Musical Intervals Research Articles

2A1-D28 FFTを用いた録音音楽データからの音程解析

2A1-D28 FFTを用いた録音音楽データからの音程解析

Neural Correlates of Consonance, Dissonance, and the Hierarchy of Musical Pitch in the Human Brainstem

Consonant and dissonant pitch relationships in music provide the foundation of melody and harmony, the building blocks of Western tonal music. We hypothesized that phase-locked neural activity within the brainstem may preserve information relevant to these important perceptual attributes of music. To this end, we measured brainstem frequency-following responses (FFRs) from nonmusicians in response to the dichotic presentation of nine musical intervals that varied in their degree of consonance and dissonance. Neural pitch salience was computed for each response using temporally based autocorrelation and harmonic pitch sieve analyses. Brainstem responses to consonant intervals were more robust and yielded stronger pitch salience than those to dissonant intervals. In addition, the ordering of neural pitch salience across musical intervals followed the hierarchical arrangement of pitch stipulated by Western music theory. Finally, pitch salience derived from neural data showed high correspondence with behavioral consonance judgments (r = 0.81). These results suggest that brainstem neural mechanisms mediating pitch processing show preferential encoding of consonant musical relationships and, furthermore, preserve the hierarchical pitch relationships found in music, even for individuals without formal musical training. We infer that the basic pitch relationships governing music may be rooted in low-level sensory processing and that an encoding scheme that favors consonant pitch relationships may be one reason why such intervals are preferred behaviorally.

Some parallels between language and music from a cognitive and evolutionary perspective

Parallels between language and music are considered as a useful basis for examining possible evolutionary pathways of these achievements. Such parallels become apparent if we compare clauses and syllables in language with phrases and notes in music: Clauses as well as musical phrases typically span about 2 sec and about 5 to 10 pulses, i.e. syllables or notes. The n of syllables per clause or intonation unit also can be used as a measure of tempo across languages and thus also as a means for a better understanding of typological co-variations in the rhythm of speech and music. Further correspondences were found between the size of the sound-relevant inventories, i.e. vowels and musical intervals: a minimum of roughly 3 and a maximum of roughly 12 elements as well as a frequency peak at 5 elements. A link between vowels and musical intervals is also indicated by our findings that in Alpine yodellers the vowels are highly correlated to melodic direction according to their F2 ordering. These parallels are discussed from an evolutionary perspective that either sees music as a precursor of language or both language and music as descendents of a common, “half-musical” precursor (Jespersen, 1895; Brown, 2000). A rather simple explanation of the parallels is reported: If singing in a broader sense of the word is the most original form of music, then the functionality of any mechanism involved in the programming and the online-control of intonation units will be reflected in language as well as in music.

Musical elements in human infants’ cries: In the beginning is the melody

Crying is the earliest sound production of human infants on their long way toward language. Here, we argue that infants’ early crying contains melodic constituents for both musical and prosodic structures. This view is based on our findings that cry melodies become increasingly complex during the first months of life and, that complex cry melodies are composed of shape-specific melody arcs. We found that cry melodies contain frequency ratios that show a certain preference of musical intervals. We also observed that young infants are capable of uttering shape-similar melody arcs at different frequency levels, that means they have an aptitude for frequency transposition from birth on. Moreover, we observed that the production of phonatory breaks within single expiratory sounds generates rhythmical elements and points to a flexible time organization. Our data support the view that in crying elementary constituents of both musicality and language faculty are unfolding. The results may elucidate the relation between emotionally charged sounds and music respectively language and suggest direction for further research.

Microswitch- and VOCA-assisted programs for two post-coma persons with minimally conscious state and pervasive motor disabilities

Intervention programs, based on learning principles and assistive technology, were assessed in two studies with two post-coma men with minimally conscious state and pervasive motor disabilities. Study I assessed a program that included (a) an optic microswitch, activated via double blinking, which allowed a man direct access to brief music intervals, and (b) a voice output communication aid (VOCA) with two channels, activated via different hand-closure movements, which allowed the man to call his mother and a research assistant who provided stimulation events. Study II assessed a program that included (a) a pressure microswitch, activated via head movements, which allowed a man direct access to video-clips and music, and (b) a VOCA device, activated via prolonged eyelid closure, which allowed the man to call the caregiver (i.e., a research assistant) who provided attention and sang to him. Each of the two participants had significant increases in both microswitch- and VOCA-related responses during the intervention phases of the studies. Moreover, purposeful choice seemed to occur between the two VOCA responses in Study I. Implications of the findings for improving the situation of post-coma persons with minimally conscious state and pervasive motor disabilities are discussed.

Pulse-coupled neuron models as investigative tools for musical consonance

We investigate the mode locking properties of simple dynamical models of pulse-coupled neurons to two tones, i.e., simple musical intervals. A recently proposed nonlinear synchronization theory of musical consonance links the subjective ranking from consonant to dissonant intervals to the universal ordering of robustness of mode locking ratios in forced nonlinear oscillators. The theory was illustrated using two leaky integrate-and-fire neuron models with mutual excitatory coupling, with each neuron firing at one of the two frequencies in the musical interval. We show that the ordering of mode locked states in such models is not universal, but depends on coupling strength. Further, unless the coupling is weak, the observed ratio of firing frequencies is higher than that of the input tones. We finally explore generic aspects of a possible synchronization theory by driving the model neurons with sinusoidal forcing, leading to down-converted, more realistic firing rates. This model exhibits one-to-one entrainment when the input frequencies are in simple ratios. We also consider the robustness to the presence of noise that is present in the neural firing activity. We briefly discuss agreements and discrepancies between predictions from this theory and physiological/psychophysical data, and suggest directions in which to develop this theory further.

Selective Subcortical Enhancement of Musical Intervals in Musicians

By measuring the auditory brainstem response to two musical intervals, the major sixth (E3 and G2) and the minor seventh (E3 and F#2), we found that musicians have a more specialized sensory system for processing behaviorally relevant aspects of sound. Musicians had heightened responses to the harmonics of the upper tone (E), as well as certain combination tones (sum tones) generated by nonlinear processing in the auditory system. In music, the upper note is typically carried by the upper voice, and the enhancement of the upper tone likely reflects musicians' extensive experience attending to the upper voice. Neural phase locking to the temporal periodicity of the amplitude-modulated envelope, which underlies the perception of musical harmony, was also more precise in musicians than nonmusicians. Neural enhancements were strongly correlated with years of musical training, and our findings, therefore, underscore the role that long-term experience with music plays in shaping auditory sensory encoding.

Exploring the acoustic basis of consonance using individual differences.

Despite its central role in music, the origins of the preference for consonant over dissonant intervals remains controversial. We applied an individual differences approach to this question. Subjects were first tested for their aversion to pure‐tone beats, and to inharmonic spectra of single complex tones. Consistent individual differences were observed in the magnitude of subjects’ aversion to beats and inharmonicity, but the two effects were uncorrelated across subjects, suggesting independent factors. Subjects then rated the pleasantness of musical intervals and three‐note chords. If particular acoustic factors determine consonance, stronger sensitivity to those factors should predict stronger musical preferences. In each of two cohorts, only the preference for harmonic spectra was consistently correlated with preferences for consonant over dissonant chords and intervals. Although the strength of a subject’s consonance preference was also correlated with their musical experience, so was their harmonicity preference, which explained most of the effect of experience on consonance ratings. The results suggest that much of consonance perception is rooted in the basic acoustic property of harmonicity. Harmonicity is evidently predictive of important structures in Western music, and with exposure to music, listeners learn to attend to it. [Work supported by NIH grant R01DC05216.]

Review: Generalized Musical Intervals and Transformations by David Lewin; Musical Form and Transformation: Four Analytic Essays by David Lewin

Review: Generalized Musical Intervals and Transformations by David Lewin; Musical Form and Transformation: Four Analytic Essays by David Lewin

Categorical gestures, the diamond conjecture, Lewin's question, and the Hammerklavier Sonata

We construct a categorical framework of gestures, generalizing the topological approach from [G. Mazzola and A. Moreno, Diagrams, gestures and formulae in music, J. Math. Music 1 (2007), pp. 23–46], and culminating in the construction of a gesture bicategory, which enriches the classical Yoneda embedding. This framework could be a valid candidate for the conjectured space X in the diamond conjecture [G. Mazzola and A. Moreno, Diagrams, gestures and formulae in music, J. Math. Music 1 (2007), pp. 23–46]. We discuss first applications thereof for topological groups, and then more concretely gestures in modulation processes in Beethoven's Hammerklavier Sonata. The latter offers a first concretization of answers to Lewin's big question from [D. Lewin, Generalized Musical Intervals and Transformations, Yale University Press, New Haven, CT, 1987] concerning characteristic gestures. Yoneda's philosophy, as traced in his famous lemma, succeeds in reinterpreting objects and morphisms in abstract categories by their intuitive set-valued functors and natural transformations, i.e. we are provided with the (Fregean) functions between (variable) sets rather than with completely encapsulated objects and arrows. This is the ‘objective’ half of Yoneda's insight. This research does not solve the second, ‘morphic’, half of Yoneda's philosophy, namely a replacement of Fregean functional abstraction by gestural dynamics, but its technical toolbox provides us with first steps towards a gestural Yoneda philosophy.

Experimenting with consonance and dissonance

Consonance and dissonance are subjective perceptions that are reactions of the human earto whether or not musical intervals sound ‘pleasing.’ The physical causes of consonance anddissonance are not as well understood as other subjective properties of sound perceived bythe ear such as pitch, loudness, and quality (timbre). What follows is an overview of someattempts to quantify these sensations, and a new study with results that can be comparedto several ‘dissonance metrics’.

Binaural sluggishness precludes temporal pitch processing based on envelope cues in conditions of binaural unmasking

Binaural sluggishness refers to the binaural system's inability to follow fast changes in the interaural configuration of the incoming sound stream. Several studies have measured binaural sluggishness by measuring signal detection in conditions of binaural unmasking when the interaural configuration of the masker is changed over time. However, it has been shown that, in conditions of binaural unmasking, binaural sluggishness also affects the perception of temporal changes in the properties of the signal (i.e., its frequency or level) and not just in the interaural configuration of the masker. By measuring the temporal modulation transfer function for sinusoidally modulated noise presented in conditions of binaural unmasking, the first experiment of the current study showed that, due to binaural sluggishness, the internal representation of binaurally unmasked sounds conveys little or no information about envelope fluctuations with rates within the pitch range (i.e., above 30 Hz). The second experiment measured the masked detection threshold for musical interval recognition in binaurally unmasked harmonic tones and showed that, in conditions of binaural unmasking, pitch wanes when the harmonics become unresolved by the cochlear filters. These results suggest that binaural sluggishness precludes temporal pitch processing based on envelope cues in binaurally unmasked sounds.

Investigating cochlear implant place-pitch perception with the Modified Melodies test

There has been speculation that cochlear implant place-of-excitation cues could be more akin to the brightness attribute of timbre (the spectral profile) than to melodic pitch. As brightness can be ordered on a low-to-high scale, it would allow high scores on pitch-ranking tests. In contrast, the Modified Melodies test measures pitch perception in a melodic context. In each trial, a familiar melody was presented twice. In one presentation, randomly selected, the pitch was deliberately modified. The subject's task was to select the un-modified melody. Six Nucleus implant recipients were tested with melodies presented as pure tones in the frequency range C5–C6 (523–1046 Hz) through the ACE strategy on the Freedom processor. All subjects were able to identify incorrect melodic contours and three subjects were able to recognize errors in musical intervals. These results are consistent with the hypothesis that cochlear implant place cues alone are sufficient to convey a melody. Copyright © 2009 John Wiley & Sons, Ltd.

Fourier Analysis of Musical Intervals

Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace.1 A recent article in The Physics Teacher aptly demonstrated the use of MacScope2 in just such a manner as a way to teach Fourier analysis.3 A logical continuation of this project is to use MacScope not just to analyze the Fourier composition of musical tones but also musical intervals.

Optimization of piano tunings by minimizing perceived beat loudness.

In order to create an ideal piano tuning that best matches the inharmonicities and spectra of each instrument, tuning frequencies are optimized using a new beat loudness perceptual model that considers the time dependence of the frequency and amplitude of individual partials. These optimized tunings are compared to prior inharmonicity‐based methods of tuning calculation. First, several pianos are prepared to an initial tuning using traditional methods. The resulting tones are recorded and analyzed in MATLAB. Each partial's frequency and amplitude are estimated at discrete time intervals over the duration of the tones. Beat rates are derived for the consonant musical intervals by employing phase‐based high resolution frequency estimation techniques on coincident partials. A beat loudness model is developed based on established perceptual theories of consonance and equal loudness contours. The total perceived beat loudness is then minimized by applying optimization and global search methods that alter the t...

Neuronal periodicity detection as a basis for the perception of consonance: A mathematical model of tonal fusion

A mathematical model is presented here to explain the sensation of consonance and dissonance on the basis of neuronal coding and the properties of a neuronal periodicity detection mechanism. This mathematical model makes use of physiological data from a neuronal model of periodicity analysis in the midbrain, whose operation can be described mathematically by autocorrelation functions with regard to time windows. Musical intervals produce regular firing patterns in the auditory nerve that depend on the vibration ratio of the two tones. The mathematical model makes it possible to define a measure for the degree of these regularities for each vibration ratio. It turns out that this measure value is in line with the degree of tonal fusion as described by Stumpf [Tonpsychologie (Psychology of Tones) (Knuf, Hilversum), reprinted 1965]. This finding makes it probable that tonal fusion is a consequence of certain properties of the neuronal periodicity detection mechanism. Together with strong roughness resulting from interval tones with fundamentals close together or close to the octave, this neuronal mechanism may be regarded as the basis of consonance and dissonance.

Acoustic analysis of musical intervals in modern Byzantine Chant scales

The goal of this work is to investigate experimentally the music intervals in modern Byzantine Chant performance and to compare the obtained results with the equal temperament scales introduced by the Patriarchal Music Committee (PMC). Current measurements resulted from pressure and electroglottographic recordings of 13 famous chanters singing scales of all the music genera. The scales' microintervals were derived after pitch detection based on autocorrelation, cepstrum, and harmonic product spectrum analysis. The microintervallic differences between the experimental values and the PMC's ones were statistically analyzed indicating large deviation of the mean values and the standard deviations. Significant interaction effects were identified among some genera and between ascending and descending scale directions.

Analysis of Flute Control Parameters: A Comparison Between a Novice and an Experienced Flautist

The sound produced by flutes depends not only on the physical characteristics of the instrument but also on the control exerted by the musician. The latter is very important in some instruments of the flute family, especially in those where the air jet is shaped with the lip of the player. Some of the most relevant parameters controlled by the flautist, such as the distance from the lips to the sharp edge, the shape of the lips hole and the speed of the jet, are experimentally measured in this paper. Data produced by an experienced and a novice flautist are collected, analyzed and compared. Subjects are studied under normal musical playing conditions, playing phrases made out of simple musical intervals with subjective dynamics. Images of performer's lips are taken together with measurements of the blowing pressure and the sound radiated by the instrument. Data analysis shows remarkable differences between the two subjects. The optimized coordination of several parameters in order to obtain a desired musical response, coupling between performer's mouth and the instrument, as well as the efficient use of the available resources are some of the differences observed.

An Experimental Study on Categorical Perception of Korean Musical Interval between Hwangjong and Jungryeo

An Experimental Study on Categorical Perception of Korean Musical Interval between Hwangjong and Jungryeo

"Acoustics vases in ancient theatres: disposition, analysis from the ancient tetracordal musical system"

The acoustics of the ancient Greek and Roman theatres has always been rated as excellent by experts, without discussion. Beyond the purely architectural aspects, in this kind of outdoor theatres some mechanisms were used in order to improve the acoustics. In this paper we have studied the texts about "theatre's vases" of the famous book "On Architecture" by Vitruvius. Different interpretations and illustrations of these vases, that several translators carried out in the sixteenth to the eighteenth centuries, have been researched. From the wide bibliography consulted in this regard we have developed a plane with the disposition of the bronze vases in the theatres. In this plane we have specified the frequency of each one of them, and explained their disposition from the tetracordal musical system acquired from the Greek culture. Finally, an analysis of the disposition of the vases has been made. We have studied and looked for the musical intervals and harmonic relations among adjacent vases.