7. Harmonic melody: instrumental-vocal.
ALEXANDER L. RINGER
Melody, defined as pitched sounds arranged in musical time in accordance with given cultural conventions and constraints, represents a universal human phenomenon traceable to prehistoric times; in some cultures, however, rhythmic considerations may always have taken precedence over melodic expression, as in parts of Africa where percussive sounds of undetermined pitch are employed in lieu of semantic communication, or as pacemakers for systematic forms of physical effort (whether in daily work or ritual dance), or both. Primary concerns with melody appear to have been related more specifically to verbal, in some instances pre-verbal, modes of social intercourse.
While the exact causal relationships between melody and language remain to be established, the broad cultural bases of ‘logogenic melody’ are no longer in question. Nor are some of its widely shared characteristics. Certain universal manifestations of the melodic impulse, for example, appear to be centred intervallically on the descending minor 3rd. Children's singsongs are a case in point, as are the calls and responses of Alpine shepherds. The most universal instance of pitch modification is, needless to say, the infant's first cry; and research in infant behaviour has shown to what extent pitch-differentiated pre-verbal utterances are employed systematically and effectively by infants to communicate physiological needs as well as affective states. If natural phenomena, such as birdsong and other forms of animal communication, are any indication at all, it should be possible in time to arrive at meaningful concepts concerning an evolutionary continuum from pathogenic to logogenic forms of pitched vocal behaviour.
The early history of melody, however, though of unquestioned scientific interest, in no way affects the phenomenology of melody as it emerges from the annals of recorded history, both written and oral. Historically, the early development of melody may well have proceeded, as Szabolcsi suggested, from simple one-step voice inflections via conjunct trichordal patterns to intervallic combinations of minor 3rds and major 2nds. The superimposition of two such patterns would account for the countless pentatonic melodies found geographically from China to Appalachia and historically from Gregorian chant to Debussy. In all probability, the combination of the simplest one-step inflection with the basic singsong interval owes its broad appeal not only to the fundamental qualities of its pitch components but also, and more decisively, to its potential for variation through configurational rotation of its pitch content. The 3rd-cum-2nd, after all, lends itself to retrograde and mirror inversion without sacrifice of its quartal contour. When two such quartal patterns are joined disjunctively or conjunctively, i.e. either separated by a 2nd or in such a way that the highest note of the lower and the lowest note of the upper trichord overlap, the motivic possibilities are maximized to the point where pure pentatonicism can provide an adequate scalar framework for some rather sophisticated melodic structures. Indeed, if a motif is defined as a minimum of melodic substance susceptible to creative manipulation in a given aesthetic context, then pentatonicism would seem to offer matchless opportunities for motivic elaborations of the 4th, the acoustically ‘perfect’ interval that determines the tuning of so many instruments as well as the structural division of the octave. Empirically speaking, it is clear that pentatonicism satisfies a broad range of musical needs from basic logogenic progressions to the most varied treatments of motivic nuclei in sacred monophony, in Renaissance polyphony and beyond, wherever and whenever purely melodic forces have prevailed. The underlying pentatonicism of such music is admittedly not always easily recognized, if only because it often affects the melodic infrastructure more directly than the surface design. It nevertheless remains true that, in the absence of Western tonal harmony, quartal melodic patterning, with or without subdivisions of the 3rd-cum-2nd variety, has spawned the bulk of melodic activity from the dawn of history and the four corners of the earth.
Ever since Hornbostel, Sharp, Kodály and Bartók suggested early in the 20th century that quartal, if not always outright pentatonic, thinking may be a worldwide phenomenon, pertinent data have been collected among the most ‘primitive’ of tribes as well as in the most complex of musical cultures and sub-cultures. Wiora, who has attempted to document music in the late palaeolithic hunting civilizations, pointed to melodies based on disjunct 4ths with an occasional passing or auxiliary note among ethnic groups as disparate as Bushmen, Lapps and Menominee Indians. The descending trichord bounded by the interval of a 4th appears in the musical recitations of the ancient Hebrew community of Djerba between Passover and the Feast of Weeks (Pentecost) and, almost identically, in the Kyrie of the Roman Easter Vigil, one of the oldest of plainchant melodies. In Hungary, even relatively extended folksongs belonging to the ‘oldest layer’ favour the descending pentatonic 4th. The Hungarian case, which has been particularly well researched thanks to the work of Kodály and Bartók, also illustrates the effective interaction of linguistic and purely ‘musical’ considerations in the formation of characteristic melodies. The declining pitch lines, both sudden and gradual, so typical of the spoken language, are reflected in the motivic and structural tendencies of Hungarian melody from ancient times to the present.
Melodic descent, to be sure, is among the most ‘natural’ of musical procedures because it requires no ‘artificial’ generation of melodic energies. Its pathogenic archetype, as Sachs has shown, is the ‘tumbling strain’ where an initial high pitch provides a melodic diving-board, as it were, permitting melodic gravity to take charge. Given the law of melodic gravity, extensions of the ‘tumbling strain’ into relatively complicated anticlimactic melodies are understandably rare. By the same token, it may well have been an awareness of ‘natural’ melody that caused the ancients to think of musical systems as descending rather than rising. Whatever the case, melodic descent permeates much of the oldest known music irrespective of geographic origin. It would almost seem that, wherever music became an intrinsic condition of life, certain common melodic procedures were necessarily adopted, because they satisfied basic physiological and biological requirements, if not the aesthetic imagination per se.
Etymologically, melody combines the ancient Greek terms for poetic order and song (melos, ōtē). That melos had early physiological associations, before it entered the realm of aesthetics, is quite in line with the characteristically Greek conception of music and poetry as organic mirrors of human, indeed cosmic existence. It was during the European Middle Ages that the Latin adaptation melodia assumed the specifically musical connotations that it retains in modern vernacular usage. Tinctoris, in the mid-15th century, no longer hesitated to identify melus with cantus, and most subsequent definitions similarly associated melody with song, though inevitably from varying stylistic perspectives. Rameau, in the 18th century, regarded melody as a product of harmony; but Rousseau claimed priority for autonomous melody. Hegel, in the early 19th century, thought of harmony and melody ‘as one compact whole, and a change in the one necessarily involves a change in the other’. For the acoustician Helmholtz, melody was the incarnation of motion in music, expressed ‘in such a manner that the hearer may easily, clearly, and certainly appreciate the character of that motion by immediate perception’. Perception was also the principal concern of Hanslick, who saw in melody the ‘archetypal configuration of beauty’ (‘Grundgestalt der Schönheit’). Hanslick's Apollonian viewpoint was, of course, diametrically opposed to the Dionysiac ideal of ‘unending melody’, expounded by Wagner, who postulated ‘an ordered series of quasi-intellectual, unfulfilled speech-sounds – indirectly representative, concentrated as image but not yet as immediate, inevitably true expression … directly addressed to feeling, unerringly vindicated and fulfilled’. When, in the mid-1920s, Watt applied Helmholtzian physics to a comparative study of the intervallic properties of selected Schubert songs and Amerindian melodies, he reached the post-Wagnerian conclusion that there was
no reason why a melody should ever stop. Every interval carries its motion farther along, so that another group of conditions must exist which modify and arrest its motion. One very natural condition of arrest is the ordinary limit of memory. No doubt the lengths of primitive melodies, if not of all melodies, are largely determined by this. But this is a condition of ending, not of arrest of motion in the musical sense.
A few years earlier Thurstone, another student of non-Western music searching for universal answers, had defined ‘the essence of melody’ as ‘unity in the perception of pitch variation’. Consonance and dissonance, those perennial bones of theoretical contention, were ruled out as criteria for ‘melodic unity’. The same could be said up to a point for harmonic considerations generally. For even in the essentially triadic melodies associated with functionally tonal music, harmony provides at most ‘an inner skeleton on which varying contours may be draped’ (Watt). Anyone attempting to appreciate the monorhythmic oboe melody in the Andantino of Tchaikovsky's Fourth Symphony in terms of its harmonic infrastructure would not only miss the point of its finely chiselled phrasing; seduced by its seeming simplicity he might well misunderstand the composer's rather complex harmonic intent. ‘Melodic unity’ is configurationally speaking an intrinsic psycho-acoustical function of melodic generation in a given historic-cultural context and must in the end be experienced as such.
The character of a given melody is determined by its range or relative position within the total pitch continuum, its ambitus or pitch spread, its contour or linear design, and its syntactic structure with respect to elements of contrast and repetition, variation and development. The smallest melodic-rhythmic unit, the motif, requires a minimum of two distinct pitch levels. Syntactically, motivic materials are arranged in phrases, the general characteristics of which are determined by the specific melodic idiom. Thus, in contrast to the larger, songlike melodic entities, which as a rule eschew a great deal of motivic differentiation, instrumental themes of the type associated with Western music from the middle of the 18th century onwards favour sharply profiled, contrasting motifs arranged in an open-ended fashion to allow for their subsequent structural development. As Schoenberg once put it, ‘a melody can be compared to an “aperçu”, an “aphorism”, in its rapid advance from problem to solution … a theme resembles rather a scientific hypothesis which does not convince without a number of tests, without presentation of proof’. A properly conceived melody is thus by and large self-sufficient, whereas a good theme generates energies needed for the formation of larger entities that exceed structurally and expressively the apparent potential of its motivic substance. But self-sufficiency is not necessarily bound to sectional repetition, as has often been asserted. None would wish to deny that note-for-note repeats of structural sub-units have been characteristic of Western song at least since medieval times. Such perennial patterns as AAB and ABA furnish ample evidence to this effect. By the same token, there is nothing to justify sectional repetition as an absolute criterion of melodic design. Schoenberg's work alone offers ample proof to the contrary, while demonstrating at the same time the structural importance of transposed or varied recurrences, or both, of motivic materials of the kind that animate so much of plainchant or, for that matter, any number of non-Western repertories. In Western composition, sectional repetition became virtually identified with melody conceived in harmonic tonal terms. It is, therefore, a hallmark of the Classical and Romantic eras. But already Berlioz, not to speak of Wagner, avoided untransposed sectional repetition in some of his most haunting melodies, perhaps because he, more than any of his contemporaries, had begun to think of melody more as a reflection of a psychological ‘stream of consciousness’ than of man's rational perception of ‘reality’.
As for thematic matter, the multi-motivic designs of Haydn, Mozart and Beethoven, geared to dramatic conflict, superseded more than a century of mono-motivic incipits (‘developmental themes’ in Kurth's terminology) that provided the decisive initial spark for considerable amounts of Baroque instrumental music. But if the early 18th century had thus managed to imbue even the most innocuous melodic-rhythmic stuff with a salutary dose of kinetic energy, the Romantic reaction to the dialecticism of the Classical masters offered entirely new mono-motivic opportunities. The cello melody in the Intermezzo movement of Schumann's Piano Concerto, not to speak of the closely related opening subject of Brahms's Fourth Symphony, reveals the previously unsuspected affective and structural potential of a single iambic two-note motif at the behest of lyrical genius. Such uniquely ‘stripped’ tunes notwithstanding, the harmonic age generally practised the art of melodic ‘drapery’ with a gusto exceeded only by that which inspired certain 17th-century keyboard works or that with which South Asian musicians go about their ever surprising raga improvisations. Meanwhile, monophonic chant and modal polyphony, the largest and most influential Western reservoirs of pure melody, were waiting in the wings of history, ready to burst on to a musical scene that sought melodic salvation increasingly from ‘exotic’ sources, including the quartal and modal folktunes of Russia.
Theoretically at least, the dogged adherence of plainchant to its ancient roots must have been the motivating force behind the plagal modes centred on a finalis a 4th above the lowest pitch in the scalar order. Similarly, the prevalence of recitation tones (tenors) a 3rd above the finalis suggests the genetic significance of the descending 3rd in the melodic practices of early European Christendom. Where, as in the case of the 4th, or Hypophrygian, mode, the tenor occurs instead a 4th above the finalis, the mode may have been generated by two conjunctive pentatonal 4ths. The ‘authentic’ recitation pitch, on the other hand, generally a 5th above the finalis (except for the 3rd mode, where practical considerations dictated a minor 6th), points to disjunct quartal origins. Quartal movement as a fundamental melodic resource is illustrated by the antiphonal rendition of Psalm cxlvii, where the recitation pitch is brought into focus by lower and upper auxiliary notes, then confirmed configurationally by a rapid descent to the finalis a 4th below (ex.1).
Careful analysis is likely to dispel any lingering doubts concerning the pentatonal foundations of plainchant. The Easter sequence Victimae paschali laudes, based on a metrical text from the first half of the 11th century, supplies a perfect model for the sophisticated manipulation of the 3rd-cum-2nd motif (ex.2). Its opening phrase features in typical chant fashion the minor 3rd flanked by upper and lower auxiliary notes. The penultimate E, which poses at first as a mere passing note, assumes structural functions in the second phrase, where it anchors the trichord A–G–E. The transposition of the original pattern to the upper 5th is followed by a move in the opposite direction to the 4th below, in conformity with a prominent melodic procedure that recalls the gradual descent of a glider released in mid-air: taking full advantage of air currents it manages to rise above the point of release; only then, lacking propulsive power, it descends gently but inevitably to the take-off level or lower altitudes.
The third section, starting at the lowest pitch level, telescopes two occurrences of the rising 3rd-cum-2nd motif, and in so doing regenerates a goodly amount of melodic energy. This ingenious, intensely dynamic procedure receives further impetus from a device that is common to a wide variety of melodic styles, because it effectively restores pitch balance in the wake of a more or less drastic drop: once the downward leap has ‘hit bottom’, an immediate directional reversal propels the melodic line up and well beyond the original jump-off point, much as a skilful trampoline gymnast is projected ever higher. In the realm of melody even the law of gravity bows to aesthetic priorities. As the trampoline effect shows, any sudden change in direction must be quickly redressed if melodic unity is not to suffer.
By the end of the first millennium, plainchant melody had evidently recognized the structural weight of the melodic finalis in a manner comparable only to the magnetic force of the harmonic tonic centuries later. Tentatively at first, but soon inescapably, Western goal-orientation led to directional diatonicism. In the Easter sequence, the final complete section summarizes, as it were, all the basic melodic forces at work in this seemingly simple yet compositionally intricate tune. After an initial repeat of the second verse, the melody ascends once more to the high C in dramatic preparation for the trampoline jump from low C to the recitation pitch A just before the final decline. A last allusion to the initial motif reconfirms the finalis in the ‘Amen Alleluia’ coda.
With respect to total structure, the gradual rise of the first verse is properly balanced by the anti-climactic design of the second section with its elaborate descent from the highest point of the melody, which in turn prepares the subsequent trampoline effect. In these and many other ways the Easter sequence is the acme of melodic efficiency and effectiveness, as is plainchant at large, perhaps because it feeds on melodic energy unadulterated by strong rhythmic intervention and unencumbered by harmonic commitments. Though necessarily emphasizing conjunct motion in keeping with its contemplative aesthetic, plainchant’s basic melodic principles remain as valid as they were at a time when the church controlled virtually all learned European music. The principle of melodic compensation by contrary conjunct motion, for one, has never ceased to affect melodic phraseology at all levels. The contingent primacy of the structural arch, on the other hand, is in no way obviated by the many melodic elaborations of the ‘tumbling strain’ or, for that matter, a number of climactic melodies with finales well above the initial pitch. In liturgical practice, such relatively infrequent types will on occasion form subdivisions of larger melodic complexes which, as cumulative entities, display features that clearly comply, at least in general terms, with the law of directional compensation.
Unlike the syllabic Easter sequence, the melismatic gradual Haec dies gives full rein to pathogenic melodic energies, though inevitably within the confines of sacred aesthetic convention (ex.3). Structurally unfettered by definition, such compositions sacrifice motivic tightness at the altar of vocal virtuosity, thriving instead on ornamental devices, including scalar and sequential passages, that tend to obscure any pentatonal remnants. But if the virtuosity of solo singers was a contributing factor in the promotion of medieval diatonicism, its principal source of encouragement was no doubt secular practice, especially in dance music, where choreographic considerations dictated rhythmic regularity from the start and with such marked consequences for all aspects of melodic articulation.
Nowhere is this more evident than in the monophonic secular dance music of the outgoing Middle Ages, as represented by the well-known estampie Kalenda maya or a typical dance-song like Moniot d'Arras's Ce fut en mai. Both are clearly in the major mode, the modus lascivius of medieval theory; both favour the tonic major triad and generally betray harmonic tendencies that are strengthened by rhythmic periodization which in turn is mandated by the underlying dance figures. Periodization of one sort or another was also a feature of the dance-determined polyphony of the same period, specifically the 12th-century clausula and the 13th-century French motet. And if melismatic organum can be said to reflect, like melismatic chant, the pathogenic ‘outpouring of the soul’ that characterizes, for example, the freely unfolding taqāsīm of Middle Eastern music, then the measured or discant style may well have been suggested by the strictly metric portions which follow the taqāsīm and provide often long delayed, and hence welcome, kinetic relief. The celebrated rhythmic modes, in turn, may have been the outcome of classicistic rationalization on the part of Christian apologists embarrassed by the veritable dance mania that swept through Europe in the later Middle Ages. From then on, at any rate, rhythmic forces, whether metrical or not, left their lasting imprint on any number of melodic types, and there can be no doubt that the seesaw relationship of rhythmic-harmonic and rhythmic-melodic factors vying for priority was a crucial factor at every stage of eight centuries of stylistic transformation. After all, the late medieval predilection for metrical organization, though seemingly superseded by the overriding melodic concerns of modal polyphony, remained alive in the Italian frottola as well as the French chanson and other dance-conditioned vocal and instrumental forms.
The prolonged struggle between these two basically antagonistic melodic-rhythmic orientations was stalemated throughout much of the 17th century. But before long, rationalistic criteria began to affect aspects of melodic organization no less than the continuing debate about melody in the hierarchy of musical values. Viewed in this light, Rousseau's promotion of popular melody, especially of the Italian variety, and Rameau's discovery of the ‘natural’ laws of functional harmony appear anything but incompatible. On the contrary, together they provided the intellectual underpinning for the harmonically conceived, periodically structured melodies of the so-called Classical era. The polyphonic heritage of the Renaissance, as codified in Zarlino's rules for composition based on melody, characteristically assumed a central position in the systematic teachings of 18th-century theorists from Fux and Martini to Albrechtsberger, the tutor of Beethoven; and Beethoven could say of himself that, unlike his predecessors, he had been born with the obbligato accompaniment. Significantly, it was Beethoven who, in his last quartets, unleashed once again the full force of pure melody as the prime carrier of musical structure and in a manner that conveys the spirit, if not always the letter, of the principles of motivic manipulation in plainchant and modal polyphony. Beethoven's ever-expanding musical universe, to be sure, reflected more directly a lasting preoccupation with J.S. Bach. Whatever his principal inspiration, the later Beethoven refined earlier methods of motivic recycling in ways that were to revolutionize the ecology of music, if only because the melodic materials saved served to generate ever new melodic energies. In this respect Wagner approached the ideals of the later Beethoven more closely than Brahms, who responded rather readily to the homophonic ‘middle period’ Beethoven. By the same token, it was because he could not and would not abandon the basically triadic-metric traditions of Italian folk music that Verdi emerged as Wagner's natural opponent.
The harmonic era, which gave birth to musical drama and to instrumental music as a functionally autonomous art, unwittingly came to rely heavily on melodic figuration, Watt's ‘drapery’, i.e. the melodic tissue that connects and covers the intermittent supports furnished by the harmonic substructure. Figuration had been a favourite device of early organists who developed the idiomatic ‘coloration’ techniques that typify the 15th-century Faenza Codex, Conrad Paumann's Fundamentum organisandi and many 16th-century keyboard tablatures. The history of vocal music, too, is replete with characteristic instances of melodic coloration, from the more florid types of plainchant and early polyphonic genres, especially those of the Italian Trecento, to the sacred polyphony of the late 16th century – which was often rendered with improvised figurations as a concession to contemporaneous monodic practices involving diminution, whether in the melodic enhancement of an extended pitch or elaborate melodic fillers bridging the outer limits of large intervals. With the development of ‘florid song’ in Italian opera, improvised figuration became the special province of the virtuoso singers who thus adorned the da capo portions of late 17th- and early 18th-century solo arias.
The essentially decorative function of so much vocal music inspired by the Italian Baroque inevitably required outright logogenic complementation, at least in opera, if any plot continuity was to be maintained. Bel canto melody, therefore, had its logogenic counterpart in the form of recitative, both simple and accompanied. Simple (semplice; or ‘dry’, secco) recitative reduced the pitch substance by and large to what was needed to render musically the most typical of speech inflections. Accompanied (or obbligato) recitative, on the other hand, assumed increasingly dramatic stances, as attempts were made to compensate for the largely lyrical nature of the vocal display pieces. In so doing, accompanied recitative developed an often highly expressive melodic idiom that was to have considerable influence on both instrumental music and musical drama, culminating in the work of Wagner. In accordance with its dramatic function, accompanied Italian recitative was characterized by intervallic leaps and generally unpredictable melodic behaviour. Structurally, it remained open-ended, like most of the action it related, in contrast to the closed, for the most part ternary, forms of the intervening arias. Moods and reflections that were not easily rendered in either recitative or aria style, were relegated to an intermediary style, the arioso, which combined features of the logogenic and pathogenic or decorative types of melody. At the same time, the growing desire for ‘natural’ musical expression, which caused the 18th-century enthusiasm for comic opera, also produced song types that eschewed the decorative element altogether in favour of an often folksy tunefulness. By the time Mozart achieved his unique operatic synthesis, he was able to draw not only on various Italian conventions but also on tragédie lyrique as transformed by Gluck with due regard to its deeply ingrained logogenic traditions – a rich melodic palette indeed, embracing the ‘driest’ of recitatives as well as the most florid of figurated song (as in the Queen of Night's aria in Die Zauberflöte).
Instrumental figuration has been a perennial favourite of composers of variation sets, particularly for keyboard, since the 16th century. The melodies underlying such variation sets are often referred to as ‘themes’. But if Schoenberg was correct in his proposition that ‘a theme is not at all independent and self-determined … it is strictly bound to consequences which have to be drawn, and without which it may appear insignificant’, such careless usage can hardly be said to benefit conceptual clarity. Variation themes, after all, must be perfectly balanced, self-sufficient melodies tending almost by definition ‘toward regularity, simple repetition and even symmetry’ (Schoenberg). In fact, composers of variations could indulge their taste for figuration and coloration only as long as they were able to rely on a firm melodic frame of reference. Generally speaking, the ‘theme and variation’ issue is typical of the terminological confusion that has always surrounded melodic matters. During the Middle Ages such Latin terms as harmonia, cantus and melodia, even modulatio, were used interchangeably; the same holds for motif, phrase and theme in more recent times. Mozart was no longer alive when Galeazzi in his otherwise important description of the sonata form could declare with impunity that ‘the motif is nothing but the principal idea of melody, the subject, the theme, one might say, of the musical discourse, and the whole composition must revolve upon it’.
A subject, to be sure, is not necessarily a theme, even though an entire composition may indeed revolve upon it. About the middle of the 16th century Zarlino could say with good cause that ‘in every musical composition, what we call the subject is that part from which the composer derives the invention to make the other parts of the work, however many they may be’. He went on to explain that such a subject may be the composer's own or somebody else's invention ‘that it may be a tenor or some other part of any composition you please, whether of plainsong or of figured music’, and that it may be taken over in its original form or in a novel adaptation. But a polyphonic subject, treated in accordance with the rules of modal counterpoint, by necessity had qualities that were incompatible with the requirements of an 18th-century theme designed not only to raise compositional problems but to ensure their resolution. If the head-motif of a late 15th- or early 16th-century motet can be said to behave at all thematically, it does so at most in the sense of an instrumental incipit, like the rising triad in long note values which sparks off the first movement of Bach's E major Violin Concerto.
In the absence of intrinsic motivic dialectics of the dramatic type, thematic development of the Classical variety was precluded in either case. That is not to say, of course, that the nature of motivic relationships, let alone of motivic substances, has remained unaffected by the stylistic vicissitudes of a world dedicated to ‘progress’. The opening bars of Mahler's Second Symphony syncretize the incipit and dramatic types in a manner that echoes the ‘Sturm und Drang’ rhetoric of some of the keyboard works of C.P.E. Bach, composed nearly a century and a half earlier. After 1900 rhetorical gestures became identified not only with the melodic idiom of ‘expressionism’ but, in association with neo-Baroque motoric energies, also with the ‘neo-classicism’ of the early 1920s.
The systematic investigation and discussion of melodic phenomena has inevitably been affected over the centuries by sundry historical perspectives and changing stylistic contexts. Still, surprisingly little has been done to sort out a host of conceptual ambiguities and vague definitions in the 40 years since an alarmed Hindemith decried the longstanding systematic neglect of melody, the element through which, in his view, the Western composer had always revealed himself most meaningfully. Already Parry, at the beginning of the 20th century, had warned ‘against the familiar misconception that scales are made first and music afterwards’. A few years later Hornbostel published his brilliant article on ‘Melodie und Skala’. But the myth of scalar priority has continued to distort the theoretical treatment of melody. None would wish to deny, to be sure, that certain types of musical instruments, whether of the Indonesian gamelan or the Western keyboard variety, have had prescriptive effects on pitch selection. Leaving aside the admittedly important issue of fixed tuning, however, scalar considerations can hardly be said to place more than very general constraints on melodic activity, if only because the scales themselves are derived from existing melodic practices. The image of the scalar tail wagging the melodic dog would seem grotesque, were it not for the implied reminder of the extent to which musical notation, with all its blessings, has narrowed Western man's understanding of a cultural phenomenon that is always aural in essence and rarely if ever graphic.
Broadly speaking, melodic styles are identifiable, like spoken languages, by their vocabulary, grammar and syntax, as well as by idioms related to function and social class. Structurally, melody may be akin to freely evolving prose or the measured balance of poetry. It may comply with harmonic requirements or obviate them. It may suggest certain forms of physical behaviour or, for that matter, rational thought; then again, it may reflect the affective complexities of the subconscious. Above all, as a social product, melody is part and parcel of the culture or sub-culture to which it owes its existence. Melodic styles, therefore, share not only specific national characteristics; they also respond to a variety of social and functional needs, as Johannes de Grocheo observed some 700 years ago when he divided 13th-century French practice into musica vulgaris, the popular monophonic music of his time, musica mensurabilis, the measured learned music of the intelligentsia, and musica ecclesiastica, the music of the church, which drew upon elements of both the popular and learned genres. More recently, Mozart (in the ballroom scene of Don Giovanni) and Berg (in the tavern scene of Wozzeck) have dealt with different social classes in characteristic melodic-rhythmic terms.
Melodic expression, in the sense of melodic associations with non-musical subject matter, whether purely emotional, physical or ‘natural’, has been an intrinsic (though by no means uncontroversial) feature of Western music at least since the early Renaissance, when so many ancient concepts, the Platonic notion of ethos included, re-entered the secular consciousness of Europe. Textual allusions of a directional nature thus found literal melodic representation both in Renaissance polyphony and the monodic art that took its place precisely for the sake of ever greater melodic expressiveness. Programmatic symbolism accounts for triadic lines in the battle and hunting chansons of Janequin and for chromatic alterations in late 16th-century Italian madrigals, for the siciliana movements in 18th-century Christmas concertos and for fanfare patterns in the symphonies of Beethoven. In the 19th century some historical references to older melodic styles were allowed to shape the ‘contemporary’ idiom. The late 17th-century passion for affective-rhetorical minutiae produced a whole array of appropriate melodic formulae as well as a complex set of rules for their ‘correct’ application, codified most successfully by Mattheson and known in Germany as the ‘doctrine of the Affections’. By the same token, if Monteverdi defended his stile concitato with the words of Plato, calling for melodies worthy of ‘the utterances and the accents of a brave man who is engaged in battle’, Mendelssohn thought of his celebrated Songs without Words as fit only for ladies.
But political movements, too, have left their imprints on specific types of melody. The tunes of the Geneva Psalter and the chorales of Martin Luther and his followers did not merely have religious connotations; their measured rhythms and sharp melodic profiles also mirror the sense of dignity with which the 16th-century reformers pursued political goals of well-nigh universal significance. Similarly, the songs of the French Revolution, exemplified by the Marseillaise, with their dotted rhythms and rising triadic patterns, not only sparked the enthusiasm of the thousands who placed their trust in the new republicanism; they also became cherished models for the fighting-songs of international socialism which produced a repertory recognized as such all over the world. And in the USA the hymn tunes of the pioneers who settled the West generations later inspired the hopeful songs of the Civil Rights movement. In other words, melodic styles have rarely been mere figments of the abstract aesthetic imagination. In Western civilization, no less than in Africa and elsewhere, melodic idioms have often been functionally determined and associated with clearly defined ideas and concrete activities. Surely, when Beethoven decided to open his violin concerto with a march tune supported by military drum rhythms, he did so with the knowledge that such an obvious reference to the Napoleonic war machine and the mental anguish it caused would be clearly understood, if only because the general procedure had by then become familiar through the violin concertos of some of his immediate French predecessors.
Similar considerations pertain, needless to say, in the folk realm as well, where songs of mourning, spinning-songs, and others associated with typical activities or social functions may actually be members of distinctive tune families. At the very least, their functional intent is reflected in identifiable melodic terms, if not always common structural characteristics. The outside observer, however, is bound to think of folksong by and large in geographic-cultural terms. Thus he will recognize that central Europe and parts of France and Italy represent triadic strongholds, while Russia is attached to quartal melodic patterns. In southern Europe, including Spain and Sicily as well as Albania and parts of Greece and the former Yugoslavia, he will sense a common Mediterranean heritage in the prevailing taste for augmented 2nds, not to speak of the general predilection for descending melodic patterns or, for that matter, intonational idiosyncracies that would be considered intolerable in the triadic north.
A given melodic style, let alone the texture of a specific tune, necessarily involves every aspect of musical order, not merely single pitch arrangements. Thus periodic structure, or melodic patterning in terms of properly balanced sub-units, was conditioned as much by textual requirements as by kinetically determined dance rhythms and the rise of functional harmony. Typically the melodic root interval, the 4th, was forced to surrender to the harmonically derived 5th, once melodic tension per se had begun to yield to harmonic concepts of consonance and dissonance. Neither was the 3rd-cum-2nd motif capable, under the circumstances, of withstanding the frontal assault of thirdal chains. To compensate for the resulting decline in pure melodic energy, rhythmic devices assumed unprecedented powers of motivic definition. The beginning of Beethoven's Fifth Symphony is often cited in this connection, and there can be no question but that during his ‘middle period’ Beethoven pushed the rhythmic potential of functionally harmonic melody to unsuspected extremes, indeed beyond the point of no return, considering the pre-eminence of melodic-polyphonic textures in his last quartets. Historically, however, the Beethovenian phenomenon, though unique within the specific context of early 19th-century music, was but one of many recurring manifestations of the fundamental dichotomy of melody and harmony – a traumatic issue in Western music that has elicited the very best from superior musicians ready to meet the challenge as a unique opportunity to achieve the well-nigh impossible yet, by the same token, has played perpetual havoc among those who have brought mere talent to their tasks. The history of music is staked out by the stylistic landmarks left behind by the few who thus survived the long trek from medieval monophony to 20th-century serialism.
Among the exceedingly limited number of modern scholars devoted to the historical or the cross-cultural study of melody, or both, Lach, in a pioneering dissertation published in the early 20th century, relied heavily on visual, especially architectural, analogies. Mindful of the age-old technique of melodic-rhythmic diminution or coloration, he distinguished between major structural (architectonic) components and ornamental ‘melic’ forces, corresponding to the weight-carrying structural skeleton of a building as opposed to its readily accessible surface characteristics. Lach also believed that certain types of ‘primitive’ melodic patterning reflected mental processes akin to those which may, in the visual domain, account for the more elementary combinations of such primary elements as dots, dashes and circles. The complex musical structures identified with at least 1000 years of Western composition, on the other hand, reminded him of the great mosques of Persia and Turkey as well as the Gothic and Baroque churches of Europe, where intricate design and sophisticated engineering went so happily hand in hand.
Whatever the merits of some of his more eccentric points, at least by implication Lach focussed long-overdue attention on the crucial analytical problems of melody as form in relation to structure as process. That he should have conceived his theory of melodic infra- and super-structures at a moment in history when non-Western, particularly Asian music in all its splendid variety, had begun to penetrate the aesthetic consciousness of the European vanguard (Der blaue Reiter appeared in 1912), was anything but accidental. By 1913 closed forms had become vestiges of the past, melodically, rhythmically, even harmonically. Gregorian chant, as restored by the monks of Solesmes, was not only the subject of a papal motu proprio, it had long since been recognized as the ultimate source of pure melody by an entire generation of French composers identified with the Paris Schola Cantorum. Debussy, for his part, had jettisoned the harmonic strictures of the musical academic world in favour of a freely evolving melodic flow inspired by the literary orientalism of symbolist poetry no less than the musical exoticism of Balakirev and Rimsky-Korsakov and the Javanese and Annamite revelations of the Paris exhibition of 1889. In central Europe, ‘open’ melodic patterning was a conditioning factor in Schoenberg's ‘emancipation of dissonance’ as well as his abiding concern for musical cohesiveness, stimulated, interestingly enough, by intensive studies of Bach and Mozart. With melody thus restored to its once dominant position in European compositional practice, reassessments from different analytical-historical perspectives were merely a matter of time. Four years after Lach, Kurth came forth with his epochal treatise on the foundations of linear counterpoint which draws general conclusions regarding the laws of melody from the specifics of Bach's style. Eventually, in his last major work, Musikpsychologie (1931), Kurth made configurational perception the ultimate touchstone of melodic experience.
In contrast to Lach's visual-architectonic approach, which emphasized the static-structural aspects of melody, Kurth found analogies in the discoveries of modern science for his discussion of melodic energy; and unlike Lach, who documented his theories with melodic excerpts from non-Western cultures on the one hand and, on the other, variation-prone eras and styles in the history of Western music, Kurth based his observations on music that represents Western teleology at its motoric musical best. Artistically, his ideas about musical energy generation had contemporaneous parallels in the neo-Baroque works of Stravinsky, Schoenberg and Hindemith, who emulated Scarlatti and Bach with melodic incipits designed to project tightly controlled groups of closely related ideas into the musical time-space continuum where they are sustained and if necessary reinforced by recurring motivic boosts, emanating as a rule from transposed restatements of the incipit or an appropriate variant. The resulting melodic lines typically reach their climax about three-quarters of the way along, when their energies begin to be spent. The completed melodic course of such motoric music is reminiscent of the well-known projectile curve where a forceful yet smooth ascent is followed by a rather rapid decline. Melodic projectile curves of this sort retain a certain expressive neutrality. They are neither dramatic nor specifically lyrical. Instead, they appeal to one's inherent sense of musical movement, especially when, as in Bach's music, rhythm and metre are perfectly synchronized to avoid any suspicion of periodicity. Periodization, of course, had sacrificed freely unfolding rhythm to the mandates of dance and metrical poetry, and had done so justifiably also in the interest of rational organization conducive to immediate appeal and ease of perception. 19th-century textbook writers, unfortunately, made periodization the principal basis for their broad generalizations concerning the essence of melody at large, the growing testimony of history to the contrary notwithstanding. Composers of the first rank, though, were quick to recognize the ‘tyranny of the bar-line’ as an additional threat to melody struggling against the paralysing effects of tonal harmony. Responding with alacrity to the rediscovery of Bach and Palestrina, among other masters of the past, they proceeded to balance periodic and non-periodic elements in their melodic idiom to the point where, in Beethoven's last quartets, polyphonic-kinetic forces take hold of the harmonic-metric sub-structure in a manner that anticipates not only the mature Wagner but also Schoenberg.
Prose-based music for the stage, meanwhile, required strong motivic contrasts if it was to do justice to swift dramatic change. The German lied, on the other hand, favoured the use of motivic variants or, at the very least, motivic family relationships in keeping with its subtle poetic moods. Lyrical melody caters to conjunct motion, just as its dramatic counterpart thrives on the sensation of tension associated with intervallic leaps. Dramatic idioms are also marked by higher degrees of rhythmic irregularity, since rhythmic analogy and metric equivalence tend to convey a sense of repose.
The opening theme of Mozart's Haffner Symphony, no.35 in D (ex.4), furnishes an excellent example, because it mirrors in instrumental terms the same kind of dramatic situation that motivates the first duet in the opera Don Giovanni. Here as there, three basic moods are represented by three sharply differentiated melodic patterns heard in immediate succession. In the symphony the first idea takes up the initial five bars, while the second idea occupies the next four, and the third concludes what is, oddly enough, a 13-bar melody. These three components do, however, share a march-like rhythm first heard in bar 4. Thanks to the ingenious use of this persistent motivic pattern, which undergoes significant changes in meaning as its relative position shifts within the melody as a whole, contrast and continuity are kept in perfect balance. The explosive energy emanating from the long initial low D prepares the startling effect of the octave leap, but it also accounts for the irregular completion of the melody in bar 13. The opening note thus fulfils a multiple function like that of the motivic incipit of Bach's E major concerto. But Mozart's theme is instructive in other ways as well. The melodic infrastructure of the first five bars consists of a conjunct descending 4th. This ubiquitous pattern is, of course, equally familiar from lyrical compositions like the celebrated ‘Largo’ in Handel's Serse. But there the conjunct descent is solemnly straightforward and immediately followed by an equally unadorned retrograde. That this directional reversal manages to overshoot the original pitch level is due to a combination of the law of melodic compensation and the ‘trampoline effect’. Mutual reinforcements of this sort can trigger even more drastic reactions to a relatively rapid descent. Handel, anxious to maintain a lyrical mood, prolonged the retrograde motion but slightly. Mozart's dramatic leap, on the other hand, unleashes compensatory forces that are further energized by the ever-so-brief shortening of the long note values. Instead of pursuing the sequential descent of the melodic line all the way, he inserted the march motif just ahead of the long trill which prepares the half-close on the dominant, perhaps because he wished to underscore the heroic implications of his work. The second thematic component picks up that same motif but softly and in conjunction with an upward leap to a long appoggiatura that lends this fragment a reflective, if not melancholy flavour. Finally, the same dotted pattern reappears at the higher octave from where it skips gaily down to the opening note, like Leporello, the buffo character, returning to his stern master.
Structurally, the Haffner theme illustrates both Lach's notion of architectonic infrastructures and Kurth's laws of musical energy. Moreover, since Mozart made the most of a simple descending 4th and did so for primary melodic reasons, one of Szabolcsi's most cherished postulates is also upheld. The general validity of these basic concepts, whatever the exact harmonic or textural context, will be confirmed by a brief examination of the first bars of Wagner's Tristan (ex.5). Here the upward leap of a minor 6th finds immediate conjunct compensation in keeping with the rules laid down by Zarlino and other early theorists. While the cellos pursue the descending line a semitone further, the oboes mirror the chromatic descent of the cellos with a semitone rise to the tonic. In essence, if not note-for-note, this procedure corresponds to the manner in which Mozart complemented the appoggiatura in bar 7 of his Haffner Symphony with a semitone rise in bar 9. Wagner, however, went two chromatic steps further to the supertonic, whereas Mozart called a dramatic halt with a three-quaver rest before moving to the minor 3rd above, as if nothing had happened. The Tristan Prelude as a whole offers a veritable compendium of melodic procedures in a chromatic-harmonic context. The cello melody beginning in bar 17 is a poignant instance, since it generates tremendous energies with a single motivic idea spurred by strict adherence to the law of directional compensation.
The remaining examples, taken from the string quartets of Schoenberg, may serve to demonstrate that the abandonment of functional tonality, far from impeding melodic forces, actually restored the well-nigh absolute rule in all matters of musical texture they had enjoyed in the final quartets of Beethoven. The soprano melody in Schoenberg's Second Quartet (ex.6) is composed almost entirely of minor 2nds. But the law of directional compensation is scrupulously observed. The appoggiatura treatment of ‘Kreisend, webend’ is in fact strikingly similar to Mozart's and Wagner's manner, while the words ‘mich in tönen’ are actually set to the ‘Jupiter’ motif. That ever popular variant of the 3rd-cum-2nd idea resurfaces in Schoenberg's Fourth Quartet, a work based coincidentally on the same melodic materials as Beethoven's String Trio op.9 no.3, the thematic precursor of the late quartets. By the same token, the recitative-like opening of Schoenberg's Largo (ex.7) demonstrates Lach's ‘melic’ concept even more forcefully than its apparent model, the Hebrew Kol nidrei, a melody which, as Schoenberg himself observed, is not so much a tune in the Western sense as a quasi-oriental series of related and interlocking ‘melodicles’.
Unlike Schoenberg, who placed himself squarely in the European tradition, as represented by Bach, Mozart and Wagner, Webern favoured octave transposition to an extent that placed the age-old laws of melodic design under severe strain. A serial work like the Symphony op.21 abandons the last vestiges of vocal constraint for the seemingly limitless possibilities of advanced instrumental techniques. A quarter of a century later musical synthesizers, computers and machines of all sorts managed to achieve what the mere serial treatment of conventional pitch materials had left unfinished. Busoni (1922) uttered indeed prophetic words when he attempted to define 20th-century melody as follows:
A row of repeated (1) ascending and descending (2) intervals which (3) organised and moving rhythmically (4) contains in itself a latent harmony and (5) which gives back a certain atmosphere of feeling; which can and does exist (6) independent of accompanying voices for form; and in the performance of which (7) the choice of pitch (8) and of instrument (9) exercise no change over its essence … This ‘absolute’ melody, at first a self-sufficient formation, united itself subsequently with the accompanying harmony, and later melted with it into oneness; out of this oneness the continually progressive polyharmony aims to free and liberate itself. It must be asserted here, in contradiction to a point of view which is deeply-rooted, that melody has expanded continuously, that it has grown in line and in capacity for expression, and that it must succeed in attaining universal command in composition.
In this sense, Webern emerged as the supreme master of ‘absolute melody’. But paradoxically, the ‘melodic rhythm’, created by the conspicuous peaks and low points of his intricate textures, recalls very similar aspects of a much simpler medieval monophony, while the spatial metaphors he employed for his essentially elliptical musical ideas recall the non-teleological music of the orient he so admired. More specifically, the disembodiment of traditional melodic continuity at the behest of the ‘tone-colour melody’, postulated by Schoenberg as early as 1911, appears to be a function of omnidirectional sonorous forays that issue from and return to a small number of stable pitch centres, not unlike the circular harmonic excursions of the mature Wagner. By assigning unprecedented aesthetic significance to single pitches as well as selected intervallic relationships, moreover, Webern accomplished for traditional melody what Wagner had done for tonal harmony. Inevitably, his unrestrained explorations of musical space at the expense of temporal factors raised serious questions about the very future of melody. It was one of the more ironic quirks of history which turned the herald of ‘absolute melody’ into the revered godfather of an avant garde that has decreed the virtual demise of melody as a primary factor in musical experience.
But melody will not die that easily. After surviving handily in eastern Europe in the name of socialist realism, it has reasserted its strength in the West under the guise of an ideologically motivated folksong revival as well as in elaborate concert pieces relying on outright quotation or, at the very least, unqualified imitation of the past. During the decades of melodic drought, popular music of the commercial variety had been the only persistent and pervasive source of melodic inspiration. Some of the best tunes of the post-World War II era issued from the pens of the Beatles, just as those of the interwar period had been written by the Gershwins, the Cole Porters and the Irving Berlins. In the later 20th century the melodic circle appeared to be closing once again. For with its devotion to small, often descending and pentatonically conditioned melodicles, Afro-American rock music has returned melody, quite unwittingly, to its very beginnings.
MGG2 (C. Dahlhaus, H. Hüschen)
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G. Zarlino: Le istitutioni harmoniche (Venice, 1558/R, 3/1573/R; Eng. trans. of pt.iii, 1968/R, as The Art of Counterpoint; Eng. trans. of pt iv, 1983, as On the Modes)
J.-P. Rameau: Traité de l'harmonie (Paris, 1722/R; Eng. trans., 1971)
J. Mattheson: Kern melodischer Wissenschaft (Hamburg, 1737)
J.-P. Rameau: Observations sur notre instinct pour la musique (Paris, 1754/R)
C. Nichelmann: Die Melodie nach ihrem Wesen sowohl als nach ihren Eigenschaften (Danzig, 1755)
J.-J. Rousseau: Dictionnaire de musique (Paris, 1768/R; Eng. trans., 1771, 2/1779/R)
J.-J. Rousseau: Essai sur l'origine des langues (Geneva, 1781)
J.F. Daube: Anleitung zur Erfindung der Melodie und ihrer Fortsetzung (Vienna, 1797–8)
A. Molleson: Melody: the Soul of Music (Glasgow, 1798)
A. Reicha: Traité de melodie (Paris, 1814)
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A. Schoenberg: Harmonielehre (Vienna, 1911, 3/1922; Eng. trans., abridged, 1948, complete 1978)
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H. Zingerle: Zur Entwicklung der Melodik von Bach bis Mozart (Vienna, 1936)
P. Hindemith: Unterweisung im Tonsatz (Mainz, 1937–9; Eng. trans., 1941–2 as Craft of Musical Composition)
Z. Kodály: A magyar népzene (Budapest, 1937, 5/1969; Eng. trans., 1960, 2/1965 as Folk Music of Hungary)
C. Sachs: The Rise of Music in the Ancient World, East and West (New York, 1943)
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R. Sessions: The Musical Experience of Composer, Performer, Listener (Princeton, NJ, 1950)
J. Smits van Waesberghe: Melodieleer (Amsterdam, 1950; Eng. trans., 1954 as A Textbook of Melody)
B. Szabolcsi: A melódia története [A history of melody] (Budapest, 1950, 2/1957; Eng. trans., 1965)
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R. Steglich: ‘Über Mozarts Melodik’, MJb 1952, 47–52
T. Georgiades: Musik und Sprache (Berlin, 1954, 2/1974/R; Eng. trans., 1982)
A.C. Edwards: The Art of Melody (New York, 1956)
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B. Nettl: ‘Notes on Infant Musical Development’, MQ, xlii (1956), 28–34
B. Nettl: Music in Primitive Culture (Cambridge, MA, 1956)
NOHM, i (1957)
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W. Apel: Gregorian Chant (Bloomington, IN, 1958, 3/1966)
K. Reinhard: ‘On the Problem of Pre-Pentatonic Scales, particularly the Third-Second Nucleus’, JIFMC, x (1958), 15–17
E. Werner: The Sacred Bridge: the Independence of Liturgy and Music in Synagogue and Church during the First Millenium (New York, 1959–84/R)
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W. Wiora: Die vier Weltalter der Musik (Stuttgart, 1961; Eng. trans., 1965)
C. Sachs: The Wellsprings of Music: an Introduction to Ethnomusicology (Leiden and The Hague, 1962/R)
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A. Schoenberg: Fundamentals of Musical Composition, ed. G. Strang and L. Stein (New York, 1967)
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M. Schneider: Geschichte der Mehrstimmigkeit (Tutzing, 1969)
K.H. Wörner: Das Zeitalter der thematische Prozesse in der Geschichte der Musik (Regensburg, 1969)
H. Thürmer: Die Melodik in den Liedern von Hugo Wolf (Giebing, 1970)
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C.R. Adams: ‘Melodic Contour Typology’, EthM, xx (1976), 179–215
C.R. Adams: ‘Melodic Contour Typology’, EthM, xx (1976), 179–215
N. Baker: ‘Heinrich Koch and the Theory of Melody’ JMT, xx (1976), 1–4
W.J. Dowling and D. Harwood: Music Cognition (Orlando, FL, 1986)
M. Baroni: ‘A Grammar for Melody: Relationships between Melody and Harmony’, Musical Grammars and Computer Analysis: Modena 1982, 201–18; repr. in Musikometrika, i (1988), 215–36
J.C. Barlett and W.J. Dowling: ‘Scale Structure and Similarity of Melodies’, Music Perception, v/3 (1988), 285–314
P. Breslauer: ‘Diminutional Rhythm and Melodic Structure’, JMT, xxxii (1988), 1–22
M. De Natale: Analisi della struttura melodica (Milan, 1988)
R.O. Gjerdingen: A Classic Turn of Phrase: Music and the Psychology of Convention (Philadelphia, 1988)
P. Karlina and V.K. Detlovs: ‘Statistische Untersuchungen von Melodiesequenzien’, Musikometrika, i (1988), 159–68
E.W. Marvin: A Generalized Theory of Musical Contour: its Application to Melodic and Rhythmic Analysis of Non-tonal Music and its Perceptual and Pedagogical Implications (diss., U. of Rochester, 1989)
E. Narmour: ‘The “Genetic Code” of Melody: Cognitive Structures Generated by the Implication-Realization Model’, CMR, iv (1989), 45–64
R. Jakobik: Klangmelodie als gemeinsamer Nenner in den Musikwerken der klassichen Moderrte (Wilhemshaven, 1990)
E. Narmour: The Analysis and Cognition of Basic Melodic Structures (Chicago, 1990)
V. Zak: O zakonomernostyakh pesennoï melodiki [On the regularities of song melodies] (Moscow, 1990)
Z. Eitan: Style and Gesture: a Study of Melodic Peaks (diss., U. of Pennsylvania, 1991)
C.L. Krumhansl: ‘Melodic Structure: Theoretical and Empirical Descriptions, Music, Language, Speech and Brain: Stockholm 1990, ed. J. Sundberg, L. Nord and R. Carlson (London, 1991), 269–83
M.E. Pocock: The Influence of Harmonic Complexity on Melodic Expectations (diss., U. of Miami, 1991)
M. Baroni, R. Dalmonte and C. Jacoboni: ‘Theory and Analysis of European Melody’, Computer Representations and Models in Music, ed. A. Marsden and A. Pople (London, 1992), 187–205
E. Narmour: The Analysis and Cognition of Melodic Complexity (Chicago, 1992; see also review by W.F. Thompson, JAMS, xlix (1996), 127–45
D. De La Motte: Melodie: eine Lese-und Arbeitsbuch (Munich, 1993)
D. McGee: Musical Rules: a Knowledge-Based Simulation of an Implication-Realization Model (diss., U. of Wisconsin, 1993)
R. Schmusch: ‘Klangfarbenmelodie’ (1994), HMT
L.L. Cuddy and C.A. Lunney: ‘Expectancies Generated by Melodic Intervals: Perceptual Judgements of Melodic Continuity’, Perception and Psychophysics, lvii (1995), 451–62
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