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 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)

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)

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)

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)

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.

Fractal structure is a ubiquitous property found in nature and biology, and has been observed in processes at different levels of organization, including rhythmic behavior and musical structure. A temporal process is characterized as fractal when serial long-term correlations and statistical self-similarity (scaling) are present. Previous studies of sensorimotor synchronization using isochronous (non-fractal) stimuli show that participants' errors exhibit persistent structure (positive long-term correlations), while their inter-tap intervals (ITIs) exhibit anti-persistent structure (negative long-term correlations). Auditory-motor synchronization has not (...) been investigated with anti-persistent stimuli. In the current study, we systematically investigated whether the fractal structure of auditory rhythms was reflected in the responses of participants who were asked to coordinate their taps with each event. We asked musicians and non-musicians to tap with 12 different rhythms that ranged from anti-persistent to persistent. The scaling exponents of the ITIs were strongly correlated with the scaling exponents of the stimuli, showing that the long-term structure of the participants' taps scaled with the long-term structure of the stimuli. Surprisingly, the performance of the musicians was not significantly better than that of the non-musicians. Our results imply that humans are able to readily adapt (rather than simply react) to the overall statistical structure of temporally fluctuating stimuli, regardless of musical skill. (shrink)

The speech-to-song illusion ( Deutsch et al., 2011 ) tracks the perceptual transformation from speech to song across repetitions of a brief spoken utterance. Because it involves no change in the stimulus itself, but a dramatic change in its perceived affiliation to speech or to music, it presents a unique opportunity to comparatively investigate the processing of language and music. In this study, native English-speaking participants were presented with brief spoken utterances that were subsequently repeated ten times. The utterances were (...) drawn either from languages that are relatively difficult for a native English speaker to pronounce, or languages that are relatively easy for a native English speaker to pronounce. Moreover, the repetition could occur at regular or irregular temporal intervals. Participants rated the utterances before and after the repetitions on a 5-point Likert-like scale ranging from “sounds exactly like speech” to “sounds exactly like singing.” The difference in ratings before and after was taken as a measure of the strength of the speech-to-song illusion in each case. The speech-to-song illusion occurred regardless of whether the repetitions were spaced at regular temporal intervals or not; however, it occurred more readily if the utterance was spoken in a language difficult for a native English speaker to pronounce. Speech circuitry seemed more liable to capture native and easy-to-pronounce languages, and more reluctant to relinquish them to perceived song across repetitions. (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)

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)

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)

ABSTRACTIt has recently been demonstrated that the reported tastes/flavours of food/beverages can be modulated by means of external visual and auditory stimuli such as typeface, shapes, and music. The present study was designed to assess the role of the emotional valence of the product-extrinsic stimuli in such crossmodal modulations of taste. Participants evaluated samples of mixed fruit juice whilst simultaneously being presented with auditory or visual stimuli having either positive or negative valence. The soundtracks had either been harmonised with consonant (...) or dissonant musical intervals. The visual stimuli consisted of images of emotional faces from the International Affective Picture System with valence ratings matched to the soundtracks. Each juice sample was rated on two computer-based scales: One anchored with the words sour and sweet, while the other scale required hedonic ratings. Those participants who tasted the juice sample while presented with... (shrink)

The article starts with various definitions of music and its components (taken es-pecially from medieval sources). Then the Statuit introit is presented as the main example useful for mathematical analysis in the paper. We discuss the distinc-tion between a musical work and its performance and give a review of possible representations/ notations of music with their short mathematical characteristics. The next point is devoted to the concept of modality, Gregorian scales and selected theories linking musical experience with (...) mathematics. We use the Statuit introit as the illustration for the construction of its statistical analysis (for notes, intervals and progresses). The results of this analysis serve as a reference point to indicate the connection between the process of musical composition and the apparatus of mathematical linguistics. Based on the above considerations we suggest that the pattern analysis could be useful as a tool unifying some aspects of music and mathematics and explaining the perception of musical works. (shrink)

La dimensione teorica della musica occidentale, nella sua evoluzione storica, ha inevitabilmente fatto uso di concetti essenziali alla definizione di come il suono è musicalmente organizzato o organizzabile. Fra questi, risultano imprescindibili le nozioni di materia, forma e ordine, che implicano rispettivamente, nei pur diversi ambiti linguistici e contesti storico-filosofici di riferimento, ciò di cui è fatta la musica, ciò a cui la materia sonora tende, e come tale tensione è realizzata. Scopo di questo contributo è una valutazione d’insieme sulla (...) valenza filosofica e l’uso di tali concetti nel pensiero musicale occidentale altomedievale e in quello del Novecento, che nonostante la distanza cronologica presentano convergenze significative. Nel Medioevo, un lungo processo di elaborazione teorico-pratica permise la matematizzazione dello spazio musicale, attraverso l’adattamento di moduli melodici, trasmessi oralmente, alle strutture scalari desunte dalla teoria greco-boeziana. La forma e l’ordo musicali furono quindi riferiti ai criteri fisico-matematici atti a distinguere nella materia sonora, in sé disorganica e indefinita, ciò che è musicale da ciò che non lo è. Tale concezione sparisce con l’affermarsi del sistema tonale, ove il suono fisico è concepito come “pre-formato” e “pre-ordinato” nella gamma scalare e nei vincoli attrattivi “naturali” degli armonici. In conseguenza, i concetti di forma e ordine abbandonano il contesto acustico, andando a definire i criteri teorici della composizione artistica, in linea con l’idea filosofica del loro esprimere la coerenza logico-sintattica dell’“insieme organico” . Nell’ambito del pensiero musicale del Novecento, la crisi del sistema tonale e la messa a punto di nuove modalità e tecniche di produzione del suono hanno riorientato la valenza significante e l’uso di questi tre concetti, implicando il loro tornare a imporsi sugli elementi primari della fisica del suono, non solo l’altezza, ma soprattutto il timbro, il volume e la durata. Già Schönberg, nel 1911, affermava come “l’ordine che chiamiamo forma artistica” è “un necessario espediente” elaborato “a causa della nostra incapacità a comprendere l’indistinto e il non-ordinato”, che è la condizione propria della materia sonora. In its historical development, the Western theory of music has inevitably made use of specific concepts to define how the sound is musically organized or organizable. Among these notions, those of matter, form and order signify – in spite of the different linguistic areas and the various historical and philosophical backgrounds – that from which music is made, that to which it tends and how such tendency is realized. This paper aims to evaluate the philosophical implications and the use of these three concepts in the musical theories of the high Middle Ages and of the twentieth century, since, in spite of their chronological distance, they present significant similarities. A long process of theoretical and practical adjustments of the melodic structures of liturgical chants to the scale-systems of the Greek and Boethian theory contributed to developing what would become a familiar notion throughout the Middle Ages: that musical intervals can be expressed in mathematical terms. According to this view, the words forma and ordo signify the mathematical measures that are applied to the “matter” of sound, which is considered as inorganic and indefinite in itself. This conception gradually disappears when the tonal system begins to emerge, since this new modality of composition implies that the physical sound is “pre-formed” and “pre-ordered” within the musical scale, according to the “natural” links of the harmonics. Consequently, the concepts of “form” and “order” do not refer any more to the context of sound generation, but are now used to define the theoretical criteria of the artistic composition, so to accomplish the new philosophic idea of their expressing the logical-syntactic coherence of the “organic-whole” . In the early twentieth century, when the tonal system starts to be replaced by new methods of composition and when new modalities and techniques of sound production emerge, those three concepts are used, again, to express the basic elements of the physics of sound: not only its height, but also its timbre, volume, and duration. In 1911, Schönberg argued that the order that we call “artistic form” is a necessary device, elaborated “because of our incapacity to comprehend the indistinct and unordered thing”, that is the own condition of the matter of sound. (shrink)

Since 2008 I have been closely following the conceptual/performance/video work of Daniel Peltz. Gently rendered through media installation, ethnographic, and performance strategies, Peltz’s work reverently and warmly engages the inner workings of social systems, leaving elegant rips and tears in any given socio/cultural quilt. He engages readymades (of social and media constructions) and uses what are identified as interruptionist/interventionist strategies to disrupt parts of an existing social system, thus allowing for something other to emerge. Like the stereoscope that requires two (...) identical images to create an illusion of a three-dimensional image, Peltz sometimes visualizes two separate elements to create an object or moment that requires space and depth to focus on its varied layers. They say your brain has to process and make meaningful sense out of all that visual information before it can accept the illusion. I say your brain has to do a similar thing when looking and seeing the divine, magical, and faithful (social) art making of Daniel Peltz. Daniel Peltz is Associate Professor of Film/Animation/Video at RISD. He divides his time between Rhode Island and Sweden and is currently at work on an exhibition at Botkyrka Konsthall, Stockholm opening February 2013 and a new project to be included in the IASKA: Spaced Biennial (Australia) in 2014. This interview took place on Skype and is part one of a two-part interview. Feliz Lucia Molina: Are you in Providence, RI? Daniel Peltz: I’m at my house in Providence. I’ve been back for six days teaching winter session at RISD and doing this workshop series—these investors’ drum circles with a group of wealth managers. a client of the firm, 2013, photo Shirin Adhami FLM: The wealth managers were all drumming together? DP: They were all drumming in response to the performance of their retirement portfolios. FLM: Is this part of the “Unrealized Gain/Loss” piece? DP: Yes, it’s part of a show I’m working on in Sweden. I can show you because it was just today. I’ll show you some of this. Lets see—share screen [click, click, click]. This is the room. I’ve been using the camera system that’s already installed in the conference rooms to record them. So the video is being recorded directly by the wealth management office’s tech staff. These are the people I worked with in the last workshop. This conference table is less wondrous. They’ve been learning to drum in response to their retirement portfolios. I started by bringing in my little bit of wealth for them to propose a management strategy, I came to the follow-up meeting with a counter proposal, which was this workshop. So they agreed to do this series of workshops instead of managing my wealth. FLM: Does everybody in the room manage your wealth? That’s kind of a lot of people. DP: That woman in the back there and Craig —they handle new client business. So when you come there with your wealth, they sit down with you and suggest to you how they would manage it. They’re very nice, responsible people. FLM: And where is this? DP: This is in Providence and the one I was showing you is in Waltham, where I was today. Then I’m going to Newport for the last one on Friday. So I will have done four of them. This is the group in Waltham that I just played with today. I played directly with the two groups in Providence and I’m working with an ethnomusicologist at Brown, Asha Tamarisa, who is facilitating the last two. She’s helped develop the workshop in terms of figuring out how to train a group to do this and thinking about the compositional challenges of working in response to retirement portfolio data. FLM: Screensharing helps me to figure out tiny bits here and there about the project. DP: I might even be able to play you a little of the audio I’ve also been working with a group of professional percussionists on what will become a quarterly public investors’ drum circle event. Their stuff was really nice, but I want you to hear what we sounded like in the workshops. They’ve all been recorded by the a/v system in the offices. We use a simple structure where the drummer investors interpret the sensation of gain or loss as embellishments to a base heartbeat rhythm. The group holds the heartbeat and, as each person experiences gain or loss, they embellish that rhythm. "Screensharing helps me to figure out tiny bits here and there about the project" FLM: Is the process all very spontaneous? DP: Its actually quite structured. We produce a custom stock ticker that shows the performance of their collective portfolios. In advance of the workshop each participant submits assets in their retirement portfolio. Then we make a stock ticker that shows the real-time performance of their assets so that they can respond to almost live data. FLM: Are they reading the stock ticker projected up on the screen in the room? Do people drum in correspondence to the visual live data of the performance of their assets? DP: Exactly. They’re looking at the stock ticker as opposed to each other, so it’s a slightly shifted drum circle. They’re looking at the ticker but they’re listening to each other—that’s what we’re practicing. For example, NVO—the price is 172.08 but it’s down -1.16 and as that moves across the screen, the person who’s retirement is invested in that asset starts to embellish when that arrow first appears, based on their experience of loss. They stop when it exits the screen and return to the heartbeat. You could have one ticker for each retirement portfolio, but the way the workshop is constructed is that we just isolate one asset from each person’s portfolio so that everyone in the group is represented in a single ticker. So they’re drumming and looking at the ticker, but they’re hearing each other experience gain and loss. We’ve removed direct visual engagement from the social structure of a drum circle but the oral engagement is still there. FLM: So they had their own sound interpretation of gain and loss? DP: Yeah and that part is quite spontaneous as you were saying. In some of the preparatory exercises we’ve been working to give the participants more strategies for interpreting the sensations of gain and loss. We’re trying to develop their capacity to embellish a heartbeat or base rhythm but I’m not invested in having a melodious result. I’m quite curious about what this kind of structure will result in without any desire for a particular result. FLM: For context, can you talk about the project you did a couple years ago in Bali, “Unrealized Gain/Loss” in relation to this current wealth management project? DP: The workshops I’ve been doing use a similar strategy to the other components in this project. It started in Indonesia on my sabbatical and I was really trying to understand where I was physically and where I was being on sabbatical—this kind of strange jubilee structure where every seventh year you’re supposed to renew your self. And it was around the time of the global financial crisis. I was on sabbatical for the global financial crisis. I remember watching my father, in particular, respond to the financial crisis by monitoring his retirement portfolio and trying to make sense of it. I realized on a visit to their home that he checked his retirement portfolio every single day and I was really struck by that because in some way our parents are mysteries to us as children, especially their moods. We know how important their moods are but we don’t know what governs them. And somehow it was like I’d figured it out, it’s the performance of the DOW! So I think there was something in that. Then I was in Indonesia and I had been drawn there by an interest in their highly ritualized Hindu culture, where so much of life is driven by a ceremonial calendar. I was interested in Bali as this predominantly Hindu pocket within a predominantly Islamic country and life there being organized by this ritual calendar functioning as a kind of resistance to the dominant global religion of free-market capitalism. So I started to explore that correlation between the ways in which this culture that I was living in was sort of “living for the afterlife” and this idea within certain segments of American society of “living for the afterwork life”. The idea that your wellbeing in the “afterwork life” is tied to forces that are unseen and largely beyond your control has strong similarities to many religious understandings of the universe. So I started to explore that and the crafts and materials that were around me were primarily Batik and percussion. Percussion is a huge part of daily life in Bali. These gamelan troupes were everywhere. And I also happened to be there for Nyepi, the day of silence, which is preceded by a very elaborate procession and construction of demonic statues. These were the things that were around me and I started studying Batik with one of the Batik artists there and also started a conversation with two master Batik artists, one who is American and her Indonesian husband. I developed these patterns that were based on symbols from the performance of my retirement portfolio and worked with the batik artists to produce two sarongs. d. peltz - 2012 In producing the designs, I treated the performance of my retirement portfolio since my arrival at RISD [7 years] as a significant interval and then I looked at the ways in which decisions are made within retirement portfolios as having an extension outwards from the individual assets that underlie the retirement portfolio, which are kind of like the base elements of the retirement world. Then there’s the allocation of your assets, which is a global way of understanding an individual according to typologies, which are often referred to in terms of risk—this notion of a ‘risk profile’. What type of ‘person’ you are is determined by your attitude towards risk, or potentiality, and I found that to be a really fascinating way of understanding the universe. I remember looking at the tabs in my retirement portfolio and finding this one for viewing ‘Unrealized Gain/Loss’ and that’s often how I work—is just going through the Cambridge Parking Code, for example, and finding this section of the code that was called ‘Crossing Non-Signalized Locations’ and just feeling “I can’t do any better than that,” you know? That’s what I was talking about in terms of ready-mades that exist in the social sphere. So I found that tab, actually, a long time ago, and I pulled it out of a journal when I was there [in Bali] working on these pieces and I wound up making these two sarongs and later on a series of porcelain vessels for holding one’s unrealized gains and losses. At the time, I knew that I wanted a performance to come out of them, but I wasn’t sure what it was. I was inspired very much by this sort of thing: Pulls out a TIAA-CREF brochure with a man in a suit seated at a table. This guy is probably an actor, and [the brochure] says “TIAA-Cref announces “Individual counseling sessions at the Rhode Island School of Design. Individual counseling sessions at no additional cost to you. You can discuss your personal financial situation with an experienced TIAA consultant on a confidential basis. We are available to help you discuss how to achieve your financial goals by investing in financial solutions such as mutual funds, brokerage, life insurance, and annuities...etc....What retirement benefits best fits your situation?” Often I encounter this and I think O.K., this is one way to prepare for the after-work life and it seems inadequate to me. But, I also find it really inspiring. I really like the visual language of it. I kind of want to be that man. I’d like to see if I could maybe buy his clothes. FLM: What it is about the man on the brochure that interests you? DP: He’s offering personalized objective advice and a detailed evaluation of everything you need to know and do. Who wouldn’t want that? But he’s also something of a contemporary priest or priestess, mediating between the unseen all-powerful universe of global capitalism and the common worker. So I started off developing Unrealized Gain/Loss directly from the charts that represent the performance of my retirement portfolio. Then I came home and I wanted to use those. I had this word in my journal “unrealized gain/loss vessel.” I had this notion of vessels that would contain unrealized gains and losses. That felt really important to me that they would have somewhere to go. I had been thinking a lot about altars and making offerings—that somehow this really fickle, massive, difficult-to-comprehend-universe of the financial world—that somehow it might be nice if you could making an offering to it. [In Bali] they made such beautiful elaborate offerings. So I studied offering making as well with one of the women there and she taught me some of the standard forms created by folding leaves and the significance of the floral arrangements. I started working in clay and then moved to porcelain and I made these unrealized gain/loss vessels. I made a few of them, they have holes on either side that you can’t get your fingers in. But something can go in there and something can go out of there. It’s a nice size for putting on an altar. Then I got this commission from Artists in Context who was interested in my doing something for this project “Artists Perspectives for the Nation” project. I proposed initiating these investors’ drum circles as a new public performance form. I’m interested in bringing together those two symbols—the symbol of the djembe and the drum circle. unrealized gain/loss vessel - d.peltz - 2012 FLM: I can imagine the public digital stock ticker performing like a soft fleeting stream of information, a kind of (meaningless) illusory comfort blanket. DP: In some way you have to understand its relevance outside of the obvious, right? Because the obvious is illogical. Nobody is actually using that data to day trade, for example. People aren’t sitting there with their computers watching the market data in Times Square or setting up an outdoor office and being like “OK it’s up 3 points or it’s up 1.56, trade! Ok now buy, Ok now sell!” That would be a kind of a nice performance, actually. But actual day traders would want more up to date data than that. To understand what that data is doing is really important. And that’s something I’ve realized—that I’m interested in a particular kind of data visualization, which is not about what data can tell people, but what data can tell people who are visualizing it. For example, in the Cambridge Project “Crossing Non-Signalized Locations” I was interested in the 10,000 excuses archive of data recording five years worth of excuses for why people thought they shouldn’t have received their parking ticket. I was not interested in making that excuse wall so that the public could see and understand this data. Inevitably the data will be seen by others but I was really interested in what the action of visualizing the data told those who were visualizing it. The parking attendants themselves were writing those excuses on the wall—I was interested in what that kind action of writing the excuses on the wall told them about the data. Similarly, I’m interested in designing a way to allow people to pass this data from the unseen universe of the market, through their own bodies, which happens through the merging of the drum and the stock ticker. I’m interested in those two also as symbols; the drum as this symbol of the earth, the body and a pagan counterculture, and the stock ticker referring to the ethereal world of global markets—bringing those two together and making them dependent. I’m often drawn to conceptual propositions that I become invested in testing in a sincere way—at first they often they sound humorous to others, but I have to remember that there is humor in them. I don’t sit around and laugh about these things. I stop finding them funny at all. I’m interested in the proposition that we could know something about the after-work life by drumming in response to our retirement portfolio. So then I become really interested in how to craft that into a viable performance form for myself and others. FLM: The aspect of using sound in “Unrealized Gain/Loss” as a way of embodying the information to the asset holder is really intriguing—using sound as a means of embodying the asset data. Was sound a medium that made sense to use immediately or were you considering other means of attempting to embody it? DP: Well I do use other mediums within the project like textile, ceramic, and batik patterns. I was first drawn to the history of Batik patterns as a socio-economic stratification system and the vessels as a way of embodying or manifesting this data of unrealized gain and loss. My first approach was to work with meditation actually—a meditation workshop with my colleagues. I was going to offer this “Unrealized Gain/Loss” workshop where you would explore the sensations of gain and loss by adapting the way yogi-nidra brings you into contact with your physical surroundings and stretches your perception. FLM: At Naropa University there are/were business & compassion workshops—a sort of mash-up of business and compassion and how compassion could be incorporated into a business model. This process and engagement of “embodying data” also has to do with “Participatory Democracy and the Future of Karaoke” you created at the DNC in Denver in 2008. DP: That kind of appropriation and instrumentalization of spiritual practice could be disturbing and thus compelling as a strategy. For various reasons, I’ve come to be drawn to both the form of a quarterly public performance and the established performance form of a drum circle. Its something I’ve seen myself do before, that is to mess up a really good functional social system like a drum circle or karaoke. I remember I was developing language for the karaoke project and started calling it “Participatory Democracy and the Future of Karaoke” and one of my assistants on the project, who’s an incredible artist, said, “but don’t you think the future of karaoke is guitar hero?” and I realized that maybe he thought I was trying to improve the form. I’m just trying to get people to have this shifted embodied experience, I need to craft the performance context so that they can do that. In the case of the karaoke project, for example, what did I need in order to be able to do this [a person to stand up in front of a bar and deliver a karaoke speech]? I realized that the body is very vulnerable so I built a podium so that the speaker can feel secure enough to do this, otherwise you couldn’t get to this state achieved by passing these speeches through the body. Then I was, like, well you need to be able to practice the lyrics because you don’t know all the “songs” by heart, which became an insert to the massive track books carried by most karaoke VJs. And then sometimes the crowd in the bar isn’t there with me, so I needed to extract the voice of the crowd cheering from the original venue and I needed the local audience to cheer if they wanted to. I’m interested in both where the form succeeds and fails. In particular, one of the most interesting things is this auditory gap between the space where you are, the reduced scale of applause in your own little bar, and this grand scale of applause at the convention center where the speech was originally delivered. FLM: How did the concept of “Participatory Democracy Karaoke” come about and why did you use karaoke as a means of engaging what was happening at the DNC in 2008? DP: I was looking at a lot of different readymade media infrastructures within the city at the time. I was interested in the emergency broadcast systems and I developed a proposal to repurpose that system and karaoke became an important symbol because it was this populist form that was already engaged in exploring the sensation of celebrity but also visualizing the gap between ourselves and those with more power and influence. So it had this readymade capacity to play with power and celebrity and I felt like the Obama presidential campaign, the first one in particular, had some very curious overlaps with this culture of celebrity. Obama of course rose to power partly based on his oratory abilities and I was interested in how karaoke as a vehicle was so adept at offering people all that was left of authentic expression in a political speech. Managing a politician and constructing their identity is such a developed practice that it becomes, kind of automatically, a metaphor for the way that our own identities are constructed. Of course the Obama campaign was very hip and savvy and deploying this notion of grassroots. It was really pioneering in its use of social media and this deployment of notions of populism. I was interested at that time in the capacity of karaoke to track speech patterns, precise tempos of anyone’s delivery, and that to me was a way of thinking about what might be left of the authentic self. I was interested in karaoke’s capacity to extract that authentic component and offer it to others. So not just to stand up and be them, but to [literally] pass their speech patterns through your own body. A long time ago, it started to strike me as odd that one would make media at all. It struck me as a kind of un-contemporary way of going about making art in an age of media overflow. That logic extended into my thinking on delivery devices and installation as well. Why would one buy a screen or even set one up when there are so many out there? And the way in which these media displays function in karaoke bars and bars in general is very interesting to me. I’m drawn to this passive consumption of media where your primary social interaction is with the bartender or a few other individuals but these screens are around you and your attention is shifting back and forth between these spaces. So much political rhetoric is spoken to a half-listening audience. I was interested in what was happening in the slippage and that karaoke was a kind of slippage amplifier. So if you put people in a bar and they are delivering a Kucinich speech and Kucinich comes up on a screen then your getting a sound bite of Kucinich and an image of Kucinich and your friend is talking to you— FLM: A kind of magic takes place in that incongruency between sound and image and the karaoke participant who’s relaying the speech-text at the same time. DP: Exactly and there’s some kind of truth in that experience of reality. FLM: Yeah, there’s something uncanny about seeing the body close-up like that as though it can’t lie to you in that moment or context. It’s a weird moment of luminous clarity. The work you’ve done and all of what you’re saying about karaoke is so very interesting to me. Growing up, my dad and uncles sang karaoke a lot (and still do) and being first-generation Filipino American is a different cultural subtext entirely. I’m also seeing it from the position of witnessing family members who are carriers of these stories and songs. And seeing them cherish these Tony Bennett, Frank Sinatra, Elvis Presley songs so much, I also see how their bodies are literal vessels of popular music that signifies something greater—it signifies their cultural and socioeconomic place in the world. The way that they cherish these American 1950s and 1960s pop songs is similar to having a certain kind of reverence for their spiritual faith or Catholicism. It’s a similar kind of care, focus, and attention exerted in karaoke and Catholicism—that these two structures and systems give something to focus on. Setsuko, Seiji and Hitoshi in Obama, Japan as Obama in Indiana — d. peltz — 2008 DP: Sure there something about the relationship we have to our candidate or the way we go about choosing a candidate, which is very similar to a deity or idol. I learned a lot about karaoke culture through this project. I’d never done karaoke. I’d never been interested in it as a form and then I travelled to Japan as part of the project when I made “Setsuko, Seiji and Hitoshi in Obama, Japan as Barack Obama in Indiana” and it was quite fascinating because my image of karaoke had always been this very public forum in a karaoke bar and then I discovered there’s this whole other world of karaoke where people even go on their own, they go and rent a room or cubicle and sing, or they go on a date—just the two of them go and sit in a room and do karaoke together. FLM: I’m interested in issues that take place within or as a result of specific karaoke culture(s). In the Philippines within the last several years there’s been occurring the “My Way Killings” phenomenon. Apparently baklas or gay men are employed by karaoke establishments to help “smooth over conflicts over karaoke singing”—these social forms of conduct, or lack thereof that arise out of the infrastructures of this social sport. In this one rural part of the Philippines there’s a village karaoke machine that the whole village shares—the Aeta indigenous people have an appointed “keeper” of the karaoke machine. I also see karaoke as a proxy to the confessional box in Catholicism where one goes to pour out their sins (minus the penance and redemption). The karaoke machine enables one to literally sing out whatever’s going on internally, but through highly saturated popular song lyrics. While karaoke is a public and social sport, it can also be a private one. Karaoke is a means of communion with each other. DP: Right, this preference for this kind of mediated communication. In Japan I was trying to organize people to work on this project and I was talking about throwing a party and they were like, well, we have to rent a karaoke machine because what else are we going to do? And I think its kind of serving that function of surrogacy—emotional surrogacy. FLM: And karaoke tools can be read as ritual tools—the magic mic that holds everything. There’s got to be some overlap at some point—between religious ceremony and devotion to the karaoke machine. DP: The way I designed the piece was so that it could slip right on top of the ready-made karaoke infrastructure. There was a flat-packed podium and it was made of a single sheet of plywood with no fasteners that slotted into itself. Those were sent out to a network of karaoke bars that I invited to become “karaoke convention centers.” The local VJs downloaded our custom-made, speech-extracted tracks that were designed to play on their existing equipment. In this sense the piece is a permanent installation. If you go to Denver today, some of the VJs still have the tracks in their library of offerings, the Ramones and Romney. It was this notion of re-purposing readymade infrastructure to create a distributable populist form. Obama was coming and the convention was in the Pepsi Center and 30,000 people were coming including 10,000 journalists. The impetus behind the larger art project that commissioned international artists to make works in Denver, was that local people weren’t going to have much access to this convention. It was like an invasion, the city was being descended upon, but if you lived a block away from the site, you had the same access as people in Zimbabwe&mash;30 second media bits excerpted from the speeches. So it seemed to me that the fundamental gesture was how do I take that signal, which was travelling out of the convention center, and create a local interruption? FLM: Is that what you mean by ‘intervention’? The term is frequently used to help describe your work. DP: It depends on the day. Around that karaoke project I had a conversation with Krzysztof Wodiczko and he was proposing that maybe rather than intervention, we should consider the word interruption. Because intervention is kind of an overused term in the field of art and it has militaristic and therapeutic associations outside of the art context. Fundamentally, the idea of intervening speaks to the readymade social world as your primary material. So it’s basically suggesting a kind of subtractive process, which gets back to this question: what is the role of the contemporary media artist in a world that’s so saturated with media? You can’t work additively in a saturated field. If you want to make a visible mark you have to work subtractively. That’s what intervention is about to me, just another way of saying “to work subtractively.” FLM: So the interventions or interruptions aren’t necessarily adding or subtracting, but are they putting orange cones there? What are they doing exactly? DP: I think you’re right about that, they’re not really subtracting. They’re adding to the scope of possibility. I’ve been thinking (with this exhibition I’m mounting next month) about the work as explorations and expansions of social possibility. Maybe it’s more insertion. I started calling the pieces ‘insertions’ that I was making in Rejmyre—a small town in Sweden where I’ve been working for six years now. My favorite site to install there is the tourist bureau. I started calling the video pieces that I made for the tourist bureau, video insertions. This idea that you’re inserting something into the readymade media infrastructure of the world resonates with me. Insertion leverages a context, creating a possibility that the inserted object might be naturalized in the process — that someone can encounter my video in Rejmyre as tourist information. And then all of a sudden tourist information can include some American guy prostrating through town and it can include really bad relationship advice. Maybe insertion is a better word. tourist information – d. peltz 2009-present  . (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)

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)

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)

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)

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)

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)

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)

Beyond the major-minor tonality that characterizes classical and contemporary Western musical genres, Turkish classical and folk music offer experimental psychologists a rich modal system in which cognition, development, and enculturation can be studied. Here, we present a cross-cultural experiment concerning implicit knowledge of musical scales. Five groups of participants—American musicians and nonmusicians, Turkish musicians and nonmusicians, and Turkish classical and folk music listeners—were asked to listen to brief melodies composed using the member tones of either the major (...) scale or the rast makam, a microtonal mode found within Turkish classical and folk genres with no equivalent in Western music. Following each melody, participants were asked to identify whether a probe tone had been presented in the melody, providing confidence ratings on a six-point scale. In general, participants’ short-term memory was influenced by implicit knowledge of musical scales, with the major scale eclipsing the rast makam even in listeners experienced with Turkish genres. Prior work and future directions in cross-cultural music cognition research are discussed. (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.

The claim that listening to extreme music causes anger, and expressions of anger such as aggression and delinquency have yet to be substantiated using controlled experimental methods. In this study, 39 extreme music listeners aged 18–34 years were subjected to an anger induction, followed by random assignment to 10 min of listening to extreme music from their own playlist, or 10 min silence (control). Measures of emotion included heart rate and subjective ratings on the Positive and Negative Affect Scale (PANAS). (...) Results showed that ratings of PANAS hostility, irritability, and stress increased during the anger induction, and decreased after the music or silence. Heart rate increased during the anger induction and was sustained (not increased) in the music condition, and decreased in the silence condition. PANAS active and inspired ratings increased during music listening, an effect that was not seen in controls. The findings indicate that extreme music did not make angry participants angrier; rather, it appeared to match their physiological arousal and result in an increase in positive emotions. Listening to extreme music may represent a healthy way of processing anger for these listeners. (shrink)

Understanding everyday behavior relies heavily upon understanding our ability to improvise, how we are able to continuously anticipate and adapt in order to coordinate with our environment and others. Here we consider the ability of musicians to improvise, where they must spontaneously coordinate their actions with co-performers in order to produce novel musical expressions. Investigations of this behavior have traditionally focused on describing the organization of cognitive structures. The focus, here, however, is on the ability of the time-evolving patterns (...) of inter-musician movement coordination as revealed by the mathematical tools of complex dynamical systems to provide a new understanding of what potentiates the novelty of spontaneous musical action. We demonstrate this approach through the application of cross wavelet spectral analysis, which isolates the strength and patterning of the behavioral coordination that occurs between improvising musicians across a range of nested time-scales. Revealing the sophistication of the previously unexplored dynamics of movement coordination between improvising musicians is an important step towards understanding how creative musical expressions emerge from the spontaneous coordination of multiple musical bodies. (shrink)

This article discusses Jerrold Levinson's theory of concatenationism, which emphasizes the moment-by-moment character of musical listeners’ basic musical understanding, and the related project of anti-architectonicism, which denies the influence of large-scale music-structural information on basic musical understanding. A reconstruction of Levinson's position reveals him to embrace a qualified architectonicism himself and shows that his remaining anti-architectonicism is afflicted with several problems. While the conceptual distinction Levinson draws between a piece of music and its structure as well as (...) his three “intuitions for concatenationism” all point toward important features of musical understanding, it is argued that none of them supports the anti-architectonicist thesis in the intended manner. Furthermore, the way Levinson relates both musical understanding and musical value to a notion of aural cogency renders it difficult to see how one could understand music that one does not value or value music that one cannot understand. It is argued that the anti-architectonicist focus of Levinson's project, together with the ensuing argumentative problems, follows from methodological commitments that might be overcome within disciplinary frameworks beyond philosophy. Suggestions are given for developing a positive concatenationism both in musicology and in philosophical aesthetics. (shrink)

This paper aims to achieve a better understanding of what Socrates means by “sumfvne›n” in the sections of the Phaedo in which he uses the word, and how its use contributes both to the articulation of the hypothetical method and the proof of the soul’s immortality. Section I sets out the well-known problems for the most obvious readings of the relation, while Sections II and III argue against two remedies for these problems, the first an interpretation of what the sumfvne› (...) n relation consists in, the second an interpretation of what sorts of thing the relation is meant to relate. My positive account in Section IV argues that we should take the musical connotations of the term seriously, and that Plato was thinking of a robust analogy between the way pitches form unities when related by certain intervals, and the way theoretical claims form unities when related by explanatory co-dependence. Section V surveys the work of IV from the point of view of the initial difficulties and suggests further consequences for the hypothetical method, including the logical relation between the sumfvne›n and diafvne›n relations, and the need for care in ordering the results of a hypothesis. -/- “But anyhow I proceeded in this way: on each occasion hypothesising the lÒgow which I judged to be strongest, I put down as true the things that seem to me to sumfvne›n with it – both about a causal account and any of the other things that are – but those things that did not I put down as false.” (Phaedo 100a3-7). -/- “But if someone clung to the hypothesis itself, you would bid him goodbye and wouldn’t answer him until you had examined its results, whether according to you they sumfvne› or diafvne› with one another.” (Phaedo 101d3-5). (shrink)