Well-Tempered Clavier Research Articles

“Through the Forest of Language”: For All We Know by Ciaran Carson

Time present and time past Are both perhaps present in time future And time future contained in time past. (T.S.Eliot, Burnt Norton, Four Quartets) Upon its publication in 2008, For All We Know was variously described in press as an intricately-worked psychological and political thriller (Sampson 2008), cryptic verse-fiction of an unusual, original kind (Brownjohn 2008) or still startlingly original and mysterious (Emmitt 2008). It was included in Collected Poems published in October of same year. Yet, it seems that work has not since been fully acknowledged, some critics preferring his later poetical works, On Night Watch (2009) and Until Before After (2010). According to Helen Emmitt, title of book would have been inspired by an eponymous popular song dating from 1934 and later taken up by Nat King Cole. In that case one might also evoke another song written film Lovers and Strangers in 1970. Both songs underline unreal and fugitive aspect of relation between two protagonists, two strangers that are Gabriel and Miranda at their first meeting. However, it appears that aim of writer goes far beyond such a conjecture, however right it may have been. As Elmer Kennedy-Andrews writes, the text--open, nonlinear, non-hierarchical, 'dimension-bending', multivoiced--resists domination by any single, unitary or totalizing narrative or perspective (Kennedy-Andrews 2009: 247). Ciaran Carson's primary interest remains language itself as he said in an interview granted to The Guardian in 2009: not that interested in ideologies, I'm interested in words, and how they sound to me, how words connect with experience, of fear, of anxiety (Eidemariam 2009: 12). Owing to fragmented construction of his poetry, and of his prose, one may say that writer is looking a form of writing that is not fixed, that would leave meaning free, suspended as it were. The polysemous phrase for all we know is a theme which runs throughout Carson's work, referring to knowledge, its nature and limits (Kennedy-Andrews 2009: 22). Indeed, as Neal Alexander has observed, Carson often returns to and reworks themes and forms employed earlier in his career, in much same manner in which a musical fugue unfolds through a series of subtly modulated repeats and refrains (Alexander 2010: 2). We shall first see what the rules of are in For All We Know then we'll look at writer's deconstruction of poetic narrative and way he reaches a new reality through a web of metaphors and images. The rules of game Significantly, book's first epigraph is an old French song, extracts from which appear at times in course of poems. The fact that wrote in afterword that he had misquoted a line from this song learnt by his sister during her school years at a Dominican convent in Belfast is another wink to readers to remind them of impossibility of conveying any certainty. As Antoine Compagnon has demonstrated, epigraph is a means author to set his text in relation with other texts and to deliver it to mirrors of literature and art: [I]t is above all an icon, in sense of a privileged entry into enunciation (1) (Compagnon 1979: 337). The second epigraph taken from Glenn Gould who is considered as one of best specialists of John Sebastian Bach, more particularly his Well-Tempered Clavier, highlights poet's aim: Fugue must perform its frequently stealthy work with continuously shifting melodic fragments that remain, in 'tune' sense, perpetually unfinished. Indeed fugue, which reached a degree of perfection in work of Cantor of Leipzig, rests upon principle of imitation, reproduction of melodic fragment at various levels of sound edifice (2) (de Cande 1977: 110), a practice that leaves absolute freedom to musician. …

Was the "Well-Tempered Clavier" Performable on a Fretted Clivichord?

Analysis of the Wohltemperirtes Clavier shows that some of the fretting schemes for clavichords used in Bach's time permit performance of the work with approximately 179 voice-leading conflicts, of which five are difficult to perform and two impossible.

Tonality and transformation

This book employs transformational theory to illuminate the experience of tonal music. In addition to providing an accessible primer on transformational theory, the book introduces new theoretical constructs to model familiar tonal effects. Two effects are central: the infusion of sounding pitches with tonal qualities (or qualia) and the orientation of pitches toward a tonic. Tonal qualities are modeled via a Generalized Interval System (or GIS), while tonic directedness is modeled by oriented transformational networks. The arrows in such networks animate a special class of transformational action called tonal intention—the directing of the listener's awareness toward a tonal center. The book divides into two parts. Part I addresses theoretical and methodological issues, while Part II comprises four extended analytical chapters. The analytical chapters explore the E-major Fugue from Book II of the Well-Tempered Clavier; the aria “Un’aura amorosa” from Mozart's Così fan tutte; Brahms's A-major Intermezzo, op. 118, no. 2; and the slow movement from Brahms's String Quintet, op. 111. Analytical vignettes are present throughout Part I as well, demonstrating the efficacy of the book's theoretical ideas in music from Bach to Mahler. The analyses place the book's novel technologies in dialogue with existing methods for tonal analysis, including Schenkerian theory and neo-Riemannian theory.

Shostakovich’s Preludes and Fugues: Context, Style, Performance (review)

Shostakovich's Preludes and Fugues: Context, Style, Performance. By Mark Mazullo. New Haven, CT: Yale Uni - versity Press, 2010. [xviii, 286 p. ISBN 9780300149432. $60.] Music examples, notes, discography, index. The past decade has seen a burgeoning interest in the and life of Shosta - kovich. Mark Mazullo here proffers an attractive if also slightly out-of-the-ordinary monograph to contribute to this growing body of scholarship. What is unusual is that this book is not intended primarily for musicologists, theorists, or scholars per se (p. xii). Mazullo wants to have a wider readership and hence has collated his insights, gained through considerable experience studying, playing, listening, and teaching Shostakovich's op. 87 cycle of preludes and fugues for piano into a book designed for Shostakovich enthusiasts-musicians and non-musicians alike-with a basic understanding of theory. Arousing further curiosity is the book's explicitly stated non-thesis: to use the author's words, it does not . . . purport to prove anything about Shostakovich or his music (p. xii). As such, this is a work of criticism written in a style similar to Donald Francis Tovey's memorable Essays in Musical Analysis (6 vols. [London: Oxford University Press, 1935-1939]). Composed in 1950-51 in under five months, the Preludes and Fugues initially encountered the hostile reception of a Soviet state under the influence of Zhdanovism, which accused Shostakovich and notable contemporaries such as Myaskovsky, Prokofiev, and Khachaturian of formalism and anti-Soviet tendencies. This gave way to a more favorable reaction thanks to the advocacy of the work's dedicatee, Tatiana Nikolayeva, who premiered in December of 1952. Since that time, and more unreservedly since the composer's formal rehabilitation by state decree in 1958, Shostakovich's op. 87 has assumed a significant, almost legendary status in the Russian canon and the pianist's repertoire alongside Bach's Well-Tempered Clavier upon which was modelled. The work took much longer to be accorded any recognition in the West, however, and has received little air time until fairly recently. Indeed, was less than a decade after its composition that Western scholars, no doubt also reflecting some cultural and politically-motivated bias, condemned the work. Read for instance the comments of T. G. Edridge, who extolled the virtues of Hindemith's Ludus Tonalis, Reger's op. 99, and even Franz Reizenstein's contribution to the prelude-and-fugue genre, but derided Shostakovich's op. 87 with the statement that although they may flicker into life occasionally, they remain on the whole an obdurately dull if impressive testimony of the skill of the most fugally minded of Russian composers (T. G. Edridge, Pre - lude and Fugue Relationships, The Musical Times 101, no. 1407 [May 1960]: 299). Mazullo calls for a circumvention of politics in the assessment of Shostakovich's and tries valiantly to evade the revisionist and counter-revisionist polemics that have plagued assessments of Shostakovich. Yet for Mazullo, this is political strictly by virtue of being personal (p. 8). He also finds its challenging to conceal his sympathy for the revisionists' viewpoints (see pp. 57-58, 97, and 133 for examples). He also finds tricky to reconcile what he believes is an invitation from the composer to listen for the plot (p. 196)-the rationale behind his support for performers to add expressive gestures not necessarily marked in the score but perhaps implied through their own programmatic readings of it)-with the fact that the preludes and fugues possess neither an official nor a 'sub-textual' program (p. 212). He attempts to reinforce the latter point through a rather vacuous exhortation we need to focus on the 'whats' and the not the 'what ifs' (p. 243), but one wonders if he believes that op. 87 can be considered prima facie a work of absolute music. Mazullo does a commendable job in surveying each prelude and fugue, describing its sounding surface, phraseology, harmonic, rhythmic, and textural profiles, relationships between prelude and fugue, and narrative associations; and provides useful performance suggestions. …

Horace Judson (1931–2011)

Horace Judson (1931–2011)

Compactness in the Euler-Lattice: A Parsimonious Pitch Spelling Model

Compactness and convexity have been shown to represent important principles in music, reflecting a notion of consonance in scales and chords, and have been successfully applied to well-known problems from music research. In this paper, the notion of compactness is applied to the problem of pitch spelling. Pitch spelling addresses the question of how to derive traditional score notation from 12-tone pitch classes or MIDI. This paper proposes a pitch spelling algorithm that is based on only one principle: compactness in the Euler-lattice. Generally, the goodness of a pitch spelling model is measured in terms of its spelling accuracy. In this paper, we concentrate on the parsimony, cognitive plausibility and generalizability of the model as well. The spelling accuracy of the algorithm was evaluated on the first book of Bach's Well-tempered Clavier and had a success rate of 99.21%. A qualitative discussion of the model's cognitive plausibility, its parsimony and its generalizability is given.

Bach for solo harpsichord

With repertory ranging from three works in the Möller Manuscript to The art of fugue, this batch of recordings spans most of J. S. Bach's creative working life. The interpretative accounts vary from traditional brilliance to enlightened experimentation, thus providing a snapshot of today's ever-diversifying throng of musicians in the arena of historically informed performance. Variety is most apparent in the two contrasting sets of Bach: Well-tempered clavier, Book 1. Whilst Luc Beauséjour (Naxos 8.557625–26, rec 2005, 111′) plays on a delicately quilled Saxon-influenced instrument, Peter Watchorn (Musica Omnia mo0201, rec 2005, 145′) uses a resonant pedal harpsichord, where the manuals are after Ruckers, Blanchet and Taskin, and the pedals follow the general scaling of the Hass workshop. With the exception of four preludes, the sonorous tones of Watchorn's instrument result in performances that are slower (and often grander) than Beauséjour’s. The independent pedal division comes into its own in the conclusive bass entries of subjects in the five-part fugues, and the ricercare-like Fugue in C♯ minor unfolds like a cataclysmic Gothic drama. Such conviction is reminiscent of Wanda Landowska and, similarly, there are some quirky mannerisms. The Prelude in E minor opens with a curious hiatus and the modulation into C major is highlighted disproportionately, suggesting that one has unwittingly become party to an aural analysis. The fugues in C, F and F♯ minors also sound somewhat laboured: but elsewhere the pacing is masterful. Contrapuntal lines are well delineated with crisp and, in the case of the Fugue in F major, characterful articulation. Registral changes are judiciously employed within pieces, allowing for essential episodic relief in the anguished ‘Crown of Thorns’ Fugue in B minor. Given the use of da capo in the Goldberg Variations, Watchorn's ensuing repeat of the opening prelude seems surprisingly unusual here. Its striking reappearance effectively completes the tonal circle.

Thematic Return in Late Bach Fugues

This article examines a technique employed in a number of Bach's late keyboard fugues, some of his finest. A subsidiary thematic element—typically (though not always) a countersubject—established at the beginning is then dropped for a large section of the music, only to return near the end. 'Returns' of this sort, over and above returns of the subject itself, are far less strong than 'recapitulations', but they affect the formal dynamic in subtle ways. The most familiar example is in the Fugue in E major from The Well-Tempered Clavier, Book 2, where the distinctive countersubject used in the opening exposition, after disappearing in the successive stretto entries of this work, returns at the end with special prominence.

An Intersubjective Approach to Music Therapy: Identification and Processing of Musical Countertransference in a Music Psychotherapeutic Context

ABSTRACT: The role of music therapist is to be there for and with client in and outside music. This article describes how music therapist in musical interaction can be there for and with client at same time as he/she is there for him/herself. This is demonstrated through clinical examples that focus on defining, identification and effective work with musical countertransference as a tool of insight and assessment. The clinical settings include private practice, postgraduate training, internship training, and a short and long term rehabilitation facility. My hope is to reach graduate and postgraduate music therapy clinicians and educators. The educational basis for my work is a Master's degree in Music Therapy, a training in Analytical Music Therapy by lhe founder of AMT Mary Priestley, a Master's degree in Music Education, and 20 years of providing Analytical Music Therapy supervision. What is role of music therapist?'The answer is simple: Being there musically and, if needed, verbally for and with client. What could this mean? We will begin with a music example from work in private practice-a piece of music from end of second session with an adult client, Erik, a 29-year-old man, who was depressed, lonely and grieving. He is vocalizing and am accompanying him on piano. am being there for and with him? Make a judgment yourself. Scheiby excerpt #1, music therapist is playing improvised version of J. S. Bach: in B minor on piano. Client is crying during music. Before music asked Erik: How would you like to end session? He answered, I was thinking that perhaps you could play something for me-something lonely, Bach perhaps. chose to play J.S. Bach's Prelude in B Minor from The Well-Tempered Clavier. My initial reason for choosing that piece by Bach was my perception of its color of sadness that could possibly match client's feelings. Equally important was that it could perform a strong holding function that he needed at that point. Soon after music started Erik began crying and crying became more intense. He had been holding back his tears after first improvisation that we had played together in session. was surprised by intensity of his crying, and it affected me in a countertransferential way. As one can hear, there is a certain heaviness in way articulated tones. When played second part of piece and Erik cried again, this time more intensely, played in a faster tempo, as if wanted it to end quickly because intensity of his expression was too much for me. Erik was grieving because his father was dying. His father had left home due to a divorce and moved to another country when Erik was very young. As a result, he also tapped into his sadness about having had so little time with his father as a child. Moreover, he was depressed because his situation at that time was one of loneliness and isolation. He was also recovering from a liver dis ease that had left him feeling depleted. The concept of countertransference was originally identified by Freud (1910): Countertransference can be regarded as a result of client's influence on his {the analyst's} unconscious (p. 145). Analytical music therapist Mary Priestley (1975) defines countertransference as the therapist's identification with unconscious feelings, self-parts (instinctive self, rational self or conscience) or internal objects of client, which, being conscious in therapist, can serve him as a guide to client's hidden life (p. 240). In above example, my countertransference, that manifested itself in music by a heavy articulation and a sudden faster tempo, was elicited by my unconscious identification with client's strong emotional expression. My own father died when was three months old, and 1 had experienced feelings of loss and sadness that were related to missing strong masculine holding at an early age. …

Perfect harmony: A mathematical analysis of four historical tunings

In Western music, a musical interval defined by the frequency ratio of two notes is generally considered consonant when the ratio is composed of small integers. Perfect harmony or an "ideal just scale," which has no exact solution, would require the division of an octave into 12 notes, each of which would be used to create six other consonant intervals. The purpose of this study is to analyze four well-known historical tunings to evaluate how well each one approximates perfect harmony. The analysis consists of a general evaluation in which all consonant intervals are given equal weighting and a specific evaluation for three preludes from Bach's "Well-Tempered Clavier," for which intervals are weighted in proportion to the duration of their occurrence. The four tunings, 5-limit just intonation, quarter-comma meantone temperament, well temperament (Werckmeister III), and equal temperament, are evaluated by measures of centrality, dispersion, distance, and dissonance. When all keys and consonant intervals are equally weighted, equal temperament demonstrates the strongest performance across a variety of measures, although it is not always the best tuning. Given C as the starting note for each tuning, equal temperament and well temperament perform strongly for the three "Well-Tempered Clavier" preludes examined.

Pianists That Time Forgot

It is same in almost every field of endeavor: big stars shine so brightly they blot out many others whose efforts are also worthwhile. Over past century of recordings, we have had many famous and excellent pianists who have made major recording careers: Sviatoslav Richter, Artur Schnabel, Artur Rubinstein, Vladimir Horowitz, Wilhelm Backhaus, Vladimir Ashkenazy, and many others. But record-collecting pianophiles know that there are also many major pianists who are forgotten by all but a handful of specialists. Here are a few of my favorites. ROSITA RENARD A hardcore pianophile friend of mine once told me that he was listening to my radio program, Grand Piano, and heard me doing a preview for next show. I referred to the greatest pianist you've never heard of, and he thought immediately of Rosita Renard (1894-1949). And he was right. Renard has one of sparsest discographies of any major pianist. Although she played several times in United States and Europe, she spent most of her career in Chile, where she recorded a handful of 78 rpms for Victor and Brunswick. During World War II she was discovered by conductor Erich Kleiber, and in 1949 she performed in New York, at Carnegie Hall, for first time in more than two decades. Her concert was a great success, and she returned to Chile to prepare for a United States tour. But she contracted encephalitis, and died at age of fifty-five. Fortunately, Renard's Carnegie Hall recital was recorded. It was originally issued in a limited LP edition by Society of Friends of Music of Bogota (perhaps a bogus organization, since LPs were only issued in United States), then reissued by International Piano Archives (IPA 120/121, 1977). Its current edition on compact disc (VAI Audio VAIA/IPA 1028-2) is supplemented by a generous selection of Renard's 78s. The recital shows a great pianist at very highest level. She plays Bach's Partita no. 1, BWV 825, and Mozart's Sonata in A Minor, K. 310, very swiftly and cleanly, and with tremendous drama. Her Chopin etudes are breathtaking. This is, frankly, one of greatest recorded live piano recitals ever issued. While material from 78s is not as exciting, lacking stimulus of live audience, it is still consistent with level of pianism and musicianship heard in live concert. There are a few more Renard 78s not part of this collection, including a set of same Mozart sonata. Some Renard Beethoven performances, from 78s and airchecks, were included on a private LP so obscure that it does not have a label name. Until some enterprising label picks up these items for another compact disc, they will be inaccessible to nearly everyone. But VAL set is enough to convince us of Renard's greatness. RICHARD BUHLIG Buhlig (1880-1952) was an American pianist and teacher. He made no commercial recordings at all, only a few piano rolls. At his home in Los Angeles in 1938, he made some private acetates, playing in his living room, which reveal him to have been a titan. Unfortunately, a serious memory slip mars fugue in Beethoven's Hammerklavier Sonata, no. 29, but otherwise (and throughout Sonata no. 30 as well) playing is engrossing and mesmerising, as it is in Bach's Chromatic Fantasy and Fugue and an excerpt from book 2 of his Well-Tempered Clavier. The sound quality of these old home recordings is quite listenable. All of this material was issued as Dante HPC 015, but recording has now disappeared from catalogs with collapse of company in 2001. It is well worth searching for. YOURA GULLER This Romanian Jewish pianist (her religion is relevant due to her obscurity during Second World War) was born in 1895 and died in 1980. In 1920s, she had a substantial career, including associations with numerous composers and such highlights as performing cycle of Beethoven violin sonatas with Joseph Szigeti. …

Two Bach Preludes/Two Chopin Etudes, orToujours travailler Bach–ce sera votre meilleur moyen de progresser

Chopin’s Ž rst acquaintance with the music of Bach dates back to his childhood in Poland and his Ž rst teacher; thus, Bach seems to have been with him from the beginning. But after his arrival in Paris in 1831 at age 21, two years after Mendelssohn had conducted the “St. Matthew Passion” in Berlin but before Bach had fully recovered from his long period of neglect, Chopin became a truly passionate devotee of Bach’s music. These were the years when he wrote the Etudes and Preludes—works, in particular, that show a strong in uence of Bach. In 1838, Chopin, in Majorca with George Sand, wrote to his friend and copyist, Julian Fontana, from “a huge deserted Carthusian monastery where in a cell with doors larger than any carriage-gateway in Paris you may imagine me with my hair unkept, without white gloves and pale as ever. The cell is shaped like a tall cofŽ n, the enormous vaulting covered with dust, the window small . . . Close to [my] bed is an old square grubby box which I can scarcely use for writing on, with a leaden candlestick (a great luxury here) and a little candle. Bach, my scrawls [Chopin refers to his Preludes] and someone else’s old papers . . . Silence . . . you can yell [but] still silence.” The next year, he wrote—this time from George Sand’s estate in Nohant, since the Majorcan trip had been largely disastrous—that “when I have nothing particular to do I am correcting for myself, in the Paris edition of Bach, not only the mistakes made by the engraver but those which are backed by the authority of people who are supposed to understand Bach—not that I have any pretensions to a deeper understanding, but I am convinced that I sometimes hit on the right answer.”1 Much later, Chopin’s piano students continued to attest to his knowledge, from memory, of much of the WellTempered Clavier.2 Thus the alternate title of this article, Chopin’s advice to his pupil Madame Dubois during his last meeting with her in 1848 (a year before his death), is advice that he himself took very seriously indeed. For quite some time now, Chopin’s debt to Bach has been well known, particularly with respect to surface resemblances between Bach’s C-major Prelude (wtc I) and Chopin’s Etude op. 10, no. 1. Early in this century, Hugo Leichtentritt even went so far as to show how Chopin’s harmonic scheme could be rendered in Bach’s Ž guration, and recently, Simon Finlow has demonstrated the reverse, as seen in Examples 1(a) and (b).3 Allen Forte and Stephen Gilbert have shown that the resemblance is more than superŽ cial—that it affects deeper-level musical structure of the

A Hierarchical Self-orginising Map Model for Sequence Recognition

This paper presents an analysis of an original hierarchical neural model on a complex sequence - the complete sixteenth fourpart fugue in G minor of the Well-Tempered Clavier (vol 1) of J. S. Bach. The model makes an effective use of context information, through its hierarchical topology and embedded time integrators, and that enables it to keep a very good account of past events. The model performs sequence classification and discrimination efficiently. It has application in domains which require pattern recognition, or particulary, which demand recognising either a set if sequences of vectors in time, or sub-sequences into a unique and large sequence of vectors in time.

Neue Bach-Ausgabe keyboard offprints

Neue Bach-Ausgabe keyboard offprints Get access Johann Sebastian Bach: Keyboard arrangements of works by other composers, i: 6 concertos after Vivaldi and others, BWV972-977, ed Karl Heller (Kassel: Barenreiter, 1997), £9.50 Johann Sebastian Bach: Preludes, fughettas composed in conjunction with The Well-tempered Clavier II, ed. Alfred Durr (Kassel: Barenreiter, 1995), £5. 95 Johann Sebastian Bach: The Art of Fugue for harpsichord (piano), bwv1080, ed. Klaus Hofmann (Kassel: Barenreiter, 1998), £19.50 David Ledbetter David Ledbetter Search for other works by this author on: Oxford Academic Google Scholar Early Music, Volume XXVII, Issue 4, November 1999, Pages 664–667, https://doi.org/10.1093/earlyj/XXVII.4.664 Published: 01 November 1999

What's Key for Key? The Krumhansl-Schmuckler Key-Finding Algorithm Reconsidered

This study examines the Krumhansl-Schmuckler key-finding model, in which the distribution of pitch classes in a piece is compared with an ideal distribution or "key profile" for each key. Several changes are proposed. First, the formula used for the matching process is somewhat simplified. Second, alternative values are proposed for the key profiles themselves. Third, rather than summing the durations of all events of each pitch class, the revised model divides the piece into short segments and labels each pitch class as present or absent in each segment. Fourth, a mechanism for modulation is proposed; a penalty is imposed for changing key from one segment to the next. An implementation of this model was subjected to two tests. First, the model was tested on the fugue subjects from Bach's Well-Tempered Clavier; the model's performance on this corpus is compared with the performances of other models. Second, the model was tested on a corpus of excerpts from the Kostka and Payne harmony textbook (as analyzed by Kostka). Several problems with the modified algorithm are discussed, concerning the rate of modulation, the role of harmony in key finding, and the role of pitch "spellings." The model is also compared with Huron and Parncutt's exponential decay model. The tests presented here suggest that the key-profile model, with the modifications proposed, can provide a highly successful approach to key finding.

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The Piece as a Whole: Studies in Holistic Musical Analysis

Preface Introduction Chopin: Prelude No. 7 in A Major The Split Fifth: A Cautionary Tale Chopin: Prelude No. 4 in E Minor Meaning in Music Some Mozart Excerpts Beethoven: Fifth Symphony Three Beethoven Excerpts Aesthetics: Aesthetics Meets Ethics Two Schumann Songs and a Bit of Brahms J. S. Bach: The Well-Tempered Clavier, Book I Wagner: Prelude to Tristan and Isolde Debussy: Prelude to The Afternoon of a Faun The Analysis of Twentieth-Century Music Suggestions for Further Reading Index

A Hierarchical Self-Organizing Map Model for Sequence Recognition

A novel neural model made up of two self-organizing maps nets – one on top of the other – is introduced and analysed experimentally. The model makes effective use of context information, and that enables it to perform sequence classification and discrimination efficiently. It was successfully applied to real sequences, taken from the third voice of the sixteenth four-part fugue in G minor of the Well-Tempered Clavier (vol. I) of J.S. Bach. The model has an application in domains which require pattern recognition, or more specifically, which demand the recognition of either a set of sequences of vectors in time or sub-sequences into a unique and large sequence of vectors in time.

Aesthetic preferences for combinations of color and music.

135 university undergraduates heard 12 preludes from J. S. Bach's Well-tempered Clavier (Vol. 1) while viewing alternating red, yellow, green, and blue colored lights. Their task was to rank-order the lights according to how well they "matched" the music. Preferences for combinations of color and music differed depending on whether the music was in a major or a minor key. The present findings along with those of some earlier studies suggest that aesthetic experience may be heightened when colors are seen that match the mental images music evokes.

Method of and apparatus for computer-aided generation of variations of a sequence of symbols, such as a musical piece, or other data, character or image sequences

A procedure for generating different variations of a sequence of symbols, such as a musical piece, based on the properties of a chaotic system--most notably, sensitive dependence on the initial condition--is described and demonstrated. This method preferably uses a fourth order Runge-Kutta implementation of a chaotic system. Bach's Prelude in C Major from the Well-Tempered Clavier, Book I serves as the illustrative example since it is well-known and easily accessible. Variations of the Bach can be heard that are very close to the original while others diverge further. The system is designed for composers who, having created a through-composed work or section, would like to further develop their musical material. The composer is able to interact with the system to select various versions and change them, if desired. Yet the compositional character of the variations remains within the artist's domain of style, expression and inventiveness. The procedure, however, is more generically applicable to other dynamic symbol sequences than music, as well.