligatory cortical response to pitch transitions during passive listening was chronically enhanced by training in musicians, and, reflecting this training-induced enhancement, the task-related modulation of this response was also different between musicians and non-musicians. These results are the first to demonstrate the long-term effects of training, short-term effects of task and the effects of their interaction on the early (~100-ms) cortical processing of pitch transitions in music. The scalp distributions of these enhancement effects were generally right dominant at temporal electrode sites, suggesting contributions from the radially oriented subcomponent of change-N1, namely, the Tb (N1c) wave of the T-complex.

Measuring the Evolution of Contemporary Western Popular Music

Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains formally unknown. Here we unveil a number of patterns and metrics characterizing the generic usage of primary musical facets such as pitch, timbre, and loudness in contemporary western popular music. Many of these patterns and metrics have been consistently stable for a period of more than fifty years. However, we prove important changes or trends related to the restriction of pitch transitions, the homogenization of the timbral palette, and the growing loudness levels. This suggests that our perception of the new would be rooted on these changing characteristics. Hence, an old tune could perfectly sound novel and fashionable, provided that it consisted of common harmonic progressions, changed the instrumentation, and increased the average loudness.

The influence of perceptual organisation on an auditory context effect

Perceptual organization of auditory scenes has a well-documented effect on subjective reports of listeners. Here, we investigated whether it also influenced an auditory context effect based on pitch. Stimuli were complexes of sinusoidal components arranged to produce ambiguous pitch transitions when presented successively. The context effect was established by preceding an ambiguous test pair with tone complexes comprising frequencies between the components of the ambiguous pair, which was found to produce a strong bias on the test [Chambers & Pressnitzer, MidWinter Meeting of the Association for Research in Otolaryngology, 2011]. We first tested whether spatial attention modulated the context effect. Two sequences inducing opposing biases were presented dichotically, followed by an ambiguous monaural test. Listeners were more likely to be biased by the attended context. Then we tested whether figure-ground segregation was required for the context effect. We embedded the context tones in random clouds of pure tones, and varied the temporal coherence between the components of the context stimuli. High coherence produced more detectability of the context and, generally, stronger context effects. Both experiments show that stream segregation of the context sequences strongly influences the resulting bias, for identical physical stimuli. This may provide an additional objective measure of streaming.

Cholesteric pitch-transitions induced by a magnetic field in a sample containing incomplete number of pitches

AbstractWe investigate the pitch transitions induced by an external bulk field in a Cholesteric Liquid Crystal slab of finite thickness ℓ that contains an incomplete number of π-twists. The analysis is performed for a magnetic field that is (i) perpendicular to the helical axis, and (ii) tilted with respect to one of the easy directions imposed by planar and rigid boundary conditions. For finite ℓ we obtain a cascade of transitions, where the bulk expels a half-pitch at a time with increasing field to avoid divergences in the elastic energy. The dependence of the threshold magnetic field inducing the expulsion on the easy axes twist angle δ is investigated for all the cascade of pitch transitions and in particular for the final one, corresponding to the Cholesteric-Nematic transition. In the ℓ → ∞ limit this dependence disappears and we reobtain the results of de Gennes for an infinite sample.

Vocal perfection in yodelling—pitch stabilities and transition times

Background. Yodelling is a special kind of vocal performance in traditional music which consists of rapid and repeated changes in pitch. It is assumed that these pitch changes are accompanied by register changes. Material and methods. We analysed, using the laryngograph, yodelling on different vowels by four professional yodelling teachers (two male, two female), four professional classically trained singers, and four untrained voices. Results. Results reveal that pitch changes in yodelling are associated with decrease of electroglottograpgic (EGG) contact quotient for the upper pitch, indicating a register shift. Furthermore, in contrast to untrained voices, for the yodellers lower and upper pitches were more stable with respect to fundamental frequency and perturbation values, and the pitch transitions were faster.

Language and music: differential hemispheric dominance in detecting unexpected errors in the lyrics and melody of memorized songs.

Using magnetoencephalography (MEG), we report here the hemispheric dominance of the auditory cortex that is selectively modulated by unexpected errors in the lyrics and melody of songs (lyrics and melody deviants), thereby elucidating under which conditions the lateralization of auditory processing changes. In experiment 1 using familiar songs, we found that the dipole strength of responses to the lyrics deviants was left-dominant at 140 ms (M140), whereas that of responses to the melody deviants was right-dominant at 130 ms (M130). In experiment 2 using familiar songs with a constant syllable or pitch, the dipole strength of frequency mismatch negativity elicited by oddballs was left-dominant. There were significant main effects of experiment (1 and 2) for the peak latencies and for the coordinates of the dipoles, indicating that the M140 and M130 were not the frequency mismatch negativity. In experiment 3 using newly memorized songs, the right-dominant M130 was observed only when the presented note was unexpected one, independent of perceiving unnatural pitch transitions (i.e., perceptual saliency) and of selective attention to the melody of songs. The consistent right-dominance of the M130 between experiments 1 and 3 suggests that the M130 in experiment 1 is due to unexpected notes deviating from well-memorized songs. On the other hand, the left-dominant M140 was elicited by lyrics deviants, suggesting the influence of top-down linguistic information and the memory of the familiar songs. We thus conclude that the left- lateralized M140 and right-lateralized M130 reflect the expectation based on top-down information of language and music, respectively.

The NEXTPITCH Learning Classifier System: Representation, Information Theory and Performance

NEXTPITCH, a learning classifier system (LCS) using genetic algorithms, inductively learns to predict the next note in a musical melody. NEXTPITCH models human music learning by developing the rules that represent actual pitch transitions in the melody. In this article, the author addresses the issues of (1) the impact of the representation of a domain (the encoding of the characteristics of the field of study) on the performance of an LCS and (2) the classification of the input (the melodies to be learned) to an LCS in order to determine the highest percentage of correct next-note predictions.

Vibrato and pitch transitions

<h2>Summary</h2> There are at least two timing variables to be considered in vocal music performance. The first is the note changes associated with the meter signature (4/4, 2/4, etc.) and the second is the vibrato rate of the performer. Because the probability is not great that these two temporal variables will always be in perfect synchrony, it was the purpose of this investigation to determine what singers do when these two timing variables come into conflict during singing. Six singers recorded a series of alternating upward and downward interval shifts of a third while singing whole notes, half notes, quarter notes and eighth notes. The same notes were then recorded with intervals of a fifth. The recorded samples were converted to a visual trace and examined for interactions between vibrato and meter. Analysis of the tracings indicated that, in the majority of the cases, the singers would alter their vibrato in order to adhere to the timing of the musical line.

A study of the pitches produced by violinists while playing a short piece of music

Computer recordings were made of the pitches produced by four violinists playing a section of a Mozart (G Major) violin‐piano sonata and a G Major scale. Twelve repetitions of the scale and sonata were recorded. The sonata was played with a recorded piano accompaniment. Selected notes in the recorded material were analyzed to study the variation in pitch from repetition‐to‐repetition of the same note, variation in pitch in different parts of the note, and to observe the pitch variations produced by vibrato. The pitch transitions between successive notes were also observed.

Experiments in Pitch Detection

This paper describes the results of experiments in the automatic detection of the quasiperiodic “pitch” frequency of the voiced portions of speech. The approach tested transforms the energy pulsations of voiced speech to frequency components that are accurately detected and measured by a novel type of spectrum analysis. Experiments have shown that correct pitch is consistently extracted from the general utterances of both male and female speakers. Initial pitch transitions and other variations are faithfully reproduced. Pitch can also be extracted from speech in which the fundamental frequency has been eliminated, as can occur in Vocoder communication systems. The technique can be implemented in a practical pitch-extraction device. Spectrograms and other demonstrations are included to show the relations of measured pitch to original speech characteristics.