|
This
is a bibliography of sources related to the Golden
Section in Music, the Fine
Arts, Architecture, Aesthetics, Gestalt Theory, Theory of Proportion etc.
For an introduction, visit Dr. Knott's pages. M.Mus.
Martin Morgenstern |
| Introduction |
| Music and the Golden Ratio |
| Psychomusicology etc. |
| Gestalt Theory and Perception |
| 'Golden' Works in Music History |
| Music Aesthetics |
Some of the books are listed
at 
UK readers: It may be cheaper to order books via the American page Amazon.com rather than buying them at Amazon.co.uk. |
|
Reis, Helmut Natur und Harmonik Series: Orpheus-Schriftenreihe zu Grundfragen der Musik. no: 67 Bonn, Germany: Verlag fur Systematische Musikwissenschaft 1993 p. 492. ISBN: 3-922626-67-0 (ouch: 56.00 Euro) Abstract:
Presents an organic vision of nature incorporating harmonic theory by discussing
a wide range of topics in their relation to harmony: music heard in terms
of whole-number relationships, colors as a wave phenomenon, properties of
crystalline structure, the spectral series of atoms, and the Golden Section
seen in the Fibonacci series applied to plant structure. The question of
symmetrical and harmonic relationships in natural numerical phenomena is
explained in an innovative way. A new harmonic perspective on color and perception
of color is opened using symmetrical theory. (author)
Boselie. F
Hausmann, Axel Norderstedt:
Book on Demand, 2001
ARCHIBALD. Raymond
Clare
Moore, Joan Moore, Joan
NEUWIRTH, G.
v. NAREDI-RAINER,
P.
Ghyka, Matila
C.
Abstract: The extensive pertinent literature
falls into two groups. One approach finds connections between the Golden
Section and elementary musical principles such as the intervallic system,
whereas another sees the Golden Section as an organizational principle in
specific works. Kepler's Harmonices mundi (1619) and the concept of "constant
division" proposed by the anthroposophist Ernst Bindel are discussed, and
analyses of compositions by Dufay, Bach, Mozart, Beethoven, Debussy, and
Bartok are presented. (author) This is a truly great article investigating
all the myths and assumptions related to the Golden Section in Music. If
you are interested in the topic and able to read German, start with this
one. Should be possible to get via any Interlibrary Loan at your local library.
Good luck! WEBSTER, J.H.D.
PANOFSKY, E.
NORDEN, H.
HOFMANN, W. Well, well.
A composer explaining why he used the Golden Ratio in his recent works. Thank
you, Herr Hofmann.
PASCOE, C.
SOLOMON, L.
J.
HAASE, R.
ADAMS-WEBBER,
J.
POWELL, N. W.
Lefebvre, Vladimir
A. Abstract: A hypothetical law governing generation of aesthetically attractive proportions in music and geometry is introduced. From this law, the just intonation set, the Golden Section, and other geometrical ratios are shown to be attractive. This hypothesis is then deduced from a formal model of a subject with many-tiered reflection.(author)
RUSKWORTH, G.
D.
Parsons, Denys A remarkable type of conformity in composers' incipits The music review, vol. 51, no.2 May 1990. p. 133-144. ISSN: 0027-4445 Abstract: The author's Directory of tunes and musical themes (RILM 75-3278) tabulates the rise, fall, or repetition of pitches of successive notes at the start of thousands of tunes. Analysis of many such pitch profiles indicates a remarkable statistical consistency in the use of different patterns by composers of all types and periods. Statistics for vocal themes vary somewhat from those for instrumental works, but overall the degree of consistency found suggests an unconscious law akin to the Golden Section in the history of art.(Duce, Roger)
Escot, Pozzi Abstract: Three songs composed and sung by the women of the Piro people, Peru, are analyzed for their nonlinear construction. These analyses reveal Golden Section proportions. Nonlinearity is relatively new to European thought. However, awareness of other cultures' nonlinear concepts of life and music is important to the understanding of contemporary European art music.(Schreiner, Martin)
MOECKEL, MAX
PERRY-CAMP,
Jane, Sweet Briar Col., Virginia, USA Abstract: Character and the means of temporal survival are revealed in a person's psychological ordering of time. 'Virtual' time, as expressed in temporal art forms (e.g., music and history), demonstrates epistemic character, i.e., a theoretical concept of external time-rhythm in relation to an aesthetic sense of internal time-rhythm. Temporal art forms can be analyzed in terms of symmetry (translatory and proportional), including golden-section symmetry-rhythm. In music, Mozart, notably in his piano sonatas, shows a decided preference for the golden section, thereby leading to speculation on that ratio's appropriateness as a metaphor for our Western sense of time. (Author)
Abstract: The musical use of the Golden Section has its origin in a scientistic musical philosophy based on Pythagoras and giving priority to the eye over the ear. In this regard, the trajectory of music history from the 'grand beginning' of ancient Greece to Xenakis has doubled back on itself. Recent developments in contemporary music reject a visually oriented rationalism in favor of a complex dialectic between the thought-out and the perceived. Exemplification is drawn from Xenakis's Metastasis and Bartok's Contrasts. (Author)
ADKINS, Donald Abstract: It may be that music is perceived in terms of clock time as well as psychological time, and that the structure of this perception often takes the form of Golden proportions. Analysis of orchestral works with composer-indicated metronome markings suggests Golden proportions often occur when sectional lengths are calculated in terms of clock time. Da capo repeats in Classic minuet-trio form create Golden proportions in a high percentage of cases. Seven of Beethoven's nine symphonies form Golden proportional structures when his metronome markings and repeats are observed. A technique for establishing tempo relationships in multi-movement works that emphasize Golden proportions is presented and applied to several orchestral works. (Author)
DORFMAN, Allen
Arthur Abstract: The relatively few considerations of musical form which focus on the proportional relationships among the parts and the whole of a composition have often centered on the Golden Section, whereby a whole is divided into two unequal parts such that the ratio of the smaller to the larger is equal to the ratio of the larger to the whole. Such methods encourage a consideration of the pace at which events that give a composition its unique structure and shape occur proportionate to the whole. The literature on the Golden Section is examined, and a theory of musical form in terms of structure and shape is introduced and applied to the 24 preludes of Chopin, op. 28. (Author)
Terhardt, Ernst Abstract: Information processing is characterized by conditional decisions on hierarchically organized levels. In biological systems, this principle is manifest in the phenomena of contourization and categorization, which are more or less synonymous. Primary contourization--such as in the visual system--is regarded as the first step of abstraction. Its auditory equivalent is the formation of spectral pitches. Hierarchical processing is characterized by the principles of immediate processing, open end, recursion, distributed knowledge, forward processing, autonomy, and viewback. In that conception, perceptual phenomena such as illusion, ambiguity, and similarity turn out to be essential and typical. With respect to perception of musical sound, those principles and phenomena readily explain pitch categorization, tone affinity, octave equivalence (chroma), root, and tonality. They are applied to the tritone paradox here, by way of example.(author) Descriptor: >perception -- cognition -- hierarchical processing
BENT, Ian D Abstract: The work being done by Allen Forte and others in syntactic analysis of music is of fundamental importance. We need a transformational syntax for music, and many of Noam Chomsky's concepts, such as embedding, nesting, and recursion, would have valuable application in music. Schenker's Schichtentheorie does not supply this need, and his Ursatz has very little in common with Chomsky's 'kernel string'. (Author) Descriptor:
Hatzis, Christos
Seifert, Uwe Abstract: Defines psychomusicology as a branch of systematic musicology. In psychomusicology, research on music theory is connected to research on music perception and cognition. Operational models--especially computer simulations and theoretical modeling--are the main methodological tools of explication in psychomusicology. Experimental research and computer modeling are viewed as complementary research strategies in psychomusicology; a general framework for experimental research and simulation studies based on the theory of recursive functions and model theory is essential. A brief introductory review of the main representational formalisms from artificial intelligence, cognitive psychology, and linguistics, as currently used in psychomusicology, is provided. Furthermore, the representational paradigm used in cognitive science is discussed with nonrepresentational views of ecological realism as advocated by the school of J.J. Gibson. A bibliography on psychomusicology is included.(journal)
Eberlein, Roland Abstract: Describes processes which have been involved in the formation of tonal syntax and exemplifies them using musical developments in the Middle Ages. Regularities within musical practice are shown to produce auditory expectations and form musical perception. These expectations cause the formulation of corresponding rules of composition and these rules may have unexpected and far-reaching consequences regarding musical practice. The influence of perceptual universals and of intellectual history on this circular system is demonstrated.(Elschek, Oskar)
Carey, Norman; Clampitt, David Abstract: Pentatonic, diatonic, and chromatic scales share the same underlying structure, that of the well-formed scale. Well-formedness is defined in terms of a relationship between the order in which a single interval generates the elements of a pitch-class set and the order in which those elements appear in a scale. Another characterization provides a recursive procedure for organizing all well-formed scales into hierarchies. Finally, well-formed scales are defined in terms of scale-step measure (aspects of the diatonic set are examined).(author) CRICKMORE, Leon
als Einführung gut geeignet:
LORA, Doris Abstract: Evidence of the perception of patterns in human behavior, structuring of aural stimuli, and response to music is examined in light of Gestalt figure-ground theory and other psychological perspectives. (Virginia Durrschmidt)
VIRET, Jacques Abstract: Studies the organization and form of melody from the psychological perspective of the Gestalttheorie (theory of form) - that the whole is something more and different than the sum of its parts - and brings to light the characteristic features by which melody can be distinguished from a casual sequence of tones. Extends the concept of the 'qualities of the form', elucidated by the theorists of the Gestalt, to the analysis of melody, and finds that the qualities that produce organic unity in melodic form are dominated by intervallic relationships.
Thomas, Roswitha Abstract: The complexities of musical events and attendant perceptual and interpretative processes, are described from the standpoint of gestalt psychology. A linear connection would seem to exist between music and those processes of gestalt apprehension and gestalt structuring that take place as one listens.(Weil, Karola)
Bielawski, Ludwik Abstract: Discussion of the integration of musical form and different facets of temporality, including the prototemporal, biotemporal, atemporal, eotemporal, and the nootemporal. Problems of perception, Gestalt psychology, and historical and cultural influences on musical form are briefly presented.(Avorgbedor, Daniel K.)
WELLECK, Albert Abstract: Since the time of Wundt and Lamprecht the relationship between psychology and the humanities has been disturbed and has regressed; this has affected musicology. Rene Chocholle's insufficient presentation 'Das Qualitatssystem des Gehors' in the 14-v. Handbuch der Psychologie (Hans Thomae) attests to this since such problems as 'absolute' hearing are not even dealt with. Current problems in the psychology of music are examined: 1) The polarity profile, whose alternatives are often stated in such loose categories that the relevant work of E. Jost, E. Kotter and others can hardly be applied; 2) Gestalt psychology and its application to music theory. A highly significant instance of special musical talent in extreme oligophreny throws light on the questions of the essence of music and corroborates the basic ideas of Schopenhauer's philosophy of music. Investigations by R. Frances, the author, and H. Federhofer rely on the objective-methodical pre-eminence of auditory and music-psychological aspects. The pre-eminence, with respect to the virtue of new music, has generally been overlooked in favor of philosophical and sociological aspects. (Hellmut Federhofer)
Stadler, Michael ; Kobs, Michael ; Reuter, Helmut Abstract: Musical experience and musical production are analyzed from the perspective of cognitive self-organization theory. While other theories postulate the perception of information issuing from the environment, the theory of cognitive self-organization assumes the generation of information in the cognitive system itself. Musical communication is a constructive process involving melody, harmony, rhythm, and dynamics, with attribution of emotional values occurring within the listener, as musical examples using gestalt-theory principles of composition demonstrate. Music as a cognitive construction exists only within a certain time-scale. Examples of multistability show the internal activity of the cognitive system. The principles of music generation are mainly the classical Gestalt laws: vicinity, similarity, symmetry, closure, common motion, and continuity. The constructive nature of musical experience is demonstrated by physically impossible sound-structures analogous to M.C. Escher's visual art. Spontaneous creation in collective improvisation occurs as a collective convergence by rhythmic resonance. The significance of the social context of musical production and reception is considered.
Muller, Martin Abstract: Hornbostel was a prototype of an interdisciplinary scientist. He had begun working under Carl Stumpf who headed the Psychological Institute at Friedrich-Wilhelms-Universitat at that time. At this institute, Hornbostel applied Stumpf's "Tonpsychologie" to different cultures and developed a special kind of "Volkerpsychologie": comparative music-psychology. In that context his most important aim was a description and explanation of musical manifestations in different cultures in a manner "adequate" to these cultures (kulturadaquate Beschreibung). Hornbostel carried positions that were already established in this domain over to other fields of cross-cultural investigation and research, i.e. intelligence. He worked together with other scholars and scientists around Stumpf, especially with Max Wertheimer, who formed what was known to become the "Berlin School of Gestalt Psychology". As a gestalt-psychologist, Hornbostel made original contributions to research in the fields of visual and aural perception and psychophysics.
Cascone, Kim Abstract: [unedited] Discusses the "glitch" or "noise" movement in avant-garde popular music, outlining some of its historical percursors in serious music. Inteprets the glitch movement's focus on acoustic detritus in terms reminiscent of Gestalt psychology.(journal)
Franek, Marek ; Mates, Jiri Abstract: David Epstein proposes that, in a piece of music, all tempo relations can be expressed by the low order whole number ratios 1:1, 1:2, 2:3, and 3:4 (or the inverse). The theory relates to the Gestalt concept in dealing with part/whole relations and coherence. This study of tempo performance examines possible underlying psychological mechanisms, experimentally investigating the ratios between neighboring tempos that occur when subjects are asked to make arbitrary modulations. Subjects were instructed to make tempo changes defined by vague terms like "small", "large", and "arbitrary" modulation. The finger tapping method was employed. Results show that tempo ratios were characterized by narrow distributions of values. Subjects rarely responded with whole number ratios. Averaged values show that in slow-down conditions (except "arbitrary"), responses were close to whole number ratios; in speed-up conditions, deviations from whole number ratios were greater. Results for speed-up conditions were influenced by systematic temporal error. Relations between neighboring tempos may better be described in terms of categories of tempo difference.
Reybrouck, Mark Abstract: Reappraises some older insights and expands Gestalt concepts from a largely intuitive to an operational approach. The use of the methodology of interdisciplinary research is strongly promoted, and the importance of the cognitive view of elaboration and processing of musical structure is stressed, emphasizing a shift from structural to functional descriptions. Attention is directed to the specificity of music as a temporal and sounding art, memory and imagination, and the tension between actuality and virtuality in the construction of musical gestalts.
Leman, Marc Abstract: Tone semantics is a psychoacoustic-based theory of gestalt perception that deals with the assignment of functional relationships between tones in a musical context. The theory provides an operational account of semantics in terms of complex dynamic systems theory and forms the basis for nonsymbolic research in musical imagination. This is applied to the automatic recognition of tone centers from acoustical input. An analysis of the basic concepts and related epistemological and methodological principles reveals a promising paradigm for research. (Author)
Holler, York ; Trans. by -Osborne, Nigel Abstract: Given a boundless choice of forms and musical elements, the modern composer must create a Gestalt, a method of delimiting space and dividing time. A work of art is like an organism; it results not from arbitrary formulation, but from the evolution of a process. A musical work might be deduced from a single cell, which, DNA-like, contains the plan of the whole. The organic forms of tonal music seem forced and arbitrary nowadays; new Gestalts need to be created. Methods of transforming a chordal Gestalt into a temporal Gestalt are given.(Brooke, Nicholas)
Albrecht, Jan Abstract: The complex interactions among individuals, society, and art are examined. Emotion is seen as the central phenomenon of life. In visual art, the subject is an object, but the point of the work is not to mimic the form, but to convey the function of the object. Since music cannot mimic in the material sense, its aim is to awaken emotion in the listener through its kinetic movement. Sound patterns are seen as units of music, and connections among structural elements are examined. The specific characteristics of music that achieve their effect by structuring the psychological conditions of the listener are analyzed. Principles of cognitive and Gestalt psychology are applied to the study.(Osborne, Suzanne)
Orlik, Franz Abstract: Edmund Husserl's thesis--that the fading away of memory is a linear process--is inappropriate to the way music is received. His theory of attention modification can help to remedy the deficiencies. Transcendental phenomenology as a doctrine of pure experience structures can form a methodological foundation for musicology.(author)
Cumming, Naomi Helen Abstract: An awareness of the potential and the limitations of functionalism and its computational metaphors is valuable to the music analyst and interpreter. The ideas of Leonard B. Meyer, Jerry A. Fodor, Hilary Putnam, Eugene Narmour, Paul Churchland, Fred Lerdahl, and Ray Jackendoff are discussed. Topics include the influence of Gestalt psychology, personal and subpersonal discourse levels, linguistic theory, the implication-realization theory, and both top-down and bottom-up systems.(McIntosh, Nadia)
Morris, Robert D. Abstract: A review of previous works on contour and their application to Schoenberg's Sechs kleine Klavierstucke, op. 19, no. 4, points to the association of the work's pitch-class set segmentations with relations among sets of equivalent contours. The concept of contour reduction algorithm is introduced, based on principles of perceptual organization from Gestalt psychology. The algorithm allows the association of nonadjacent contour pitches according to their degree of salience. Contours can be reduced to one of a set of irreducible prime contours that define their characteristic depth. The application of the algorithm to the six phrases of the Schoenberg piece matches the conclusions of the previous contour/pitch-class set analysis. The hierarchic nature of the algorithm also helps organize the many classes of equivalent contours. The definition of a contour as the association of any two sets leads to the construction of a taxonomy including all possible contours. Contours that include replication and simultaneities are defined by categories in mathematical relation theory. The role of salience in musical structure is discussed. The contour reduction algorithm is compared to reductive methodologies of tonal music and the perceptual Gestalt theories of James Tenney and Larry Polansky. (Author)
Zbikowski, Lawrence Michael Abstract: Systems of grouping are used for analyzing passages, phrases, or sections of music. The idea of a group is similar to that of a gestalt, a concept explored in a proposed theory of cognition drawn from recent research in artificial intelligence, linguistics, anthropology, and the psychological processes associated with categorization. A formalization of systems of grouping for the analysis of musical rhythm, based on this theory, is offered. Taking rhythm as a continuous succession of musical events, grouping systems define groups and relationships between groups as a means of describing changes in this succession of events. Grouping systems are developed for the analysis of 17th-c. works for lute and keyboard, the Vivace from Beethoven's F-major string quartet, op. 135, and Tento 2 from Henze's Kammermusik 1958.(author)
Rothfarb, Lee Allen Abstract: A presentation in translation
of a few passages from Kurth's treatise, providing a historical context for
understanding its significance. The book moves away from formalized, purely
syntactical views of musical events toward a psychological interpretation
of those events, as heard. Going beyond tone-psychological research, Kurth
worked toward a music psychology that would deal with musical phenomena
in context. In this quest, he was stimulated by the fusion concept of Carl
Stumpf, but his mode of thought is closer to the then-emerging holistic views
of Gestalt psychology.(author)
'Golden' Works in Music History HOWAT, Roy Abstract: Since their first publications in the 1950s, the analyses of Bela Bartok's music by Erno Lendvai have been both influential and controversial, but have received little critical evaluation. Lendvai's claims of Golden Section construction in the proportions of many works of Bartok are examined in two of his books, Bela Bartok: an analysis of his music (RILM 1976-00801) and The workshop of Bartok and Kodaly (Budapest: Editio Musica, 1983). Despite some small inaccuracies and ambiguous nomenclature, the author corroborates Lendvai's claims by more detailed analyses of Sonata for two pianos and percussion and Music for strings, percussion, and celesta and refers to analytical work by Elliott Antokoletz and George Perle. The relationship of the conscious and subconscious in Bartok's technique is examined, and symbolic and technical connections to the works of Bartok are traced in music by Claude Debussy, Maurice Ravel, and Zoltan Kodaly. (Author)
Mohr, Jonathan
J.J. Abstract: Examines the extent to which the Golden Section is evident in the form of each movement of Bartok's six string quartets. The relationship between this formal principle and traditional music forms used by Bartok is elucidated. Bartok used the Golden Section as an aid to composition, based in part on the evidence of proportionally unrelated sections that appear to have been later additions to an original fully proportioned scheme. There is also evidence that Bartok used the Golden Section to reinforce musical relationships in the block architecture of his works.(author)
Locke, Derek Abstract: Bartok's use of Golden proportions and Fibonacci numbers is traced through the string quartets nos. 4-6 and other works. The purpose was not so much a matter of obtaining "aesthetic" proportions as of avoiding arbitrariness.(Yaraman, Sevin)
Tusa, Erzsebet Abstract: Traces the relationship of Bartok's forms and proportions with organic (especially plant) structures and with the Fibonacci series and the medial section (the limes of Fn$/ over Fn+1$/).(author)
Sabo, Anica Abstract: An analysis of the first movement of Bartok's Music for strings, percussion, and celesta in terms of the Golden Section and the Fibonacci series. All parameters of the music interact with these mathematical factors to yield the overall pattern of the movement. Tempo change and axis symmetry are disequilibrating forces lying outside the mathematical logic of the Golden Section and the Fibonacci series.
BACHMANN, Tibor
; BACHMANN, Peter J Abstract: Citing examples where the golden section and Fibonacci numerical sequences are used as a structural foundation, the author concludes that Bartok's music is built on and is directly a function of these devices, which clarify and focus the balance and proportion existing in his music. (Nancy M. Bren)
Crystall, Ellen
Barbara Abstract: The role esoteric traditions and the occult have played in the lives and musical works of composers and their associates between 1900 and 1920 is examined. The Golden Section, the Fibonacci number series, and esoteric traditions--belief systems that move beyond the bounds of traditional religion and physical reality--are defined. Background is presented supporting the ancient "music of the spheres" concept that music has power that affects everyone. Pre-20th-c. philosophers discussed are Fabre d'Olivet, Nodier, and Schopenhauer. The extensive influence exerted by esoteric traditions on the arts between 1900 and 1920 is discussed with reference to the Priory of Sion, Theosophy, spiritualism, occultism, Rosicrucians, Freemasons, Society for Psychical Research, the Hermetic Order of the Golden Dawn, Tarot cards, and synaesthesia. Individuals who are discussed include Anton Mesmer, Rudolph Steiner, Georges Gurdjieff, Delacroix, Kandinsky, Mallarme, Papus, Josephin Peladan, and Edmond Bailly. Composers involved with the esoteric have included Mozart, Schumann, Mahler, Wagner, Debussy, Satie, Ravel, Skrjabin, Thomas Hartmann, Parry, Holst, Varese, Schoenberg, Webern, Messiaen, and Stockhausen. The music of Cyril Meir Scott, composer and member of a secret, elitist esoteric circle, is analyzed to demonstrate his use of the Golden Section and musical esoteric references, especially in the piano sonata, op. 66.(author)
Jacobitz, Joachim Abstract: Examines whether and to what extent the Golden Section is evident in rock songs of the 1970s. The mathematical basis and musical application of the principle are discussed, and the songs Child in time by Deep Purple and Holiday by the Scorpions are analyzed. The harmonic structure is so evident on the basis of structogram analysis that it constitutes the basic form of the works. Since it is unlikely that rock musicians will have heard of the Golden Section, its formative presence in the music must have to do with natural intuition.(Wagner, Dorothea)
Berger, Gunter Abstract: A formal analysis of Kayser's concerto for organ. In the first movement the varied repetition of motives is elaborated to create the larger form. The motives of this movement permeate the entire work. The second movement, a scherzo, exhibits proportionality according to the Golden Section, and is somewhat reminiscent of Bartok. The third movement is a rondo based on the last movement of Stravinsky's Le sacre du printemps. The fourth movement is a fugue of up to 8 voices and leads directly to the fifth movement, a finale with tarantella sections.(author)
Roig-Francoli,
Miguel Angel Abstract: Examines the compositional techniques Ligeti uses in building net-structures, webs of finely woven, interacting lines or repeated patterns involved in a process of continual transformation. Pitch reductions are used to analyze the net-structures in Ramifications as well as in the fifth movement of the string quartet no. 2 and the first movement of the chamber concerto. These pitch reductions are based on the chromatic fluctuation of melodic microstructures and those that result from the constant transformation of harmonic cells by means of intervallic expansion or contraction. Ligeti's net-structures are supported by carefully balanced harmonic processes which display both symmetrical arrangements and long-range intervallic structural relationships. The harmonic and textural transformations in net-structure compositions are the main generating elements of large-scale formal designs governed by the Golden Section and other proportional relationships.(author)
Hoffmann-Erbrecht,
Lothar Abstract: The term Klangflachenpraludium is defined and various movements by Fischer, Kuhnau, and Christoph Graupner are examined as well as J.S. Bach's prelude in C-major, Wohltemperirtes Clavier I. Bach's prelude and Kuhnau's works are built on the first- and second-order Golden Section; Graupner prefers an axial structure. Fischer's work is of neither the one nor the other type. Even if one does not accept the doctrine of the Golden Section, the extremely strict proportionality of Kuhnau and Bach is unmistakable.(author)
Linton, Michael
Roy Abstract: The C-major prelude, BWV 870, with which J.S. Bach headed his second volume of Das wohltemperirte Clavier, exists in three authenticated forms. Comparison of these versions suggests that Bach revised his music to more closely fit a formal scheme based on the Golden Section (the various points of the Golden Section in the final version being precisely articulated by Neapolitan chords). The Golden Section form is superimposed on a chiastic form that articulates symmetrical subdominant relationships. Bach's purpose for using this double chiastic design was theological.(author)
KEE, Piet Abstract: Continues the analysis of Bach's organ passacaglia BWV 582 (see RILM 1982-02338-ap). Discusses Bach's use of number symbolism, including the convergence of the point of the golden section (13:21) and the Bach number (14). Other symbolism in the piece equates the thema fugatum with 'Amen' while the two-voiced subject together with the countersubject represents the Trinity. In addition to musical and rhetorical analysis, manuscript sources and questions of interpretation and performance are discussed. The author also addresses the hypothesis that the work was written 'in memoriam' Dietrich Buxtehude. (Author)
Sabatier, Francois Abstract: Traces Bach's episodic application of the Golden Section in his chamber works with organ BWV 541, 542, 547, and 552.
TODUTA, Sigismund
; TURK, Hans Peter Abstract: Examines mathematical relationships (axis symmetry and the golden section), morphological relationships (an organizational interaction of heterogeneous structural principles), and the symbolic meaning with respect to the figures of rhetoric. Compares Bach's practice to the maqam principle, a specific intonation-scheme and summarizing factor. (Armin Schneiderheinze)
Adams, Courtney
S. Abstract: Four of Satie's multimovement sets and six individual movements contain Golden Section proportions that are exact or within a 1% deviation. The sets are the Trois gymnopedies, Les trois valses, Avant-dernieres pensees, and the first three nocturnes. The individual movements are Le fils I, Sonneries I and III, and each of the Trois melodies of 1916. The dates of the Golden Section usage fall both early (1887-92) and late (1914-19). It is hard to say whether the early usage was deliberate, instinctive, or coincidental, but the usage in the late period is too precise and continuous to be other than intentional. Three of Satie's close artist friends were also known to be using Golden Section proportions at the same later period.(Yarmey, Kenneth E.)
Hammill, Jennifer
Lee Abstract: In Mompou's early works, a highly characteristic idiom emerges: the total reharmonization of repeated untransposed melodies. Attention to motivic detail increases steadily. Mompou learns to vary and develop phrases and as a consequence to construct ever larger internal sections. The works of Mompou's Parisian years (1921-41) are characterized by a larger size and formal scope, a more bravura pianistic idiom, and a more open and extroverted emotional tone. During his later years in Barcelona, intellectual and spiritual concerns come to dominate his style. Pianistic textures are simplified, length is reduced, and the harmonic idiom grows more difficult. Every procedure distills and concentrates. An increasing preoccupation with formal concerns leads to the use of the Golden Mean. Contrary to the conventional view, Mompou developed new technical means throughout his career.(author)
Escot, Pozzi Abstract: Mathematical relationships in the music of Continuum for harpsichord and Harmonies underlie the structural proportions of the compositions. In particular, Golden proportions and the Fibonacci series are considered in relation to the unfolding of pitches, intervals, and measured patterns. In both works the pattern of patterns becomes a nebulous constellation of sonic design, yet the mathematical models obtain the overall accomplished plan.(Schreiner, Martin)
HOWAT, R.
RYSCHAWY, H.
/ STOLL, R.W.
SANDRESKY, Margaret
Vardell Abstract: At least three of Dufay's motets were composed for events involving princely families of the Byzantine Empire. Analysis of these works, composed at widely spaced intervals in his career, reveals the composer's use of the golden section as a structural device. The number 13 is used as the basis of form in each motet. Dufay may have chosen this number as a symbol, since the Byzantine emperor was considered to be the 13th apostle of Christ. (Robert Richart)
ATLAS, Allan
W.
BOWERS, Roger
ROGERS, Michael
R Abstract: Analyzes the harmonic and melodic ambiguities of Chopin's prelude in A minor, op. 28, no. 2 and clarifies them by discussing their relationship to the temporal proportion of the golden section (more fully recognized in the visual arts). Offers for comparison a brief analysis of harmonic/tonal golden ratios in the first movement of Beethoven's piano sonata op. 27, no. 2 ('Moonlight'). Pitch details of many tonal compositions can be illuminated by the discovery of durational codes involving pacing and timing. (Author)
KIRK, Kenneth
Patrick Abstract: Each of the 24 preludes, op. 28, exhibits a turning point (TP) after which musical motion is better characterized as 'toward the end' than 'away from the beginning'. Statistical analysis shows that the proportional placement of the 24 TPs cluster around the Golden ratio (.618). The clustering of the TPs around this point and other approximately Golden sections of the preludes are important to the form and aesthetic of the pieces. (Author)
Naredi-Rainer,
Paul Abstract: Several analogies exists between the architecture of Fischer von Erlach and the music of Fux: a mix of early and later techniques, specificity of proportions, and the utilization of the Golden Section.
NEUMEYER, David Abstract: Hindemith made deliberate formal use of principles of proportional structure in his compositions of the 1940s. Relationships of duration, such as the harmonic mean and Golden Section, elucidate Hindemith's 'balanced cooperation' between tonality and form. Several tonal schemes from Hindemith's sketches, tonal/ formal plans for class composition projects, three proportional schemes, and tonal and proportional analyses of Hindemith's Symphonia serena, the wind septet, and the horn concerto are considered. (Katherine A. Richards)
SMITH, Janet
Bass Abstract: Golden proportions were found in 71 percent of the sections or movements. In an interview, the composer mentions his interest in the proportion but states that he had not intentionally used the ratio in his works.
SABY, Pierre Abstract: Beyond its great aural clarity, Nuits by Iannis Xenakis employs a subtle formal organization that activates the play of the proportions of the Golden Section and certain key dimensions of the 'modulor' of Le Corbusier. The search by these means for an architectural 'harmony' in music is an important aspect of Nuits.
Moeller, H.
WILDER, Pamela
Wright Abstract: A study of performance problems, compositional techniques (especially the use of the Golden Section), and the influence of the painter Arnold Bocklin. (Author)
La Motte-Haber,
Helga de In: Conversation
on music, 1984, Salzburg Abstract: The dynamic relationship between mathematical proportion and the representation of emotion in music, makes clear the arbitrariness of mathematical speculations in the constructivism of 20th-c. music. Mathematics and music were able to converge as thought systems only when a common form of divine reason was assumed behind both. (Ruth E. Muller)
Schopenhauer, Arthur The World as Will and Representation (Vol. 1) transl. by E. F. Payne Dover, 1969 (ISBN: 0486217612) note
his thoughts about music having the highest aesthetic value, and its ability
to help to escape |
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