Musical analysis is the attempt to answer the
questionA question may be either a linguistic expression used to make a request for information, or else the request itself made by such an expression. This information may be provided with an answer....
how does this musicMusic is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
work?. The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to
Ian BentIan Bent is Professor Emeritus, after retiring from Full Professor of Music, at Columbia University and Honorary Professor in the History of Music Theory at the University of Cambridge. He is the editor of the Cambridge Studies in Music Theory and Analysis series and an area for second edition of...
(Bent, 1987), analysis is "an approach and method [that] can be traced back to the 1750s ... [though] it existed as a scholarly tool, albeit an auxiliary one, from the
Middle AgesThe Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...
onwards." A.B. Marx was influential in formalising concepts about composition and music understanding towards the second half of the 19th century.
The principle of analysis has been variously criticized, especially by composers, such as
Edgard VarèseEdgard Victor Achille Charles Varèse, , whose name was also spelled Edgar Varèse , was an innovative French-born composer who spent the greater part of his career in the United States....
's claim that, “to explain by means of [analysis] is to decompose, to mutilate the spirit of a work” (quoted in Bernard 1981, 1).
Analyses
Some analysts, such as
Donald Francis ToveySir Donald Francis Tovey was a British musical analyst, musicologist, writer on music, composer, conductor and pianist...
(whose
Essays in Musical AnalysisDonald Francis Tovey's Essays in Musical Analysis are a series of analytical essays on classical music.The "essays" actually came into existence as programme notes written by Tovey to accompany concerts given by the Reid Orchestra in Edinburgh. Between 1935 and 1939 they were published in six...
are among the most accessible musical analyses) have presented their analyses in prose. Others, such as
Hans KellerHans Keller was an influential Austrian-born British musician and writer who made significant contributions to musicology and music criticism, as well as being an insightful commentator on such disparate fields as psychoanalysis and football...
(who devised a technique he called
Functional AnalysisWordless functional analysis is a method of musical analysis developed in the 1950s by the Austrian-born British musician and writer Hans Keller. The method is notable in that, unlike other forms of musical analysis, it is designed to be presented in musical sound alone, without any words being...
) used no prose commentary at all in some of their work.
There have been many notable analysts other than Tovey and Keller. One of the best known and most influential was
Heinrich SchenkerHeinrich Schenker was a music theorist, best known for his approach to musical analysis, now usually called Schenkerian analysis....
, who developed
Schenkerian analysisSchenkerian analysis is a method of musical analysis of tonal music based on the theories of Heinrich Schenker. The goal of a Schenkerian analysis is to interpret the underlying structure of a tonal work. The theory's basic tenets can be viewed as a way of defining tonality in music...
, a method which seeks to reduce all
tonalTonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...
classical works to a simple
contrapuntalIn music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent . It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period,...
sequence.
Ernst KurthErnst Kurth, was a Swiss music theorist.- Career :Kurth studied musicology with Guido Adler in Vienna, and earned his Ph.D with a thesis about Christoph Willibald Gluck's's operatic style...
coined the term of 'developmental motif'.
Rudolph RétiRudolph Reti , was a musical analyst, composer and pianist. He was the older brother of the great chess master Richard Réti ....
is notable for tracing the development of small melodic
motifsIn music, a motif or motive is a short musical idea, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition....
through a work, while
Nicolas RuwetNicolas Ruwet was a linguist, literary critic and musical analyst. He was involved with the development of generative grammar.Ruwet was born in Saive in Belgium and studied philology in Liège...
's analysis amounts to a kind of musical semiology.
Musicologists associated with the
new musicologyThe New Musicology is a term applied to a wide body of musicology with focus upon the cultural study, analysis, and criticism of music, with influences from feminism, gender studies, queer theory, and postcolonial studies...
often use musical analysis (traditional or not) along with or to support their examinations of the performance practice and social situations in which music is produced and which produce music, and vice versus. The insights gained from the social considerations may then yield insight into the methods of analysis, and vice versa.
Edward Cone ("Analysis Today") argues that musical analysis lies in between description and prescription. Description consists of simple non-analytical activities such as labeling chords with Roman numerals or tone-rows with integers or row-form, while the other extreme, prescription, consists of "the insistence upon the validity of relationships not supported by the text." Analysis must, rather, provide insight into listening without forcing a description of a piece that cannot be heard.
Techniques
Many techniques are used to analyze music.
MetaphorA metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
and figurative description may be a part of analysis, and a metaphor used to describe pieces "reifies their features and relations in a particularly pungent and insightful way: it makes sense of them in ways not formerly possible." Even
absolute musicAbsolute music is a concept in music that describes music as an art form separated from formalisms or other considerations; it is not explicitly about anything; it is non-representational. In contrast to program music, absolute music makes sense without accompanying words, images, drama, or...
may be viewed as a "metaphor for the universe" or nature as "perfect form." (Guck cited in Bauer 2004, p. 131)
Discretization
The process of analysis often involves breaking the piece down into relatively simpler and smaller parts. Often, the way these parts fit together and interact with each other is then examined. This process of
discretizationIn mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers...
or segmentation is often considered, as by
Jean-Jacques NattiezJean-Jacques Nattiez, CM, CQ, FRSC is a musical semiologist or semiotician and professor of Musicology at the Université de Montréal...
(1990), necessary for music to become accessible to analysis.
Fred LerdahlAlfred Whitford Lerdahl is the Fritz Reiner Professor of Musical Composition at Columbia University, and a composer and music theorist best known for his work on pitch space and cognitive constraints on compositional systems or "musical grammar[s]." He has written many orchestral and chamber...
(1992, 112-13) argues that discretization is necessary even for perception by learned listeners, thus making it a basis of his analyses, and finds pieces such as
Artikulation by
György LigetiGyörgy Sándor Ligeti was a composer of contemporary classical music. Born in a Hungarian Jewish family in Transylvania, Romania, he briefly lived in Hungary before becoming an Austrian citizen.-Early life:...
inaccessible,(Lerdahl 1988, 235) while Rainer Wehinger (1970) created a "Hörpartitur" or "score for listening" for the piece, representing different sonorous effects with specific graphic symbols much like a
transcriptionIn music, transcription can mean notating a piece or a sound which was previously unnotated, as, for example, an improvised jazz solo. Further examples include ethnomusicological notation of oral traditions of folk music, such as Béla Bartók's and Ralph Vaughan Williams' collections of the national...
.
Composition
Analysis often displays a compositional impulse while composition often expresses "display[s] an analytical impulse" but where "intertextual analyses often succeed through simple verbal description there are good reasons to literally compose the proposed connections. We actually hear how these songs resonate with one another, comment upon and affect one another...in a way, the music speaks for itself".(BaileyShea 2007) This analytic bent most obviously in recomposition including the
mash-upsA mashup or bootleg is a song or composition created by blending two or more pre-recorded songs, usually by overlaying the vocal track of one song seamlessly over the instrumental track of another...
of popular music.
Analytical situations
Analysis is an activity most often engaged in by musicologists and most often applied to western classical music, although music of non-western cultures and of unnotated
oral traditionOral tradition and oral lore is cultural material and traditions transmitted orally from one generation to another. The messages or testimony are verbally transmitted in speech or song and may take the form, for example, of folktales, sayings, ballads, songs, or chants...
s is also often analysed. An analysis can be conducted on a single piece of music, on a portion or element of a piece or on a collection of pieces. A musicologist's stance is his or her analytical situation. This includes the physical dimension or corpus being studied, the level of stylistic relevance studied, and whether the description provided by the analysis is of its immanent structure, compositional (or poietic) processes, perceptual (or esthesic) processes (Nattiez 1990: 135-6), all three, or a mixture.
Stylistic levels may be hierarchized as an inverted triangle:
- universals of music
- system (style) of reference
- style of a genre or an epoch
- style of composer X
- style of a period in the life of a composer
- (Nattiez 1990: 136, he also points to Nettl 1964: 177, Boretz 1972: 146, and Meyer)
Nattiez outlines six analytical situations, preferring the sixth:
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Inductive
poietics |
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poietics |
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| Communication between the three levels |
- (Nattiez 1990: 140)
Examples:
- "...tackles only the immanent configuration of the work." Allen Forte's musical set theory
- "...proceed[s] from an analysis of the neutral level to drawing conclusions about the poietic." Reti's (1951: 194-206) analysis of Debussy's la Cathédrale engloutie
- The reverse of the previous, taking "a poietic document -- letters, plans, sketches -- ... and analyzes the work in the light of this information." Paul Mie's "stylistic analysis of Beethoven
Ludwig van Beethoven was a German composer and pianist. A crucial figure in the transition between the Classical and Romantic eras in Western art music, he remains one of the most famous and influential composers of all time.Born in Bonn, then the capital of the Electorate of Cologne and part of...
in terms of the sketches (1929)"
- The most common, grounded in "perceptive introspection, or in a certain number of general ideas concerning musical perception ... a musicologist ... describes what they think is the listener's perception of the passage." Meyer's (1956: 48) analysis of measures 9-11 of Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...
's C minor fugue in Book I of the Well-Tempered Clavier
- "Begins with information collected from listeners to attempt to understand how the work has been perceived ... obviously how experimental psychologists would work"
- "The case in which an immanent analysis is equally relevant to the poietic as to the esthesic." Schenker
Schenker is a German family name.Schenker may refer to:* Alexander M. Schenker , American slavist* Heinrich Schenker , Austrian music theorist* Rudolf Schenker, German guitarist, founding member of Scorpions...
ian analysis, which, based on the sketches of Beethoven (external poietics) eventually show through analysis how the works must be played and perceived (inductive esthesics)
Compositional analysis
Jacques Chailley (1951: 104) views analysis entirely from a compositional viewpoint, arguing that, "since analysis consists of 'putting oneself in the composer's shoes,' and explaining what he was experiencing as he was writing, it is obvious that we should not think of studying a work in terms of criteria foreign to the author's own preoccupations, no more in tonal analysis than in harmonic analysis."
Perceptual analysis
On the other hand, Fay (1971: 112) argues that, "analytic discussions of music are often concerned with processes that are not immediately perceivable. It may be that the analyst is concerned merely with applying a collection of rules concerning practice, or with the description of the compositional process. But whatever he [or she] aims, he often fails -- most notably in twentieth-century music -- to illuminate our immediate musical experience," and thus views analysis entirely from a perceptual viewpoint, as does Edward Cone (1960: 36), "true analysis works through and for the ear. The greatest analysts are those with the keenest ears; their insights reveal how a piece of music should be heard, which in turn implies how it should be played. An analysis is a direction for performance," and Thomson (1970: 196): "it seems only reasonable to believe that a healthy analytical point of view is that which is so nearly isomorphic with the perceptual act."
Analyses of the immanent level
Analyses of the immanent level include analyses by Alder,
Heinrich SchenkerHeinrich Schenker was a music theorist, best known for his approach to musical analysis, now usually called Schenkerian analysis....
, and the "
ontological structuralism" of the analyses of
Pierre BoulezPierre Boulez is a French composer of contemporary classical music, a pianist, and a conductor.-Early years:Boulez was born in Montbrison, Loire, France. As a child he began piano lessons and demonstrated aptitude in both music and mathematics...
, who says in his analysis of
The Rite of SpringThe Rite of Spring, original French title Le sacre du printemps , is a ballet with music by Igor Stravinsky; choreography by Vaslav Nijinsky; and concept, set design and costumes by Nicholas Roerich...
(1966: 142), "must I repeat here that I have not pretended to discover a creative process, but concern myself with the result, whose only tangibles are mathematical relationships? If I have been able to find all these structural characteristics, it is because they are there, and I don't care whether they were put there consciously or unconsciously, or with what degree of acuteness they informed [the composer's] understanding of his conception; I care very little for all such interaction between the work and 'genius.'"
Again, Nattiez (1990: 138-9) argues that the above three approaches, by themselves, are necessarily incomplete and that an analysis of all three levels is required.
Jean MolinoJean Molino is professeur ordinaire at the University of Lausanne and a semiologist. His students include Jean-Jacques Nattiez.-Bibliography:*Musical Fact and the Semiology of Music, trans. J. A. Underwood, Music Analysis 9/2 : 113-156....
(1975a: 50-51) shows that musical analysis shifted from an emphasis upon the poietic vantage point to an esthesic one at the beginning of the eighteenth century (Nattiez 1990: 137).
Nonformalized analyses
Nattiez distinguishes between nonformalized and formalized analyses. Nonformalized analyses, apart from musical and analytical terms, do not use resources or techniques other than language. He further distinguishes nonformalized analyses between impressionistic, paraphrases, or hermeneutic readings of the text (
explications de texte). Impressionistic analyses are in "a more or less high-literary style, proceeding from an initial selection of elements deemed characeristic," such as the following description of the opening of
Claude DebussyClaude-Achille Debussy was a French composer. Along with Maurice Ravel, he was one of the most prominent figures working within the field of impressionist music, though he himself intensely disliked the term when applied to his compositions...
's
Prelude to the Afternoon of a Faun: "The alternation of binary and ternary divisions of the eighth notes, the sly feints made by the three pauses, soften the phrase so much, render it so fluid, that it escapes all arithmetical rigors. It floats between heaven and earth like a
Gregorian chantGregorian chant is the central tradition of Western plainchant, a form of monophonic liturgical music within Western Christianity that accompanied the celebration of Mass and other ritual services...
; it glides over signposts marking traditional divisions; it slips so furtively between various keys that it frees itself effortlessly from their grasp, and one must await the first appearance of a harmonic underpinning before the melody takes graceful leave of this causal
atonalityAtonality in its broadest sense describes music that lacks a tonal center, or key. Atonality in this sense usually describes compositions written from about 1908 to the present day where a hierarchy of pitches focusing on a single, central tone is not used, and the notes of the chromatic scale...
." (Vuillermoz 1957: 64)
Paraphrases are a "respeaking" in plain words of the events of the text with little interpretation or addition, such as the following description of the "Bourée" of Bach's
Third Suite: "An anacrusis, an initial phrase in D major. The
figureA musical figure is the shortest idea in music, a short succession of notes, often recurring. It may have melodic pitch, harmonic progression and rhythmic . The 1964 Grove's Dictionary defines the figure as "the exact counterpart of the German 'motiv' and the French 'motif'": it produces a "single...
marked (a) is immediately repeated, descending through a third, and it is employed throughout the piece. This phrase is immediately elided into its consequent, which modulates from D to A major. This figure (a) is used again two times, higher each time; this section is repeated." (Warburton 1952: 151)
"Hermeneutic reading of a musical text is based on a description, a 'naming' of the
melodyA melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity...
's elements, but adds to it a hermeneutic and phenomenological depth that, in the hands of a talented writer, can result in genuine interpretive masterworks.... All the illustrations in Abraham's and Dahlhaus's
Melodielehre (1972) are historical in character; Rosen's essays in
The Classical Style (1971) seek to grasp the essence of an epoch's style; Meyer's analysis of Beethoven's
Farewell Sonata (1973: 242-68) penetrates melody from the vantage point of perceived structures." He gives as a last example the following description of
Franz SchubertFranz Peter Schubert was an Austrian composer.Although he died at an early age, Schubert was tremendously prolific. He wrote some 600 Lieder, nine symphonies , liturgical music, operas, some incidental music, and a large body of chamber and solo piano music...
's
Unfinished Symphony: "The transition from first to second subject is always a difficult piece of musical draughtsmanship; and in the rare cases where Schubert accomplishes it with smoothness, the effort otherwise exhausts him to the verge of dullness (as in the slow movement of the otherwise great A minor Quartet). Hence, in his most inspired works the transition is accomplished by an abrupt
coup de théâtre; and of all such
coups, no doubt the crudest is that in the Unfinished Symphony. Very well then; here is a new thing in the history of the symphony, not more new, not more simple than the new things which turned up in each of Beethoven's nine. Never mind its historic origin, take it on its merits. Is it not a most impressive moment? (Tovey 1978:213)"(1990, 162-163)
Formalized analyses
Formalized analyses propose models for melodic functions or simulate music. Meyer distinguishes between global models, which "provide an image of the whole corpus being studied, by listing characteristics, classifying phenomena, or both; they furnish statistical evaluation," and linear models which "do not try to reconstitute the whole melody
in order of real time succession of melodic events. Linear models ... describe a corpus by means of a system of rules encompassing not only the hierarchical organization of the melody, but also the
distribution, environment, and context of events, examples including Chenoweth's (1972, 1979) explanation of "succession of pitches in New Guinean chants in terms of distributional constraints governing each melodic interval," Herndon's (1974, 1975) transformational analysis, and Baroni and Jacoboni's (1976) "grammar for the
sopranoA soprano is a voice type with a vocal range from approximately middle C to "high A" in choral music, or to "soprano C" or higher in operatic music. In four-part chorale style harmony, the soprano takes the highest part, which usually encompasses the melody...
part in Bach's
choraleA chorale was originally a hymn sung by a Christian congregation. In certain modern usage, this term may also include classical settings of such hymns and works of a similar character....
s [which] when tested by computer ... allows us to generate melodies in Bach's style."
Global models are further distinguished as analysis by traits, which "identify the presence or absence of a particular variable, and makes a collective image of the song, genre, or style being considered by means of a table, or classificatory analysis, which sorts phenomena into classes," one example being Helen Roberts' (1955: 222) "trait listing", and classificatory analysis, which "sorts phenomena into classes," examples being Kolinski's (1956) universal system for classifying melodic contours. Classificatory analyses often call themselves taxonomical. "Making the basis for the analysis explicit is a fundamental criterion in this approach, so
delimiting units is always accompanied by carefully
defining units in terms of their constituent variables."
Intermediary analyses
Nattiez lastly proposes intermediary models "between reductive formal precision, and impressionist laxity." These include Schenker, Meyer (classification of melodic structure in 1973: Chapter 7), Narmour, and Lerdahl-Jackendoff's "use of graphics without appealing to a system of formalized rules," complementing and not replacing the verbal analyses. These are in contrast to the formalized models of Babbitt (1972) and Boretz (1969). According to Nattiez Boretz "seems to be confusing his own formal, logical model with an immanent essence he then
ascribes to music," and Babbitt "defines a musical theory as a hypothetical-deductive system ... but if we look closely at what he says, we quickly realize that the theory
also seeks to legitimize a music yet to come; that is, that it is also normative ... transforming the
value of the theory into an aesthetic
norm ... from an anthropological standpoint, that is a risk that is difficult to countenance." Similarly, "Boretz enthusiastically embraces logical formalism, while evading the question of knowing how the data -- whose formalization he proposes -- have been obtained." (167)
Divergent analyses
Typically a given work is analyzed by more than one person and different or divergent analyses are created. For instance, the first two bars of the prelude to
Claude DebussyClaude-Achille Debussy was a French composer. Along with Maurice Ravel, he was one of the most prominent figures working within the field of impressionist music, though he himself intensely disliked the term when applied to his compositions...
's
Pelléas et MélisandePelléas et Mélisande is an opera in five acts with music by Claude Debussy. The French libretto was adapted from Maurice Maeterlinck's Symbolist play Pelléas et Mélisande...
:
are analyzed differently by Leibowitz, Laloy, van Appledorn, and Christ. Leibowitz analyses this succession harmonically as D minor:I-VII-V, ignoring melodic motion, Laloy analyses the succession as D:I-V, seeing the G in the second measure as an ornament, and both van Appledorn and Christ analyses the succession as D:I-VII.
Nattiez (173) argues that this divergence is due to the analysts' respective analytic situations, and to what he calls transcendent principles (1997b: 853, what George Holton might call "themata"), the "philosophical project[s]", "underlying principles", or a prioris of analyses, one example being Nattiez's use of the tripartitional definition of
signA sign is understood as a discrete unit of meaning in semiotics. It is defined as "something that stands for something, to someone in some capacity" It includes words, images, gestures, scents, tastes, textures, sounds – essentially all of the ways in which information can be...
, and what, after epistemological historian Paul Veyne, he calls
plots.
Van Appledorn sees the succession as D:I-VII so as to allow the interpretation of the first chord in measure five, which Laloy sees as a dominant seventh on D (V/IV) with a diminished fifth (despite that the IV doesn't arrive till measure twelve), while van Appledorn sees it as a French sixth on D, D-F#-Ab-[C] in the usual second inversion. This means that D is the second degree and the required reference to the first degree, C, being established by the D:VII or C major
chordA chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...
. "The
need to explain the chord in measure five establishes that C-E-G is 'equally important' as the D-(F)-A of measure one." Leibowitz gives only the bass for chord, E indicating the progression I-II an "unreal" progression in keeping with his "
dialecticDialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...
between the real and the unreal" used in the analysis, while Christ explains the chord as an augmented eleventh with a bass of Bb, interpreting it as a traditional tertian
extended chordIn music, extended chords are tertian chords or triads with notes extended, or added, beyond the seventh. Ninth, eleventh, and thirteenth chords are extended chords...
.
Not only does an analyst select particular traits, they arrange them according to a plot [intrigue].... Our sense of the component parts of a musical work, like our sense of historical 'facts,' is mediated by lived experience." (176)
While John Blacking (1973: 17-18), among others, holds that "there is ultimately only one explanation and ... this could be discovered by a context-sensitive analysis of the music in culture," according to Nattiez (1990: 168) and others, "there is never
only one valid musical analysis for any given work." Blacking gives as example: "everyone disagrees hotly and stakes his [or her] academic reputation on what Mozart really meant in this or that bar of his
symphoniesA symphony is an extended musical composition in Western classical music, scored almost always for orchestra. A symphony usually contains at least one movement or episode composed according to the sonata principle...
,
concertoA concerto is a musical work usually composed in three parts or movements, in which one solo instrument is accompanied by an orchestra.The etymology is uncertain, but the word seems to have originated from the conjunction of the two Latin words...
s, or
quartetIn music, a quartet is a method of instrumentation , used to perform a musical composition, and consisting of four parts.-Western art music:...
s. If we knew exactly what went on inside Mozart's mind when he wrote them, there could be only one explanation". (93) However, Nattiez points out that even if we could determine "what Mozart was thinking" we would still be lacking an analysis of the neutral and esthesic levels.
Roger Scruton (1978: 175-76), in a review of Nattiez's
Fondements, says one may, "describe it as you like so long as you hear it correctly ... certain descriptions suggest wrong ways of hearing it ... what is obvious to hear [in Pélleas et Mélisande] is the contrast in mood and atmosphere between the 'modal' passage and the bars which follow it." Nattiez counters that if compositional intent were identical to perception, "historians of musical language could take a permanent nap.... Scruton sets himself up as a universal, absolute conscience for the 'right' perception of the
Pélleas et Mélisande. But hearing is an active symbolic process (which must be explained):
nothing in perception is self-evident."
Thus Nattiez suggests that analyses, especially those intending "a semiological orientation, should ... at least include a comparative critique of already-written analyses, when they exist, so as to explain why the work has taken on this or that
image constructed by this or that writer: all analysis is a representation; [and] an explanation of the analytical criteria used in the new analysis, so that any critique of this new analysis could be situated in relation to that analysis's own
objectives and
methods. As Jean-Claude Gardin so rightly remarks, 'no physicist, no biologist is surprised when asked to indicate, in the context of a new theory, the physical data and the mental operations that led to its formulation' (1974: 69). Making one's procedures explicit would help to create a
cumulative progress in knowledge." (177)
Further reading
- Cook, Nicholas (1992). A Guide to Musical Analysis. ISBN 0-393-96255-5.
- Hoek, D.J. (2007). Analyses of Nineteenth- and Twentieth-Century Music, 1940-2000. ISBN 0-810-85887-8.
- Kresky, Jeffrey (1977). Tonal Music: Twelve Analytic Studies. ISBN 0-253-37011-6.
External links