Ancient Greek music was purely or predominantly melodic; and in such music subtleties of intonation count for much. If our sources of information about the intervals used in Greek music are not always easy to interpret, they are at any rate fairly voluminous. On the one hand we have Aristoxenus, by whom musical intervals were regarded spatially and combined and subdivided by the processes of addition and subtraction; for him the octave consisted of six tones, and the (...) tone was exactly divisible into fractions such as the half and quarter, so that the fourth was equal to two tones and a half, the fifth to three tones and a half, and so on. On the other hand we have preserved for us in Ptolemy's Harmonics the computations of a number of mathematicians, who realized correctly that intervals could only be expressed as ratios , that the octave was less than the sum of six whole tones and that this tone could not be divided into equal parts. These authorities are Archytas, the Pythagorean of the early fourth century, Eratosthenes , Didymus and Ptolemy himself . To these we must add the scale of Plato's Timaeus and, closely related to it, the computations of the pseudo-Philolaus and of Boethius himself . Aristoxenus is less easy to understand than the mathematicians because of the unscientific nature of his postulates. His importance, however, is very great, not only from his comparatively early date but because he claims to champion the direct musical consciousness against the scientific approach of some of his predecessors and contemporaries. (shrink)

The object of this article is to discuss, defend, and supplement the only definite piece of evidence we possess which deals with the musical scalesreferred to by Plato in the Republic . In this first section I shall consider the list of scales given by Aristides Quintilianus and suggest the source from which it is derived; in the second part the employment of certain abnormal intervals will be established and elucidated; and finally the evidence of the preceding (...) sections will be reviewed from the standpoint of the Pythagorean musical theory. (shrink)

The object of this article is to discuss, defend, and supplement the only definite piece of evidence we possess which deals with the musical scalesreferred to by Plato in the Republic. In this first section I shall consider the list of scales given by Aristides Quintilianus and suggest the source from which it is derived; in the second part the employment of certain abnormal intervals will be established and elucidated; and finally the evidence of the preceding sections (...) will be reviewed from the standpoint of the Pythagorean musical theory. (shrink)

The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of (...) musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. (shrink)

A fascinating and hugely original book that explains how a vexing technical puzzle was solved, making possible some of the most exquisite music ever written. From the days of the ancient Greeks, the creation of music was thought to be governed by divine and immutable mathematical certainties. But over time skeptics came to understand that those rules limited harmonic possibilities. In Temperament , we see the traditionalists and the innovators battling across the centuries, engaging great thinkers like Newton, Kepler, and (...) Descartes as well as musicians, craftsmen, church leaders, and heads of state. At the heart of their dispute is the question of how the tones of a musical scale should be selected. The breakthrough came in the eighteenth century, when the modern keyboard was given perfect musical symmetry through a tuning of equal temperament, each pitch reliably equidistant from the ones that precede and follow it. This tuning allows a musical pattern begun on one note to be duplicated when starting on any other; it creates a musical universe in which the relationships between tones are reliably, uniformly consistent--a universe of greatly expanded possibility, one that allowed Liszt, Chopin, Brahms, Debussy, and all those who followed to compose the piano music we listen to today. Stuart Isacoff relates the story of the reinvention of the piano--a story that encompasses social history, religion, philosophy, and science as well as musicology--in a concise and sparkling narrative. Temperament is a jewel of a book. (shrink)

Two experiments were conducted for the derivation of psychophysical scales of the following audio descriptors: spectral centroid, spectral spread, spectral skewness, odd-to-even harmonic ratio, spectral deviation, and spectral slope. The stimulus sets of each audio descriptor were synthesized and independently controlled through appropriate synthesis techniques. Partition scaling methods were used in both experiments, and the scales were constructed by fitting well-behaving functions to the listeners' ratings. In the first experiment, the listeners' task was the estimation of the relative (...) differences between successive levels of a particular audio descriptor. The median values of listeners' ratings increased with increasing feature values, which confirmed listeners' abilities to estimate intervals. However, there was a large variability in the reliability of the derived interval scales depending on the stimulus spacing in each trial. In the second experiment, listeners had control over the stimulus values and were asked to divide the presented range of values into perceptually equal intervals, which provides a ratio scale. For every descriptor, the reliability of the derived ratio scales was excellent. The unit of a particular ratio scale was assigned empirically so as to facilitate qualitative comparisons between the scales of all audio descriptors. The construction of psychophysical scales based on univariate stimuli allowed for the establishment of cause-and-effect relations between audio descriptors and perceptual dimensions, contrary to past research that has relied on multivariate stimuli and has only examined the correlations between the two. Most importantly, this study provides an understanding of the ways in which the sensation magnitudes of several audio descriptors are apprehended. (shrink)

Intonation (musical and phonetic) in Hindustani classical music.

To know the scale of an aulos it is necessary to have a complete instrument. None of the surviving auloi are complete. It is the purpose of this article to attempt to reconstruct the missing parts of several auloi and thus to determine their scales. All musical sounds consist of regular vibrations. The interval between two notes may be expressed as the rate of vibration of the higher note divided by the rate of vibration of the lower note. (...) This ratio is very roughly the same as the length of the air column for the lower note divided by the length of the air column for the higher note. This gross over-simplification has been used for all calculations in this article. The width of the air column, the size of the holes, and the reed itself affect the pitch considerably. The player also has a large control over the precise note played. And so the notes obtained by the ancients might have been very different from the notes obtained by ignoring these factors; although the player's control over pitch might have been used to lessen the effects of the other factors. (shrink)

Of S. S. Stevens's well-known classification of nominal, ordinal, interval and ratio ‘scales of measurement’, perhaps its least-known aspect is its most distinctive, namely the distinction between interval and ratio scales. This article investigates the circumstances of the typology's origins among the experimental psychologists at Harvard in the 1930s and the unique fusion of personal, technical and intellectual forces this setting represented. It shows how it came to be that an influential psychologist reconceptualized measurement from first principles in (...) such a way as to both preserve the distinction between psychology and physics in this regard and yet implicitly classify his own work as the latter. The article concludes with the general suggestion that, if it is necessary to measure something, it might as well be something tangible enough to be measured usefully. (shrink)

This work aims to demonstrate that a universal model of man can be constructed using the precise mathematical formulation of a few philosophical theses about the nature of human beings. The author uses it to find theoretical solutions for several unexplained phenomena in psychophysics.

The ‘Αρμονικ Στοιχεα of Aristoxenus, being the earliest treatise on Greek Music extant, have hitherto held an unchallenged position as the foundation of much of our knowledge of ancient musical theory. Mr. R. P. Winnington-Ingram's shrewd and critical examination of the many difficulties involved in Aristoxenus’ treatment of subtleties of intonation is a very welcome contribution to a thorny subject; and it is in the hope of furthering our understanding that I venture to offer these comments on one or (...) two points where alternatives or modifications may be suggested. (shrink)

Leonard B. Meyer has proposed that when musical tendencies or expectations are inhibited by musical ambiguity or the unexpected, those inhibitions and their subsequent resolutions are likely to be provocative or engaging. Music, Tendencies and Inhibitions will explore the relevance of this theory to music and various other disciplines, and to psychological and natural processes. Each chapter consists of two parts: a presentation and consideration of an aspect of Meyer's theory, and a more associative or rhapsodic section of (...) "Reflections" on this aspect. The book will focus on Meyer's aesthetic rather than his music-theoretical proclivities, and is intended for academics and students in various fields as well as educated non-academics. The music scene is fluctuating, Meyer suggests, in that new and original styles or techniques are continuously emerging or developing on a small scale; it is static in that many of these developments seem unrelated, and are not likely to be grasped or progress as a whole. It will be posited that this theory foreshadowed and reflects important ideologies of contemporary culture, including postmodernism. (shrink)

This thesis is directed towards a philosophy of music by attention to conceptions and perceptions of space. I focus on melody and harmony, and do not emphasise rhythm, which, as far as I can tell, concerns time rather than space. I seek a metaphysical account of Western Classical music in the diatonic tradition. More specifically, my interest is in wordless, untitled music, often called 'absolute' music. My aim is to elucidate a spatial approach to the world combined with a curiosity (...) about the nature of the Pythagorean intervals. Thus one question I seek to answer is: What do the Pythagorean intervals import to music? In their original formulation by Pythagoras, and further, by Plato, their import seemed mystical and analogous to a 'harmony of the spheres.' In this spatial approach, the Pythagorean intervals are indicative of infinite depth. The faculty of hearing alone does not ordinarily spatially locate sources. Hearing is ordinarily combined with sight in order to spatially locate a sound. Yet we talk about music as if it were spatially located, that is, as if it were a visible object with a surface and themes or 'objects'. I explore the faculty of vision and consider in what ways the processes of vision might be similar to and distinct from audition. My source for this approach is David Marr's book 'Vision' and his theory of the 2 1/2-dimensional sketch. In a medium in which there is no spatial location, it is important to situate the listener. Newton solved the problem of location by demonstrating the effects of gravity. P. F. Strawson claims that an analogy of distance is required in hearing to situate the listener, that is, a sense of nearer to and further from a source or object that permits a perception of distance. I claim that in music, the key signature and the scalar relations of musical themes provide this analogy of distance. The works of Plato, Aristotle, Descartes, Leibniz, and Newton are studied for their accounts of motion, bodies, and space. From these metaphysicians can be gleaned elements of music that include form, motion, timbre, dynamics, and attraction. By incorporating motion, I aim to show that although we may not know the true nature of space, we can learn from hearing music that space is perceptible in other than three dimensions. (shrink)

Known today mostly as an author of Romantic short stories and fairy tales for children, Prince Vladimir Odoyevskiy was a distinguished thinker of his time, philosopher and bibliophile. The scope of his interests includes also history of magic arts and alchemy, German Romanticism, Church music. An attempt to understand the peculiarity of eight specific modes used in chants of Russian Orthodox Church led him to his own musical theory based upon well-known writings by Zarlino, Leibniz, Euler, Prony. He realized (...) his theoretical ideas in an enharmonical piano with nineteen notes for every octave. His call for a different musical scale remained largely ignored in the nineteenth century, until the topic was raised anew by twentieth-century composers and musicians. (shrink)

A new construct, termed music receptivity, is introduced and discussed in this work. Music receptivity can be defined as a measure of the extent of internalization that an individual has, to a given piece of music, as measured at the point of listening. Through three studies, we demonstrate the psychometric properties of the construct—the Music Receptivity Scale. Exploratory factor analysis on a sample of 313 revealed good psychometric validity, with a four-factor solution, with a Cronbach’s alpha of 0.89, and a (...) two-factor solution, with a Cronbach’s alpha of 0.87. The tool also had a good test–retest reliability. Overall, the tool had 20 items in the long form and 12 items in the short version. The MRS could distinguish musicians and non-musicians supporting its discriminant validity. We have also discussed the implication of the MRS in the field of music psychology. (shrink)

In this study we evaluated heart rate variability changes in a pianist, playing in a laboratory, to investigate whether HRV changes are guided by music temporal features or by technical difficulty and/or subjective factors. The pianist was equipped with a wearable telemetry device for ECG recording during the execution of 4 classical and 5 jazz pieces. From ECG we derived the RR intervals series, and, for each piece, analyzed HRV in the time and frequency domains and performed non-linear analysis. (...) We also studied the correlation between the time course of music volume envelope and tachogram. Results showed a general reduction of parasympathetic and an increase of sympathetic activity, with the greatest changes during the classical pieces execution, the pianist appraised as more demanding than the jazz ones. The most marked changes occurred during the most technically/emotionally demanding piece, and correlation analysis revealed a negative association between music volume envelope time course and tachogram only for this piece, suggesting a modulation of the limbic system on the synchronization between heart rhythm and music temporal features. Classical music was also associated with the increase of entropy with respect to rest, indicating its effectiveness in driving flexible, healthy, heart dynamics. In conclusion, HRV seems modulated not only by the music temporal features, but also by the pianist’s emotional involvement, which is greatly influenced, in a non-trivial manner, by the technical demands and musician expertise. (shrink)

Current artificial neural network or connectionist models of music cognition embody feature-extraction and feature-weighting principles. This paper reports two experiments which seek evidence for similar processes mediating recognition of short musical compositions by musically trained and untrained listeners. The experiments are cast within a pattern recognition framework based on the vision-audition analogue wherein music is considered an auditory pattern consisting of local and global features. Local features such as inter-note interval, and global features such as melodic contour, are derived (...) from a two-dimensional matrix in which music is represented as a series of frequencies plotted over time.Manipulation of inter-note interval affected accuracy and reaction time measures in a discrimination task, whereas the same variables were affected by manipulation of melodic contour in a classification task. Musical training is thought of as a form of practice in musical pattern recognition and, as predicted, accuracy and reaction time measures of musically trained subjects were significantly better than those of untrained subjects. Given the evidence for feature-extraction and weighting processes in music recognition tasks, two connectionist models are discussed. The first is a single-layer perceptron which has been trained to discriminate between compositions according to inter-note interval. A second network, using the back-propagation algorithm and sequential input of patterns, is also discussed. (shrink)

From the Tin Pan Alley 32-bar form, through the cyclical forms of modal jazz, to the more recent accumulation of digital layers, beats, and breaks in Electronic Dance Music, repetition as both an aesthetic disposition and a formal property has stimulated a diverse range of genres and techniques. From the angles of musicology, psychology, sociology, and science and technology, Over and Over reassesses the complexity connected to notions of repetition in a variety of musical genres. The first edited volume (...) on repetition in 20th- and 21st-century popular music, Over and Over explores the wide-ranging forms and use of repetition - from large repetitive structures to micro repetitions - in relation to both specific and large-scale issues and contexts. The book brings together a selection of original texts by leading authors in a field that is, as yet, little explored. Aimed at both specialists and neophytes, it sheds important new light on one of the fundamental phenomena of music of our times. (shrink)

The present study explored the correlation between music preference and mental health of college students to make an empirical contribution to research in this field. The self-reported music preference scale and positive mental health scale of college students were adopted to conduct a questionnaire survey in college students. Common method variance was conducted to test any serious common method bias problem. No serious common method bias problem was observed. The results showed that college students’ preference for pop music, Western classical (...) music, and Chinese traditional music has a significant and positive correlation with their mental health. Furthermore, college students’ preference for heavy music has a significant and inverse correlation with their mental health. This research presents a correlational study; therefore, no causality can be inferred. (shrink)

This study investigated the effects of music therapy and pictorial illustration on the attention span of children with mild intellectual difficulties. A pre-test, post-test and control group quasi-experimental research design was used with a sample of children diagnosed with mild intellectual disability from three special schools in Ibadan, Nigeria. Fifty children were randomly selected and assigned to one of three groups: music therapy, pictorial illustration, or control. Twenty-four sessions of music therapy and pictorial illustration classes were held with the experimental (...) group only. The Moss Attention Rating Scale was used before and after the intervention to collect data on participants’ attention span. Analysis of Covariance indicated that there was a significant statistical difference between pre-test and post-test results of the two groups. The estimated marginal means of post-attention span by treatment indicated that pictorial illustration had the highest post-attention span score, followed by music therapy, while post-attention span score for the control group was the least. Based on the findings, it is recommended that teachers, caregivers, and parents of children with mild intellectual disability adopt pictorial illustration and music therapy as teaching strategies to enhance their attention span. (shrink)

Our families are our first and most important ethical training grounds. But what is the family? And what are our ethical commitments to our family members and to the broader moral community? After a brief introductory chapter on basic ethical concepts and theories, the essays in this volume provide readers with ethical analyses of issues ranging from same-sex marriage to a controversial proposal to "license" parents. The chapters cover love, sex, marriage, parents and children, the relationship between the family and (...) the larger moral community, and the influence of emerging technologies on the ethical issues inherent in family life. The volume is intended to open up this exciting territory in applied ethics to those interested in philosophy, family studies, social work, and to anyone who wants a deeper understanding of the ethical forces at work in this most basic social institution. (shrink)

There is a received view on measurement scales. It includes both a classification of scales and a set of prescriptions regarding measurement inferences. This article casts doubt on the adequacy of this received view. To do this, I propose an epistemic characterization of the ordinal/interval distinction, that is, one in terms of researchers’ beliefs. This novel characterization reveals the ordinal/interval distinction as too coarse grained and thus the received view as too restrictive of a framework for measurement research.