Musical Intervals Research Articles

Probing the neural dynamics of musicians’ and non-musicians’ consonant/dissonant perception: Joint analyses of electrical encephalogram (EEG) and functional magnetic resonance imaging (fMRI)

The perception of two (or more) simultaneous musical notes, depending on their pitch interval(s), could be broadly categorized as consonant or dissonant. Previous literature has suggested that musicians and non-musicians adopt different strategies when discerning music intervals: while musicians rely on the frequency ratios between the two fundamental frequencies, such as “perfect fifth” (3:2) as consonant and “tritone” (45:32) as dissonant intervals; non-musicians may rely on the presence of ‘roughness’ or ‘beats’, generated by the difference of fundamental frequencies, as the key elements of ‘dissonance’. The separate Event-Related Potential (ERP) differences in N1 and P2 along the midline electrodes provided evidence congruent with such ‘separate reliances’. To replicate and to extend, in this study we reran the previous experiment, and separately collected fMRI data of the same protocol (with sparse sampling modifications). The behavioral and EEG results largely corresponded to our previous finding. The fMRI results, with the joint analyses by univariate, psycho-physiological interaction, and representational similarity analysis (RSA) approaches, further reinforce the involvement of central midline-related brain regions, such as ventromedial prefrontal and dorsal anterior cingulate cortex, in consonant/dissonance judgments. The final spatiotemporal searchlight RSA provided convincing evidence that the medial prefrontal cortex, along with the bilateral superior temporal cortex, is the joint locus of midline N1 and dorsal anterior cingulate cortex for the P2 effect (for musicians). Together, these analyses reaffirm that musicians rely more on experience-driven knowledge for consonance/dissonance perception; but also demonstrate the advantages of multiple analyses in constraining the findings from both EEG and fMRI.

Consonance in the carillon.

Previous psychological studies have shown that musical consonance is not only determined by the frequency ratios between tones, but also by the frequency spectra of those tones. However, these prior studies used artificial tones, specifically tones built from a small number of pure tones, which do not match the acoustic complexity of real musical instruments. The present experiment therefore investigates tones recorded from a real musical instrument, the Westerkerk Carillon, conducting a "dense rating" experiment where participants (N = 113) rated musical intervals drawn from the continuous range 0-15 semitones. Results show that the traditional consonances of the major third and the minor sixth become dissonances in the carillon and that small intervals (in particular 0.5-2.5 semitones) also become particularly dissonant. Computational modelling shows that these effects are primarily caused by interference between partials (e.g., beating), but that preference for harmonicity is also necessary to produce an accurate overall account of participants' preferences. The results support musicians' writings about the carillon and contribute to ongoing debates about the psychological mechanisms underpinning consonance perception, in particular disputing the recent claim that interference is largely irrelevant to consonance perception.

Musical harmonies and its relationship with emotional processing: An ERP study in young adults

Music has been used to express and communicate emotional states through its different dimensions such as tone, rhythm, melody, and harmony. Consonant harmonies consistently are rated as pleasant whereas dissonant are considered unpleasant. The aim of this study was to explore the effect of consonant and dissonant musical harmonies used as prime on the emotional classification of images, as indexed by event-related potentials. Thirty volunteers (ages 21–27, 50 % women) were presented with a task consisting of 4 musical intervals in the C major scale, divided into consonant and dissonant harmonies, followed by 180 positive, negative, or neutral images from the International Affective Picture System (IAPS). Participants had to rate the images as pleasant or unpleasant. We found a bias effect on negative images rated as positive when preceded by a consonant musical interval. A N200 component, non-sensible to the valence of the images, was found. On the other hand, a significant difference was found in the amplitude of the P300 component, with a greater amplitude in the consonant-positive images condition compared to the dissonant-positive images. Lastly, a late positivity component around 500–700 ms was found in both negative conditions dissonant and consonant, but with a larger amplitude for the consonant condition when followed by a negative image. These results indicate that additionally to the P300 processing the relevance of the stimulus there are processes like recognition memory involved. As part of the novelty effect this late positive activity may also be related to the emotional content integration of the relevant stimulus.

Classification of musical intervals by spiking neural networks: Perfect student in solfége classes.

We investigate a spike activity of a network of excitable FitzHugh-Nagumo neurons, which is under constant two-frequency auditory signals. The neurons are supplemented with linear frequency filters and nonlinear input signal converters. We show that it is possible to configure the network to recognize a specific frequency ratio (musical interval) by selecting the parameters of the neurons, input filters, and coupling between neurons. A set of appropriately configured subnetworks with different topologies and coupling strengths can serve as a classifier for musical intervals. We have found that the selective properties of the classifier are due to the presence of a specific topology of coupling between the neurons of the network.

Pythagorean Music Theory and Its Application in Renaissance Architectural Design

This article concerns Alberti's approach to architectural design integrates Pythagorean consonance ratios from music theory, not by direct application but as a conceptual guide for aesthetic ratios in buildings. He expands spatial dimensions using methods derived from past artisans, adhering to and building upon the foundational consonance ratios. While applying these two-number proportions to width and length poses no problem, calculating height in a three-dimensional space requires a three-number proportion. Alberti resolves this issue by adopting the mean value strategy from music theory, where the mean is typically the middle value in an octave ratio, to determine the height in the spatial configuration. Alberti advocates for architects to leverage the insights of skilled artisans. However, his own architectural work demonstrates deviations from his theoretical principles. This study highlights Alberti's application of musical intervals such as the major and minor thirds, sixths, and sevenths, which were not traditionally emphasized in the musical science of the quadrivium, focused primarily on octaves, fifths, and fourths. These choices reflect the broader evolution of music during the 15th century, marking a shift towards "practical music" and signaling music's departure from the liberal arts to become a significant element of the fine arts, showcasing the influence of Pythagorean consonance in European music and arts through the 16th century. Thus, this article reflects the interactions between music and architecture of knowledge received from ancient Greek civilization in the Renaissance. The art of music in this period is founded on the philosophy and knowledge of Pythagoras.

Culture influences conscious appraisal of, but not automatic aversion to, acoustically rough musical intervals.

There is debate whether the foundations of consonance and dissonance are rooted in culture or in psychoacoustics. In order to disentangle the contribution of culture and psychoacoustics, we considered automatic responses to the perfect fifth and the major second (flattened by 25 cents) intervals alongside conscious evaluations of the same intervals across two cultures and two levels of musical expertise. Four groups of participants completed the tasks: expert performers of Lithuanian Sutartinės, English speaking musicians in Western diatonic genres, Lithuanian non-musicians and English-speaking non-musicians. Sutartinės singers were chosen as this style of singing is an example of 'beat diaphony' where intervals of parts form predominantly rough sonorities and audible beats. There was no difference in automatic responses to intervals, suggesting that an aversion to acoustically rough intervals is not governed by cultural familiarity but may have a physical basis in how the human auditory system works. However, conscious evaluations resulted in group differences with Sutartinės singers rating both the flattened major as more positive than did other groups. The results are discussed in the context of recent developments in consonance and dissonance research.

Distinctive Features of Traditional Singing in Sri Lanka

It is evident that Sri Lankan musicologists have mainly used the meanings of traditional folk poetry/verses and the occasions on which they are sung to categorize them. The authors of this paper attempt to introduce a classification that can be used according to the characteristics of the melody/pitches, focusing on seepada, currently only known as a poetic stanza in Sinhala folk songs. The authors explain the distinctive features of seepada identified employing yathi and the notion of ‘Cents’, a logarithmic unit used for measuring musical intervals, and reveal those characteristics, acknowledging seepada as a traditional singing style unique to Sri Lanka. Suggestions for sustaining this fading art form are presented in this article including the urgent need for action by stakeholders to preserve the identity of traditional Sinhala folk songs, music and melodies of Sri Lanka.

A Celebration of Kepler’s Third Law: Harmony, Power Laws, and Keplerian Orbits

Kepler’s greatest achievements are contained in his three laws, which today reappear constantly at the cutting edge of modern astrophysics. The modified third law has been the major workhorse of astronomy and astrophysics in determining the mass of objects throughout the universe. Kepler never revealed why he chose the integers, 2 and 3, to test using Tycho’s data. Because of his attachment to Pythagorean ideas and his knowledge of musical theory, I suggest he was guided by the musical interval known as the perfect fifth, for which the ratio of frequencies is 3/2. The perfect fifth is the most consonant of all intervals except the octave, and, as such, is the basis of all the tuning of stringed instruments. If Kepler had recognized the significance of the perfect fifth in analyzing Tycho’s data, it suggests a very pleasing historical parallelism between music and astronomy. In discovering the third law, Kepler also chanced upon the world's first known power law, which is now found in many forms throughout the earth and heavens. In discovering that the Galilean moons of Jupiter also obeyed the third law, Kepler encountered the phenomenon of scale independence, which is responsible for the ubiquity of power laws across the universe. The third law also played a crucial role in Newton’s discovery of the inverse square law of gravity in 1666. Not only did it provide Newton with a crucial mathematical step, but the third law also had the authority of Tyco’s observations. Christopher Wren and Edmund Halley relied similarly upon the third law for their apparent independent discoveries of the inverse square law.

Comparison of independent, participant-led, high-resolution studies of pitch-matching in post-lingual single-sided cochlear implant recipients

Understanding “what the world sounds like to someone else“ is fundamental to developing technologies and therapies to improve auditory perception for people with hearing impairment. Post-lingual single-sided deaf (SSD) cochlear implant (CI) recipients can play a special role here through their ability to compare perceptions of sounds heard acoustically and “electrically.” Pitch is, ostensibly, a sonic attribute that can be quantitatively compared, and pitch perception has been studied by asking SSD CI recipients to rank or discriminate limited sets of pitches, mindful of the burden on experimental participants. Through unusual circumstances, we have independently conceived and conducted two sets of participant-driven pitch-matching experiments on authors WM and DL gaining more data and richer insights than reported elsewhere. While our findings are consistent with existing lower-resolution studies (e.g., sounds perceived via CI are at higher pitch than via normal hearing), we have gained much more detailed quantitative and qualitative descriptions of those perceptual differences. Results can be meaningfully compared after accounting for individual differences and suggest that the CI transformation of pitch information for these two recipients could be individually adjusted to improve music appreciation, particularly with respect to restoring perception of musical intervals between successive notes.

The role of carrier spectral composition in the perception of musical pitch.

Temporal envelope fluctuations of natural sounds convey critical information to speech and music processing. In particular, musical pitch perception is assumed to be primarily underlined by temporal envelope encoding. While increasing evidence demonstrates the importance of carrier fine structure to complex pitch perception, how carrier spectral information affects musical pitch perception is less clear. Here, transposed tones designed to convey identical envelope information across different carriers were used to assess the effects of carrier spectral composition to pitch discrimination and musical-interval and melody identifications. Results showed that pitch discrimination thresholds became lower (better) with increasing carrier frequencies from 1k to 10k Hz, with performance comparable to that of pure sinusoids. Musical interval and melody defined by the periodicity of sine- or harmonic complex envelopes across carriers were identified with greater than 85% accuracy even on a 10k-Hz carrier. Moreover, enhanced interval and melody identification performance was observed with increasing carrier frequency up to 6k Hz. Findings suggest a perceptual enhancement of temporal envelope information with increasing carrier spectral region in musical pitch processing, at least for frequencies up to 6k Hz. For carriers in the extended high-frequency region (8-20k Hz), the use of temporal envelope information to music pitch processing may vary depending on task requirement. Collectively, these results implicate the fidelity of temporal envelope information to musical pitch perception is more pronounced than previously considered, with ecological implications.

Automatic Exercise Generation for Exploring Connections between Mathematics and Music

Abstract Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being the Pythagorean tuning and scale based on arithmetic principles. Another interesting link between Mathematics and Music is the geometric approach to musical composition. Geometric patterns are present in different musical style compositions and some composing techniques, such as the 12-tone technique, use geometric transformations, involving also applications of modular arithmetic and set theory to Music. The aim of this work is to present existing relations between Mathematics and Music and to propose automatic exercise generation for exploring and studying those relations. The exercises are generated using the system MVGEN and the LaTeX package MusiXTeX. The generation process and the automatically generated exercises can be used for creating learning and assessment materials for education in Mathematics and Music, linking Science and Art.

“Of the octave the relation 2:1”: how an exemplary case of formal causation turned against the Neo-Aristotelians

ABSTRACT In this paper, I address how music theory, generally, and the case of the octave more specifically, played an instrumental and under-appreciated role in the development of seventeenth-century mechanization of sensory perception. In particular, I argue that investigation into the causes of the octave, Aristotle’s chosen example of a formal cause, and other musical intervals like it served to undermine the Neo-Aristotelian framework, while also providing key evidence in support of a mechanistic account of sensory perception. I begin by discussing how the case of the octave was understood in Scholastic Neo-Aristotelian philosophy and how this framework was applied in sixteenth-century music theory. Following this, I show how developments in music theory and acoustics challenged the status of formal causes and real qualities in this Neo-Aristotelian framework. Finally, I show how these developments provided a much needed detailed, empirically supported example of the mechanistic-style metaphysics of sensory perception that was prevalent in the Early Modern period, focusing primarily on Descartes.

Heart Response to Harmonic Music Interval Stimuli Via Deep Learning Structures

The effect of music on the heart is reflected in variables such as heart rate and electrocardiographic (ECG) signals. ECG is a record of heart electrical activity and is a useful tool in diagnosing various cardiopathies. Artificial intelligence techniques have recently been implemented to analyze ECG and RR-interval data and are used thus in the present study to examine the influence on the heart of harmonic musical intervals and colored noise. Harmonic intervals were chosen because of their emotional response, while noise has been linked to positive responses such as improved sleep quality. A deep learning system was implemented, employing the ResNet-18 and GoogLeNet pre-trained networks to discriminate 31 different classes of ECG and RR-interval responses to the sound stimuli. Following an exploratory approach, deep learning was selected as an alternative to traditional analysis with the expectation that it could be incorporated into future music perception research. Classification revealed the ability of the implemented system to demonstrate heart response to the stimuli. ECG signals performed best, with 97% accuracy and Matthew’s coefficient of 0.97, while RR-interval achieved a 93% accuracy and Matthews coefficient of 0.93, suggesting that the considered stimuli of harmonic musical intervals and noise produced different responses in the heart. Moreover, the Matthews coefficient values above 0.7 and close to 1 imply a correlation between the two types of stimuli and the heart response, as measured by ECG and RR-interval signals.

Musical consonance in simple, static auditory stimuli and perceived pleasantness: The role of musical interval, harmonicity, and stimulus duration

Many investigations on the emotional responses to music focus on the use of music pieces that contain a plethora of characteristics. This multitude of characteristics hampers the detection of the specific acoustic properties that contribute to the evoked emotions. In the present study, we were interested in the potential contribution of specific acoustical parameters of consonance to induced emotions. We, therefore, manipulated consonance by creating auditory stimuli that lacked the complexity of music by being very well defined in terms of their musical and acoustical characteristics. Specifically, Stimulus Set A was manipulated as a function of musical interval and harmonicity, with frequency components that followed and did not follow the harmonic series, and musical intervals that were consonant or dissonant, while Stimulus Set C was based on a previously utilized consonance manipulation in musical pieces. A duration manipulation was also included given the changes that might occur as a stimulus unfolds in time. Using pleasantness ratings, we found that consonant musical intervals—usually perceived as pleasant—were rated as unpleasant when the component tones contained inharmonic frequencies, while dissonant intervals remained unaffected by harmonicity. These results demonstrate, for the first time, that acoustical and psychoacoustical manipulations of consonance interact and contribute to listeners’ pleasantness ratings. Α trend was observed for the duration with stimuli becoming more unpleasant as their duration increased. Subsequent qualitative comparison of our stimulus manipulation with musical excerpts showed that our stimuli were, in general, judged as less pleasant and that consonant musical excerpts were judged as more pleasant as duration increased, thus potentially pointing to the role of music completion.

Computer-based musical interval training program for Cochlear implant users and listeners with no known hearing loss.

A musical interval is the difference in pitch between two sounds. The way that musical intervals are used in melodies relative to the tonal center of a key can strongly affect the emotion conveyed by the melody. The present study examines musical interval identification in people with no known hearing loss and in cochlear implant users. Pitch resolution varies widely among cochlear implant users with average resolution an order of magnitude worse than in normal hearing. The present study considers the effect of training on musical interval identification and tests for correlations between low-level psychophysics and higher-level musical abilities. The overarching hypothesis is that cochlear implant users are limited in their ability to identify musical intervals both by low-level access to frequency cues for pitch as well as higher-level mapping of the novel encoding of pitch that implants provide. Participants completed a 2-week, online interval identification training. The benchmark tests considered before and after interval identification training were pure tone detection thresholds, pure tone frequency discrimination, fundamental frequency discrimination, tonal and rhythm comparisons, and interval identification. The results indicate strong correlations between measures of pitch resolution with interval identification; however, only a small effect of training on interval identification was observed for the cochlear implant users. Discussion focuses on improving access to pitch cues for cochlear implant users and on improving auditory training for musical intervals.

Functional Plasticity Coupled With Structural Predispositions in Auditory Cortex Shape Successful Music Category Learning.

Categorizing sounds into meaningful groups helps listeners more efficiently process the auditory scene and is a foundational skill for speech perception and language development. Yet, how auditory categories develop in the brain through learning, particularly for non-speech sounds (e.g., music), is not well understood. Here, we asked musically naïve listeners to complete a brief (∼20 min) training session where they learned to identify sounds from a musical interval continuum (minor-major 3rds). We used multichannel EEG to track behaviorally relevant neuroplastic changes in the auditory event-related potentials (ERPs) pre- to post-training. To rule out mere exposure-induced changes, neural effects were evaluated against a control group of 14 non-musicians who did not undergo training. We also compared individual categorization performance with structural volumetrics of bilateral Heschl’s gyrus (HG) from MRI to evaluate neuroanatomical substrates of learning. Behavioral performance revealed steeper (i.e., more categorical) identification functions in the posttest that correlated with better training accuracy. At the neural level, improvement in learners’ behavioral identification was characterized by smaller P2 amplitudes at posttest, particularly over right hemisphere. Critically, learning-related changes in the ERPs were not observed in control listeners, ruling out mere exposure effects. Learners also showed smaller and thinner HG bilaterally, indicating superior categorization was associated with structural differences in primary auditory brain regions. Collectively, our data suggest successful auditory categorical learning of music sounds is characterized by short-term functional changes (i.e., greater post-training efficiency) in sensory coding processes superimposed on preexisting structural differences in bilateral auditory cortex.

Event-Related Potential Evidence for Involuntary Consciousness During Implicit Memory Retrieval.

Classical notion claims that a memory is implicit if has nothing to do with consciousness during the information retrieval from storage, or is otherwise explicit. Here, we demonstrate event-related potential evidence for involuntary consciousness during implicit memory retrieval. We designed a passive oddball paradigm for retrieval of implicit memory in which an auditory stream of Shepard tones with musical pitch interval contrasts were delivered to the subjects. These contrasts evoked a mismatch negativity response, which is an event-related potential and a neural marker of implicit memory, in the subjects with long-term musical training, but not in the subjects without. Notably, this response was followed by a salient P3 component which implies involvement of involuntary consciousness in the implicit memory retrieval. Finally, source analysis of the P3 revealed moving dipoles from the frontal lobe to the insula, a brain region closely related to conscious attention. Our study presents a case of involvement of involuntary consciousness in the implicit memory retrieval and suggests a potential challenge to the classical definition of implicit memory.

A BRIEF OVERVIEW OF THE HISTORY OF TEMPERAMENT

Bu çalışma bir derleme makalesi olup, piyano ve sabit perdeli çalgıların akort sistemi olarak bilinen eşit
 tamperemanın tarihsel gelişim sürecini incelemeyi amaçlamaktadır. Tampereman, kısaca müzikal aralıkların
 doğal (Just Intonation) dizideki karşılıklarından belirli oranlarda değiştirilmesi şeklinde tanımlanmaktadır.
 1300’lü yılların sonu itibariyle klavyeli çalgıların çoğunda seslerin tampere edildiği bilinmektedir. Yazılı
 olarak tarifi yapılan ilk yöntem, “ara-ses” adı verilen tamperemandır. Bu yöntemde üçlülerin doğal veya doğala
 yakın olmasına önem verilmiş, öte yandan beşliler bir miktar pesleştirilmiştir. Ara-ses tamperemanında bazı
 aralıklarının aşırı tiz veya pes olması ve kullanılamayan tonalitelerin bulunması düzensiz tamperemanların
 ortaya çıkmasına sebep olmuştur. Düzensiz tamperemanlarda aynı isimli birden fazla aralık bulunmasına
 rağmen, tüm tonların kullanılabilir olması sebebiyle, bu yöntem iki yüzyıl kadar klavyeli çalgılarda
 uygulanmıştır. Ara-ses tamperemanı ve düzensiz tamperemanlar kullanılırken dahi, eşit tamperemanın
 önemi ve gerekliliği teorisyenlerin hep savunduğu bir konu olmuştur. Eşit tampereman 1570’li yıllarda
 perdeli çalgılarda uygulanmaya başlamış, klavyeli çalgılarda ise çok daha geç tarihlerde kabul görmüştür.
 1876 yılında Alexander J. Ellis’in ortaya koymuş olduğu cent sistemi eşit tamperemanın hesaplanmasında
 dönüm noktasıdır. 20. yüzyılda uluslararası sanat müziğinde 12 ton müziğinin yaygınlaşması ile eşitsiz
 tamperemanların sonu gelmiş, klavyeli ve perdeli çalgılar için ortak bir akort sistemi olarak kabul görmüştür.

Nice and easy: Mismatch negativity responses reveal a significant correlation between aesthetic appreciation and perceptual learning.

Neurocomputational models of cognition have framed aesthetic appreciation within the domain of knowledge acquisition and learning, suggesting that aesthetic appreciation might be considered as a hedonic feedback on successful perceptual learning dynamics. Such hypothesis, however, has never been empirically demonstrated yet. In order to investigate the relationship between aesthetic appreciation and learning, we measured the EEG mismatch negativity (MMN) response to more or less appreciated musical intervals, which is considered as a reliable index of perceptual learning. To this end, we measured the MMN to frequency (Hz) standard and frequency deviant musical intervals (Experiment 1) while participants were asked to judge their beauty. For each single stimulus, we also computed an information-theoretic index of perceptual learning (Bayesian surprise). We found that more appreciated musical intervals were associated with a larger MMN responses, which, in turn, correlated with trial-by-trial fluctuations in Bayesian surprise (Experiment 1). Coherently with previous results, Bayesian surprise was also found to correlate with slower RTs in a detection task of the same stimuli, evidencing that motor behavior is inhibited in presence of surprising sensory states triggering perceptual learning (Experiment 2). Our results provide empirical evidence of the existence of a positive correlation between aesthetic appreciation and EEG indexes of perceptual learning. We argue that the sense of beauty might have evolved to signal the nervous system new sensory knowledge acquisition and motivate the individual to search for informationally profitable stimuli. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Ostinatos in Black-Atlantic traditions: generic-specific similarity and proximity

Ostinatos of sub-Saharan Africa, South America, and the Caribbean are continually repeated rhythms also known as “timelines.” Taking as a starting point the ostinato termed the “Standard Pattern,” generic and specific features of Black-Atlantic ostinatos are analyzed: in European-derived theory, these features correspond to the quantity and quality of musical intervals. Like the standard pattern, other ostinatos that have been employed in several Black-Atlantic traditions and comprise a rhythmic structure that corresponds to the structure of hyperdiatonic scales in contemporary European-derived pitch theory; other widespread ostinatos considered have a complementary, hyperpentatonic structure. Interpreted in terms of Gestalt grouping principles, both of these kinds of ostinatos maximize similarity and proximity. Other ostinatos of these traditions can be construed as variants of hyperdiatonic or hyperpentatonic ostinatos. Differences of similarity and proximity that these variants manifest are analyzed in terms of adjacent swaps, fusions and fissions, and moduli that encompass two or more ostinatos’ least common multiples. In turn, similarity and proximity measures for rhythmic ostinatos are shown to parsimoniously clarify aspects of pitch relations, including the general notion of evenness, within 1- dimensional frameworks for pitch and time.