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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.

THIS STUDY TESTED WHETHER CHORDS THAT DO not differ in acoustic roughness but that have distinct affective connotations are strong enough to prime negative and positive associations measurable with an affective priming method. We tested whether musically dissonant chords low in valence (diminished, augmented) but that contain little acoustic roughness are strong enough in terms of negative affective connotations to elicit an automatic congruence effect in an affective priming setting, comparable to the major-positive/minor-negative distinction found in past studies. Three out of 4 hypotheses were supported by the empirical data obtained from four distinct sub-experiments (approximately N = 100 each) where the diminished and augmented chords created strong priming effects. Conversely, the minor chord and the suspended fourth failed to generate priming effects. The results demonstrate how automatic responses to consonant/ dissonant chords can be driven by acquired, cultural concepts rather than exclusively by acoustic features. The obtained results of automatic responses are notably in line with previous data gathered from self-report studies in terms of the stimuli’s positive vs. negative valence. The results are discussed from the point of view of previous affective priming studies, cross-cultural research, as well as music historical observations. [ABSTRACT FROM AUTHOR]

A previous study explored the potential to influence the perception of consonance by controlling the spectral components of simultaneous pitches within a chord in sound synthesis using the additive method. This approach involves considering spectral components across in all simultaneously sounding pitches constituting a chord. Components within the range of beatings and roughness are adjusted to gradually enhance or weaken both phenomena. So far, the idea and method were implemented in a basic additive synthesizer, producing simple, abstract, time-invariant timbres. The current study extends this research and addresses challenges associated with implementing the aforementioned consonance-altering mechanism in a more advanced additive synthesizer, applied to the task of resynthesizing the sound of selected acoustic instruments. This study deals with natural, independent evolution of spectral components, wherein consonance undergoes gradual variations over time. Additionally, it presents a solution to mitigate the impact of the mechanism on the overall signal level, arising from the attenuation of selected spectral components. [ABSTRACT FROM AUTHOR]

In pitched sounds the ratios between frequencies of spectral components remain close to natural numbers. In acoustic instruments these ratios deviate from exact values due to damping or boundary conditions, complicating use of musical systems defining frequency ratios associated with musical intervals. If such system is imposed on the fundamental frequencies of pitches consisting a chord, higher spectral components may deviate noticeably, strengthening or weakening the effects of beating and roughness caused by their proximity, and changing chord characteristics in terms of consonance-dissonance gradation. Unlike acoustic instruments, sound synthesizers can precisely adjust components of generated signal, and use this phenomenon as a controllable timbre effect. For this purpose spectral components of a chord within the range of beating and roughness are modified to gradually strengthen or weaken both phenomena. The study presents the assumptions of the effect and its implementation in a sound synthesizer based on the additive method. [ABSTRACT FROM AUTHOR]

Previous empirical studies have suggested that the perceived consonance/dissonance (C/D) of a musical chord depends on its psychoacoustic smoothness (lack of roughness), spectral harmonicity (perceptual fusion), and/or musical familiarity. We tested the dependence of C/D on smoothness and harmonicity in a hearing experiment that included all 19 possible trichords in musical pitch-class set theory. In each trial, a listener heard a chord (duration: 300 or 500 ms) and rated its C/D on an 11-point scale. Each trichord was presented 10 times: 4 times constructed from octave-complex tones (OCTs, sounding like an electronic organ) and 6 times from natural piano tones. Each OCT chord was presented in 4 different transpositions. The piano chords were in close or open position, and root position or 1st/2nd inversion (2 levels of spacing x 3 levels of inversion = 6 levels of voicing). We found no main effect of timbre (OCT versus piano) and no interaction between trichord and timbre. Results correlated closely with predictions of simple models of roughness and harmonicity. The roughness model performed better, and the predictions correlated with each other. A combined model was not superior to roughness alone. The results were consistent with a multifactorial model of the C/D of a musical chord, the main factors being roughness, harmonicity, and familiarity.

This article examines a unique family of six-four sonorities in the works of Richard Strauss. These six-fours typically sound with 6 ^ , 4 ^ , or 2 ^ (or modal variants thereof) in the bass but occur immediately prior to a cadential dominant, and thus impart a sense of predominant function despite their unstable inversion. In examining how the sixth and fourth behave, I suggest that rather than hearing these chords as consonant inversions of a triad, they can instead be interpreted as accented six-fours; in other words, reading the sixth and fourth as dissonances, whose resolution to a fifth and third is deferred to occur over a subsequent harmony. I suggest that the sense of fragmentation that coalesces through the process of suspension creates a conflict between phenomenological and analytic hearings of this music, which reflects a type of modernism typically overlooked in Strauss's late music. [ABSTRACT FROM AUTHOR]

Previous empirical studies have suggested that the perceived consonance/dissonance (C/D) of a musical chord depends on its psychoacoustic smoothness (lack of roughness), spectral harmonicity (perceptual fusion), and/or musical familiarity. We tested the dependence of C/D on smoothness and harmonicity in a hearing experiment that included all 19 possible trichords in musical pitchclass set theory. In each trial, a listener heard a chord (duration: 300 or 500 ms) and rated its C/D on an 11-point scale. Each trichord was presented 10 times: 4 times constructed from octave-complex tones (OCTs, sounding like an electronic organ) and 6 times from natural piano tones. Each OCT chord was presented in 4 different transpositions. The piano chords were in close or open position, and root position or 1st/2nd inversion (2 levels of spacing x 3 levels of inversion = 6 levels of voicing). We found no main effect of timbre (OCT versus piano) and no interaction between trichord and timbre. Results correlated closely with predictions of simple models of roughness and harmonicity. The roughness model performed better, and the predictions correlated with each other. A combined model was not superior to roughness alone. The results were consistent with a multifactorial model of the C/D of a musical chord, the main factors being roughness, harmonicity, and familiarity. [ABSTRACT FROM AUTHOR]

Zeqirja Ballata (1943), a Kosovar composer, is in step with the works of his time, more precisely belonging to the postmodernist period. Throughout his musical opus, he showed consistency to the contemporary stylistic elements of the second half of the twentieth century. Among the 157 musical works by the Kosovar composer Zeqirja Ballata, this paper brings the results of the analysis of the musical language used in Echi delle Montagne Maledette. The work in question is atonal, with dominant dissonance followed by short consonance. Comparing with other piano works of Z. Ballata, this work has less dissonant elements. The purpose of this study is to identify stylistic compositional characteristics, and evaluate their impact on the promotion of the contemporeanous style, for which, the analytic format of T. Mançev (2001) served as a theoretical base. The type of research is case study. Employing a qualitative research method, or analysis, the work was analysed including the following musical parameters: general and historical data of the piece, structure, linear expression, consonant structures, rhythm and its components, dynamics and synthesis of musical parameters in the process of concretization. The paper also contains notation tables and examples illustrating concretization moments. [ABSTRACT FROM AUTHOR]

• This study investigates musicians' and nonmusicians' consonant and dissonant perceptions. • Behavioral results show that (non)-/musicians used different features in consonant judgments. • ERP results show similar N1/P2 effects in midline and left-lateralized electrodes. • Musicians' fMRI reveals functional connectivity between MPFC and left auditory cortex. • Spatiotemporal searchlight RSA results show the locus of musicians' N1 in MPFC and auditory cortex, P2 in dACC. 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. [ABSTRACT FROM AUTHOR]

• Existing and preferred teleworking arrangements are examined. • The concept of telework frequency dissonance (TFD) is introduced. • A novel bivariate ordered-response probit model is formulated. • The results inform land-use-transportation planning professionals. The remote work arrangement trend engendered by the pandemic continues to be prevalent today in most work sectors. But some employers have reverted to an all in-person office workday system recently, with no allowance for remote work despite their employees' desire for such flexibility. At the same time, some employees may prefer more office-based workdays than what their employer is able to offer today based on office rotation schemes and office downsizing. The challenge to find a harmonious balance between employee and employer preferences and perceptions regarding telework raises the issue of telework frequency dissonance (TFD). The purpose of this study is to investigate this pandemic-induced TFD. The data for our study is derived from the third wave of the COVID Future Panel Survey which was deployed across the United States in the Fall of 2021. The survey includes information regarding employees' existing telework frequency (ETF) and ideal telework frequency (ITF). These two dimensions are jointly modeled as a function of socioeconomic and demographic explanatory variables. The findings from this study provide important insights regarding how best to balance employee and employer preferences regarding work arrangements. Given the important effects of work arrangements on commute and non-commute travel, the findings from our study should help inform land use and travel models regarding predicting our transportation future. [ABSTRACT FROM AUTHOR]

The perception of consonance and dissonance in intervals and chords is influenced by psychoacoustic and cultural factors. Past research has provided conflicting observations about the role of frequency in assessing musical consonance that may stem from comparisons of limited frequency bands without much theorizing or modeling. Here we examine the effect of register on perceptual consonance of chords. Based on two acoustic principles, we predict a decrease in consonance at low frequencies (roughness) and a decrease of consonance at high frequencies (sharpness). Due to these two separate principles, we hypothesize that frequency will have a curvilinear impact on consonance. A selection of tetrads varying in consonance were presented in seven registers spanning 30 to 2600 Hz. Fifty-five participants rated the stimuli in an online experiment. The effect of register on consonance ratings was clear and largely according to the predictions; The low registers impacted consonance negatively and the highest two registers also received significantly lower consonance ratings than the middle registers. The impact of register on consonance could be accurately described with a cubic relationship. Overall, the influence of roughness was more pronounced on consonance ratings than sharpness. Together, these findings clarify previous empirical efforts to model the effect of frequency on consonance through basic acoustic principles. They further suggest that a credible account of consonance and dissonance in music needs to incorporate register. [ABSTRACT FROM AUTHOR]

Previous studies using an affective priming paradigm have shown that valenced chords (e.g., consonant–positive; dissonant–negative) facilitate the evaluation of similarly valenced target words. The role of numerosity (the total number of pitches in a chord) and timbre has not yet been systematically investigated in previous priming studies using consonant/dissonant chords. An experiment was conducted in which 40 participants evaluated positive and negative target words with consonant/dissonant chords used as affective primes. Eight distinct chords (four consonant and four dissonant) were used as primes; the consonant and dissonant chords were equally divided to comprise either two (i.e., interval) or four (i.e., tetrad) pitches. Each chord was played with two distinct timbres (piano and harmonium), resulting in a total of 16 chords. Results showed that congruent chord–word pairings resulted in faster reaction times, and this finding was in line with previous research using consonant/dissonant chords as primes. However, this effect was present only with tetrad chords, suggesting that numerosity influences affective priming done with chords. There were no significant effects of timbre or the musical sophistication of the participants. Arguments are made as to why higher pitch numerosity in chords (resulting in acoustic complexity) might influence the evaluation of valenced target words. [ABSTRACT FROM AUTHOR]

Eerola and Lahdelma ([10]) took the parsimony of the tonal consonance/dissonance idea by Johnson-Laird et al. ([24]) a step further still by collapsing minor and other scales together to create a simple implementation called the I Tonal Dissonance Model i , which assesses whether a pitch combination can be constructed from a major scale (1) or not (0). Keywords: consonance; dissonance; harmonicity; roughness; tonality; psychoacoustics; familiarity EN consonance dissonance harmonicity roughness tonality psychoacoustics familiarity 1 5 5 01/31/22 20220128 NES 220128 1. If the revision of harmonicity's role in consonance/dissonance preferences is indeed firmly grounded, we may have come full circle in identifying the key components predicting these preferences: Helmholtz ([18]) already drew the conclusion that consonance/dissonance is dependent on a psychoacoustic (roughness) and on a cultural factor (tonality). [Extracted from the article]

Reservoir computing with neuromorphic synaptic elements is an emerging, but very successful approach towards processing and classification of various signals. It can be described as a model of a transient computation, where the influence of input changes the internal dynamics of a chosen computational system. Trajectory of these changes represents computation performed by the system. The selection of a suitable computational substrate capable of non-linear response and rich internal dynamics ensures the implementation of simple readout protocols. Signal evolution based on the rich dynamics of the memristive synapse layer helps to emphasize differences between given signals thus enabling their clustering. Here we present a simple neuromorphic computing system (single node echo-state machine based on the memristive synaptic bridge) implemented on the Multisim platform as a tool for clustering of musical intervals according to their consonant or dissonant character. The system generates a series of “epochs” – images of input signal at different stage of evolution. A readout layer based on peak counting in their Fourier spectra allows clustering of musical intervals in a way similar to human subjects or specialized algorithms. The result of this data evolution closely resembled the sensory dissonance curve, with some significant differences. Interestingly, clustering is performed without any reference to the theory of music. This study shows a high potential for exploiting a simple neuromorphic system for advanced information processing. Furthermore, they indicate that the notions of consonance and dissonance may have the neurophysiological background. [ABSTRACT FROM AUTHOR]

The research aimed at a comprehensive retrospective analysis of the development of "consonance and dissonance" as a musical and aesthetic category in physical and mathematical interpretation; defining the notion of consonance as a musical theoretical and aesthetic category, confirming the relevance of its use in physical and mathematical terminology to explain acoustic phenomena. Research methodology is based on the use of the retrospective method (or the retrospection method), which allowed identifying the theories of consonance and dissonance in the historical retrospective. The periodization method was used to find out individual stages in the development of science in order to discover the leading directions of scientific thought, identify new elements relating to various aspects of "consonance" and "dissonance". The study of the retrospective review of the development of the notions of consonance and dissonance in the physical and mathematical interpretation involved an interdisciplinary method a way of organizing research work, providing for the interaction of music and mathematics in the study of consonance and dissonance. Scientific novelty. This study is the first to reflect the general tendency towards the mathematization of the humanities and the humanitarization of the physical and mathematical areas of modern culture. Some provisions of musical acoustics were clarified in the context of creating a harmonious conceptual structure. The article presents the author's concept of clarifying the notion of phase in relation to the spectral structure of an audio signal based on the notion "slightly mistuned consonance". Conclusions. A retrospective review of the development of the notions of consonance and dissonance in the physical and mathematical interpretation was carried out and presented as a comprehensive description and review of the formation of concepts in the temporal sequence of their creation. Retrospectiveness through a review of significant discoveries and achievements in music and natural science allowed tracing the formation of the theories of consonance and dissonance from the standpoint of the interdisciplinarity of modern knowledge in the humanities. The further process of the development of sound musical art technologies requires a significantly higher scientific level of their study, the creation of a coherent conceptual system based on modern physical and mathematical sciences as well as computer science to explain sound acoustic phenomena. [ABSTRACT FROM AUTHOR]

The majority of research in the field of music perception has been conducted with Western participants, and it has remained unclear which aspects of music perception are culture dependent, and which are universal. The current study compared how participants unfamiliar with Western music (people from the Khowar and Kalash tribes native to Northwest Pakistan with minimal exposure to Western music) perceive affect (positive versus negative) in musical chords compared with United Kingdom (UK) listeners, as well as the overall preference for these chords. The stimuli consisted of four distinct chord types (major, minor, augmented, and chromatic) and were played as both vertical blocks (pitches presented concurrently) and arpeggios (pitches presented successively). The results suggest that the Western listener major‐positive minor‐negative affective distinction is opposite for Northwest Pakistani listeners, arguably because of the reversed prevalence of these chords in the two music cultures. The aversion to the harsh dissonance of the chromatic cluster is present cross‐culturally, but the preference for the consonance of the major triad varies between UK and Northwest Pakistani listeners, depending on cultural familiarity. Our findings imply not only notable cultural variation but also commonalities in chord perception across Western and non‐Western listeners. [ABSTRACT FROM AUTHOR]

Background Previous studies have shown that music preferences are influenced by cultural “rules”, and some others have suggested a universal preference for some features over others. Methods We investigated cultural differences on the “consonance effect”, consisting in higher pleasantness judgments for consonant compared to dissonant chords—according to the Western definition of music: Italian and Himalayan participants were asked to express pleasantness judgments for consonant and dissonant chords. An Italian and a Nepalese sample were tested both at 1,450 m and at 4,750 m of altitude, with the further aim to evaluate the effect of hypoxia on this task. A third sample consisted of two subgroups of Sherpas: lowlanders (1,450 m of altitude), often exposed to Western music, and highlanders (3,427 m of altitude), less exposed to Western music. All Sherpas were tested where they lived. Results Independently from the altitude, results confirmed the consonance effect in the Italian sample, and the absence of such effect in the Nepalese sample. Lowlander Sherpas revealed the consonance effect, but highlander Sherpas did not show this effect. Conclusions Results of this pilot study show that neither hypoxia (altitude), nor demographic features (age, schooling, or playing music), nor ethnicity per se influence the consonance effect. We conclude that music preferences are attributable to music exposure.

Clinical trials routinely involve multiple hypothesis testing. The closed testing procedure (CTP) is a fundamental principle in testing multiple hypotheses. This article presents an improved CTP in which intersection hypotheses can be tested at a level greater than α such that the control of the familywise error rate at level α remains. Consequently, our method uniformly improves the power of discovering false hypotheses over the original CTP. We illustrate that an improvement by our method exists for many commonly used tests. An empirical study on the effectiveness of a glucose-lowering drug is provided. [ABSTRACT FROM AUTHOR]

CONSONANCE AND DISSONANCE ARE BASIC phenomena in the perception of chords that can be discriminated very early in sensory processing. Musical expertise has been shown to facilitate neural processing of various musical stimuli, but it is unclear whether this applies to detecting consonance and dissonance. Our study aimed to determine if sensitivity to increasing levels of dissonance differs between musicians and nonmusicians, using a combination of neural (electroencephalographic mismatch negativity, MMN) and behavioral measurements (conscious discrimination). Furthermore, we wanted to see if focusing attention to the sounds modulated the neural processing. We used chords comprised of either highly consonant or highly dissonant intervals and further manipulated the degree of dissonance to create two levels of dissonant chords. Both groups discriminated dissonant chords from consonant ones neurally and behaviorally. The magnitude of the MMN differed only marginally between the more dissonant and the less dissonant chords. The musicians outperformed the nonmusicians in the behavioral task. As the dissonant chords elicited MMN responses for both groups, sensory dissonance seems to be discriminated in an early sensory level, irrespective of musical expertise, and the facilitating effects of musicianship for this discrimination may arise in later stages of auditory processing, appearing only in the behavioral auditory task. [ABSTRACT FROM AUTHOR]

Background: Previous studies have shown that music preferences are influenced by cultural "rules", and some others have suggested a universal preference for some features over others. Methods: We investigated cultural differences on the "consonance effect", consisting in higher pleasantness judgments for consonant compared to dissonant chords-- according to the Western definition of music: Italian and Himalayan participants were asked to express pleasantness judgments for consonant and dissonant chords. An Italian and a Nepalese sample were tested both at 1,450 m and at 4,750 m of altitude, with the further aim to evaluate the effect of hypoxia on this task. A third sample consisted of two subgroups of Sherpas: lowlanders (1,450 m of altitude), often exposed to Western music, and highlanders (3,427 m of altitude), less exposed to Western music. All Sherpas were tested where they lived. Results: Independently from the altitude, results confirmed the consonance effect in the Italian sample, and the absence of such effect in the Nepalese sample. Lowlander Sherpas revealed the consonance effect, but highlander Sherpas did not show this effect. Conclusions: Results of this pilot study show that neither hypoxia (altitude), nor demographic features (age, schooling, or playing music), nor ethnicity per se influence the consonance effect. We conclude that music preferences are attributable to music exposure. [ABSTRACT FROM AUTHOR]

Consonance and dissonance are frequently invoked in discussions of Gubaidulina's music, particularly in terms of the composer's intentional contrasts between timbres and her golden section-oriented formal planning. In this paper, I use the notion of dissonance to mediate between several competing theories of Gubaidulina's music and theories of timbre more broadly. Certain passages in her Meditation on the Bach Chorale "Vor deinen Thron tret' ich hiermit" (1993) are identified as dissonant based on her compositional theories and on sketch material from the Paul Sacher Stiftung, and on further examples drawn from her Am Rande des Abgrunds (2002). Broadly speaking, "dissonant" sounds are closer to white noise than "consonant" sounds, aligning with empirical studies of dissonance perception as well as with spectralist compositional theories. However, Gubaidulina's music uses this extended notion of dissonance particularly musically; dissonances have specific structural roles in a work and resolve to consonances. [ABSTRACT FROM AUTHOR]

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 500 participants, and modeling three Western musical corpora representing more than 100,000 compositions. We conclude that simultaneous consonance is a composite phenomenon that derives in large part from three phenomena: interference, periodicity/harmonicity, and cultural familiarity. We formalize this conclusion with a computational model that predicts a musical chord's simultaneous consonance from these three features, and release this model in an open-source R package, incon, alongside 15 other computational models also evaluated in this paper. We hope that this package will facilitate further psychological and musicological research into simultaneous consonance. [ABSTRACT FROM AUTHOR]

The harmonic distance between two pure tones, in the sense used by Tenney, is generalised to chords whose pitches are harmonic fractions. In the tonal graph generated by the harmonics involved in a chord, which for n-TET systems has its equivalent in the Tonnetz, the melodic distance between the lowest common ancestor and the lowest common harmonic of the pitches composing the chord is a measure of the relative dissonance. This notion, rooted in just intonation, is extended to Pythagorean tuning and is used as an approximation for equal temperament scales. Harmonic distance and sensory dissonance are compared and discussed for chords in different tuning systems. It is borne out that proximity of chords in the Tonnetz is not exactly related to the harmonic distance. [ABSTRACT FROM AUTHOR]

We counted trichords in a database of vocal polyphony. In modern terminology, the most common in the thirteenth to sixteenth centuries were major (in semitones: 047), minor (037), suspended (027), unnamed (025, 035), and diminished (036). Prevalence profiles correlated with predictions of simple models of roughness and harmonicity; sometimes also with evenness (pitch-class spacing), but not diatonicity. From the thirteenth to the fifteenth century, 047 and 037 became more relatively prevalent, after which profiles stabilized. Our results imply that today the C/D of trichords depends mainly on familiarity, roughness, and harmonicity. C/D is best understood in an interdisciplinary, psychohistoric approach. [ABSTRACT FROM AUTHOR]

Consonant musical intervals tend to be more readily processed than dissonant intervals. In the present study, we explore the neural basis for this difference by registering how the brain responds after changes in consonance and dissonance, and how formal musical training modulates these responses. Event-related brain potentials (ERPs) were registered while participants were presented with sequences of consonant intervals interrupted by a dissonant interval, or sequences of dissonant intervals interrupted by a consonant interval. Participants were musicians and non-musicians. Our results show that brain responses triggered by changes in a consonant context differ from those triggered in a dissonant context. Changes in a sequence of consonant intervals are rapidly processed independently of musical expertise, as revealed by a change-related mismatch negativity (MMN, a component of the ERPs triggered by an odd stimulus in a sequence of stimuli) elicited in both musicians and non-musicians. In contrast, changes in a sequence of dissonant intervals elicited a late MMN only in participants with prolonged musical training. These different neural responses might form the basis for the processing advantages observed for consonance over dissonance and provide information about how formal musical training modulates them. [ABSTRACT FROM AUTHOR]

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Different accounts have been given in order to face the problem of the emergence of musical consonance and dissonance. Getting a more adequate comprehension of such phenomenology may require a systemic view to integrate such multidimensionality into a unitary picture in which every partial solution enlightens a particular aspect of the very same problem. Such a systemic viewpoint shifts the focus from different explanations to analytic dimensions that seem to be embedded in music perception. Taking into consideration these dimensions means understanding consonance and dissonance in an embodied context, in which arithmetic, physics, psychology and physiology are part of a complex and dynamic process of understanding, which is not reducible to any privileged explanatory level.

Consonance is a perception phenomenon that evokes pleasant feelings when listening to complex sounds. Since Pythagoras, people have attempted to explain consonance and dissonance, using various methodological means, with limited success and without providing convincing underlying causes. We demonstrate that a specific auditory spectral distribution caused by nonlinearities, as a first phenomenon, and the Hebbian neuroplasticity as a second, are sufficient set of phenomena a system should possess so it could generate the consonance pattern - the actual two-tone interval list ordered by consonance. The emergence of this pattern is explained in a step-by-step manner, utilizing an artificial neural network model. In a reverse engineering manner, our simulations are testing all the possible spectral distributions of auditory stimuli (within particular precision scales and applying certain abstractions) and reveal those that produce a result with a pattern perfectly matching the consonance ordered two-tone interval list, the one that is widely accepted in the Western musical culture. The results of this study suggest that the consonance pattern could be an expected outcome in any system containing the asserted set of features (including the higher animals). The intent of this study is not to realistically model the human auditory system, but to demonstrate a set of features an abstract and generic system should possess so it could produce the consonance pattern. [ABSTRACT FROM AUTHOR]

The article presents the author's view on the cognitive modelling processes application to enhance the management of public-private partnerships (PPPs) in the regions of Ukraine. The authors have formed a factors system for public and private partners, that have a positive or negative effect on the PPPs activation (target concept "Investments"). It was proposed to use cognitive maps to investigate causal relationships among factors. It was developed the cognitive model concepts influence set of the target concept "Investments" and it was made its static analysis (it was identified concepts that carry the greatest dissonance of the system). [ABSTRACT FROM AUTHOR]

The article presents the authors’ view on application of the cognitive modelling when managing processes of activation of the public-private partnership (PPP) in Ukrainian regions. The authors formed a system of concepts of the public and private sectors of economy, which make positive or negative impact upon activation of PPP(target component “Investments”). In order to study the cause-effect relations between the concepts of the public and private sectors, the article offers to use cognitive maps, which showed themselves in the analysis and study of semi-structured systems. It develops a cognitive model of influence of a multitude of concepts upon the target concept “Investments” and conducts its statistical analysis (reveals concepts that perform the biggest dissonance of the system).В статье изложен авторский взгляд на применение когнитивного моделирования при управлении процессами активизации публично-частного партнерства (ППП) в регионах Украины. Авторами сформирована система концептов публичного и частного секторов экономики, оказывающих положительное или отрицательное воздействие на активизацию ППП (целевой концепт «Инвестиции»). С целью исследования причинно-следственных связей между концептами публичного и частного секторов предложено использование когнитивных карт, которые хорошо зарекомендовали себя при анализе и исследовании слабоструктурированных систем. Разработана когнитивная модель влияния множества концептов на целевой концепт «Инвестиции» и осуществлен ее статический анализ (выявлены концепты, осуществляющие наибольший диссонанс системы).

In his most recent contribution to an important and well-framed series of papers on auditory grouping and the perception of polyphonic music, David Huron seeks further evidence for his working hypothesis that J.S. Bach controls the employment of perfect consonances by desynchronizing their onsets, thereby inhibiting the perceptual fusion of polyphonic voices. However the more novel contribution of the present study would seem to be its demonstration that Bach also regulates the employment of dissonant tones by consistently desynchronizing their onsets. This finding provides the first concrete evidence for Wright and Bregman’s otherwise untested hypothesis that the control and salience of dissonance in polyphonic music are closely related to principles of auditory stream segregation (Wright, 1986; Wright & Bregman, 1987).

Cook & Fujisawa (2006) point out that, contrary to the predictions of psychoacoustic models, the diminished triad is more consonant and prevalent in western tonal music than the augmented. A possible simple explanation is that the diminished triad often functions as an incomplete dominant (major-minor) seventh chord, the most prevalent tetrad in mainstream tonal music.

The phenomena of consonance and dissonance are thought to involve both learned and innate components. Work by Greenwood (1961) and Plomp and Levelt (1965) established that an aspect of dissonance perception can be traced to unique physiological properties of the hearing organ. This aspect of dissonance is commonly referred to as sensory dissonance. Two computable models of sensory dissonance are described and discussed—those of Kameoka and Kuriyagawa (1969a; 1969b) and Hutchinson and Knopoff (1978). Software implementations of both models are provided, and their behaviors explored. Both models exhibit a number of conceptual and technical problems.

The narrative is that a child was born on 14th August 1947 by the name of Pakistan. The little one was Muslim by birth and the rite of saying azan in the ears of the newborn is an Islamic ritual. However, this child went through the ritual of not one, but two 'political' azans. The First Azan was that of a nation-state with well-defined frontiers where people have commonality of interest, having national anthem and a flag, aspirations for the future and a rational national interest to pursue within the framework of High and Low politics. The Second Azan dictated that Pakistan's center of gravity is non-geographic, its focus and essence is not confined to geography or space and that it will have to answer to the call wherever it may occur or come from. The Second Azan stood for pan-Islamism and pan-Islamic aspirations. The two are totally contradictory. Pakistani perception mixes one with the other, takes one for the other. The First Azan is driven by the geography; the Second Azan is oblivious to it and belongs to the space of MIND. [ABSTRACT FROM AUTHOR]

TWO EXPERIMENTS EXAMINEDWHETHER DISCRIMINATION of component pitches in a harmonic interval is affected by the consonance or dissonance of the interval. A sin- gle probe pitch (B or C) was followed by a two note harmonic interval including that pitch (e.g., C then C-F# or C-G) or not including it (e.g., C then B-F# or B-G). On each trial, subjects indicated by key press whether the probe note was repeated in the following interval. The target note in the interval either matched the probe or differed by one semitone (B or C). The other note produced a consonant (e.g., perfect fifth) or dissonant (e.g., tritone) context for the target. Pitch discrimination was faster and more accurate in consonant intervals than dissonant, when the context note was higher than the target (Experiment 1), but there was no effect of consonance when the target was higher (Experiment 2). We conclude that the perception of the lower but not the upper pitch in a two note harmonic interval is affected by the interval's consonance or dissonance. We discuss the results in terms of the theoretical framework of processing fluency and aesthetics proposed by Winkielman, Schwarz, Fazendeiro, and Reber (2003). [ABSTRACT FROM AUTHOR]

Mashinter’s (2006) mathematical model of sensory dissonance neglects the dependence of roughness on waveform, the role of masking, the distribution of roughness across critical bands, the possible positive contribution of fusion or toneness to euphony, and the familiarity and music-theoretical functions of a sonority. Of course not all these aspects can reasonably be included in a model, but they can affect the data with which its predictions are compared.