Tonal Center Research Articles

The Interplay of Set Content and Temporal Context in a Functional Theory of Tonality Perception

The purpose of this study was to provide evidence for the perceptual component of an analysis of pitch relationships in tonal music that includes consideration of both formal analytic systems and musical listeners' responses to tonal relationships in musical contexts. It was hypothesized (1) that perception of tonal centers in music develops from listeners' interpretations of time-dependent contextual (functional) relationships among pitches, rather than primarily through knowledge of psychoacoustical or structural characteristics of the pitch content of sets or scales and (2) that critical perceptual cues to functional relationships among pitches are provided by the manner in which particular intervallic relationships are expressed in musical time. Excerpts of tonal music were chosen to represent familiar harmonic relationships across a spectrum of tonal ambiguity/specificity. The pitch-class sets derived from these excerpts were ordered: (1) to evoke the same tonic response as the corresponding musical excerpt, 2) to evoke another tonal center, and (3) to be tonally ambiguous. The effect of the intervallic contents of musical excerpts and strings of pitches in determining listeners' choices of tonic and the effect of contextual manipulations of tones in the strings in directing subjects' responses were measured and compared. Results showed that the musically trained listeners in the study were very sensitive to tonal implications of temporal orderings of pitches in determining tonal centers. Temporal manipulations of intervallic relationships in stimuli had significant effects on concurrences of tonic responses and on tonal clarity ratings reported by listeners. The interval rarest in the diatonic set, the tritone, was the interval most effective in guiding tonal choices. These data indicate that perception of tonality is too complex a phenomenon to be explained in the time-independent terms of psychoacoustics or pitch- class collections, that perceived tonal relationships are too flexible to be forced into static structural representations, and that a functional interpretation of rare intervals in optimal temporal orderings in musical contexts is a critical feature of tonal listening strategy.

Tonal Implications and the Role of the Symmetrical Hexachord in Alban Berg's Four Pieces for Clarinet and Piano, Opus 5, No. 2

Abstract In this paper I demonstrate that the Berg Four Pieces for Clarinet and Piano, Opus 5, No. 2, is a veiled tonal piece, with its background tonal center of Bb generated by a five‐note set, (10,1,2,5,6), a subset of the all‐combinatorial hexachord [0,3,4,7,8,11]. A combination of a Schenker‐style reductive technique and Forte‐style pitch‐class set theory is used in this analysis.

The Tonal Chromatic Scale as a Model for Functional Chromaticism

Some recent empirical studies concerning the perception of tonal melodies are based upon the theoretical assumption that it is adequate to distinguish "tonal" from "atonal" tunes with reference to diatonic and chromatic pitch collections, respectively. Such a principal of demarcation, however, fails to account for the intuitive sense that melodies may display relative degrees of "tonal-ness" and that chromaticism may function to establish and reinforce tonal centers. What appears necessary for the evaluation of results of such studies, as well as for the formulation of further experiments, is a tonal-functional theory of chromaticism that will allow the distinction between "tonal" and "atonal" to be appropriately clarified. This article presents an informal model for a functional theory of chromaticism based upon a "tonal chromatic" scale. Drawing upon a critique of a functional model formulated by Deutsch and Feroe, this study develops concepts central to the notion of chromatic function. These concepts are then employed in a critique of four proposed forms of chromatic scales, specifying weaknesses in each. Following this, the author proposes a "tonal chromatic" scale which overcomes difficulties inherent in previously proposed scale forms. Analytical examples are offered that illuminate the structural implications of the model.

Structure as Hermeneutic Guide to The Magic Flute

STUDIES of Mozart's The Magic Flute have generally ignored the overall musical structure of the opera as a resource for discerning its meaning. Failure to consider its musical structure limits understanding of the work, particularly in preparing it for the stage. The tendency to reorder musical numbers provides a supposedly more coherent version of the plot but seriously disrupts the musical organization.' In striking contradiction to this trend, Eugen Schmitz's Formgesetze in Mozart's Zauberflite2 presented a schema in which he identified each musical number by key as a means of demonstrating the unity of the opera. Yet Schmitz's analysis typifies the view that the order of tonal centers is in some measure haphazard. For example, he points to what he sees as an imbalance between the coherence of the first act and the extra-

The Color of Melody

The vocabulary of color perception often enters the description of music and musical experience. However, analysis of the color—note or colorkey associations often reported for "synesthetic" musicians is problematic: color and music associations do not appear to preserve the organizational principles contained within the separate modalities. This study, influenced by recent work on parallel principles for color and speech/timbre perception, proposed that the operation of color principles in melody occurs not at the level of single-tone recognition but at a higher level of auditory organization. This level may be represented by the relationship among key or tonal centers projected on the cycle of fifths. Experimental work tested the prediction that perceived structure of various sequential mixtures of tonal centers would follow the general principles of color mixture. The prediction was supported by the data from fifteen musical listeners; it did fail, however, with a small group of selfreportedly "tone-deaf" listeners. Implications of the color metaphor for the study of tonality are discussed.

A Methodology for the Discussion of Contour: Its Application to Schoenberg's "Music"

Accounts of continuity in tonal music have generally been accounts of pitch relations. This can be justified because of the gravitational power of the tonal center in defining cadences and because of the decisiveness of consonance-dissonance relations for hearing meter. For twentieth-century music, theories of pitch-class relations have attempted to play a similar role, reassuring all doubters that pitch class not only accounts for relations at the surface level, but is the only true source of deeper structural relations. Pitch-class relations, however, by their very nature, are incapable of exerting the same degree of control over the musical surface as could be attributed to pitch relations in tonal music. Whereas pitch relations are the bearers of linear continuity in tonal music via scale steps, pitch-class relations in post-tonal music, no matter how rigorously controlled, cannot make a comparable claim. We are confronted, then, with a serious gap between the vivid realities of the surface of twentieth-century music and our accounts of the rather remote abstractions that are supposed to be its prime determinants. Recent work on timbre, meter, and attack point relations has begun to remedy the one-sided pitch-class favoritism, but these parameters too often are relegated to the margins as surface phenomena. The radical music of the classical twelve-tone period most often has

Tonal Structure versus Function: Studies of the Recognition of Harmonic Motion

Two empirical studies identified and tested strengths of dynamic cues that assist listeners in identifying tonal centers. The hypothesis that it is rare intervals, rather than physical properties of tones or static representations such as scales and triads, that play a significant role in a musician's perceptual process of key identification led to the first experimental study of context sufficiency in perception of tonality. Musicians extrapolated tonal centers upon aural presentation of subsets of a major diatonic set with an accuracy mean of 87%. Univalent trichords gave 100% clearer indication of tonal center than did multivalent trichords. The strength of the tonality percept was further explored by examining effects of temporal ordering and by evaluating relationships between formal training and test scores. In a second experiment, listeners judged appropriateness of tonal centers after hearing paired dyads consisting of the rarest intervals in the major set: the tritone and the two minor seconds. Listeners indicated strongest impressions of tonal center when the tritone was heard as a simultaneity. Test performance showed a stronger correlation with listeners' abilities to identify tonal centers in actual music than with listeners' status as musicians or nonmusicians. These results are interpreted as evidence of a widespread cognitive skill that interprets tonality as a system of tonal relations rather than just an abstracted collection of tones or a system governed by the psychophysical attributes of tones.

The Effects of Age, Singing Ability, and Instrumental Experiences on Preschool Children's Melodic Perception

This study investigated the effects of age, singing ability, and training with pitched instruments on preschool children's auditory perception of five melodic components: absolute pitch level, melodic rhythm, melodic contour, tonal center, and melodic interval. The results of the study, based on the vocal responses of 91 3- to 5-year-old subjects, revealed the following: (a) significant differences associated with age were found in preschool children's perception of melodic rhythm, melodic contour, and melodic interval; (b) high-ability singers scored higher than low-ability singers on perception of melodic rhythm, melodic contour, tonal center, and melodic interval; (c) instrumental and noninstrumental treatment groups did not differ significantly in perception of the melodic components.

Musical key structure and its influence on perceived harmonic relations

A structural description of musical key distance was derived from the tone‐profile technique in which listeners rate how well each chromatic‐scale tone follows a key‐defining element (scale, tonic triad chord, or chord cadence). The rating profiles, reflecting the music‐theoretic hierarchy of tonal stability, were shifted to all possible tonics, intercorrelated, and analyzed using multidimensional scaling. The four‐dimensional solution placed the 24 major and minor keys on a torus simultaneously accommodating the circle of fifths and relative and parallel relations between major and minor keys. Two subsequent experiments investigated the effect of interkey distance on perceived harmonic relations between chords. The magnitude of three independent context effects (measured in both direct relatedness judgments and memory confusions) was found to depend systematically on the distance between the keys in which the chords function and the key of the broader context in which they are embedded. The results provide strong evidence that listeners interpret chords in their tonal functions and have internalized structure at the level of abstract tonal centers. [Work supported by NSF.]

Key distance effects on perceived harmonic structure in music.

Two experiments provide convergent evidence for the hypothesis that listeners interpret chords in terms of their harmonic functions in a system of interrelated keys. The perceived associations between chords undergo significant changes depending on the broader tonal framework in which they are embedded. Three independent context effects are identified, and their magnitude is found to be a systematic function of the distance between the context key and the key lot keys) of which the chords are members. In the first experiment, listeners rate how musically related one chord is to a second chord; the chords are those that function within two maximally distant major keys (C major and F# major). All possible chord pairs from this set are presented in each of three context keys: G major which is close to C major and distant from F# major), A major (which is moderately distant from both C major and F# major), and B major (which is close to F# major and distant from C major). The second experiment measures recognition memory for the same chords embedded in tonal sequences in C, G, A, or B major keys, or random sequences. In the two experiments, the distance between the context key and the key of the chords on the circle-of-fifths affects: (1) the probability that a repeated chord is correctly recognized, (2) the strength of association between chords from the same key measured in terms of both confusion errors and direct relatedness judgments, and (3) asymmetries in confusion errors and relatedness judgments when the chords are in different keys. Perceived harmonic relations are thus found to be strongly context dependent, but the context effects are lawful functions of interkey distance. We conclude that listeners possess a highly articulated system of knowledge about the harmonic functions of chords in musical keys and an appreciation of musical structure at the level of abstract tonal centers.

Music and Visual Color: A Proposed Correlation

The author tells of events leading up to finding a possible link between musical harmony and visual color based on complementarity. He points out that an equal division of the musical octave into 12 half-steps permits one to recognize chords built on tones occurring at the interval of half an octave or the tritone interval as being complementary to each other. This corresponds to the equal spacing of 12 hues on a color circle in which complementary hues are located diametrically opposite each other. A circularform of the musical octave divided according to the chromatic scale of 12 half- stepsplaces tones serving as rootsfor complementary chords diametrically opposite each other also. There seems to be a parallel between the equal division of the color circle into 3 primaries and 3 secondaries and the equal division of the musical circle into 6 whole steps or the whole-tone scale. In both circles, colors and chords that can be classified as secondaries are complementary to the primaries and vice versa. The near-complements of a color lying on either side of its complement are more subdued in contrast with the color than the complement is. Chords built on tones on either side of a tritone intervalfrom a given tonal center on the musical circle also produce subdued contrast with a chord built on the tonal center. The relationship of the adjacent chords to a chord built on the tonal center is as of sub-dominant to tonic and dominant to tonic, which is the harmonic basis of the diatonic system. I.

Tonal Organization in Schoenberg's Six Little Piano Pieces, Op. 19

Tonal Organization in Schoenberg's Six Little Piano Pieces, Op. 19. Un article de la revue Canadian University Music Review / Revue de musique des universités canadiennes (Numéro 1, 1980, p. 1-159) diffusée par la plateforme Érudit.

Tonality and Atonality in the Prologue to Orlando di Lasso's Prophetiae Sibyllarum: Some Methodological Problems in Analysis of Sixteenth-Century Music

a triadic texture erode any sense of a stable tonal center. . . . In the first nine bars of the prologue to the prophecies Lasso uses all twelve tones; he builds triads on ten different degrees, six of which result in harmonies foreign to the mode if we take the mode as Mixolydian since the piece ends on G. Lasso strays as far as B-flat major and C minor in one direction, and B major in the other. This phrase, although beginning on a C major and ending on a G major chord, has no stable frame of tonal reference. Through the excessive modulation within so small a space we lose all orientation.2

Interaction between rhythmic prominences and intonation

Students played scales on equipment which provided altermative tunings of scale notes. When instructed to dwell on one or another note, they chose different tunings for the subsequent notes of the scale. This suggests that when a note is made prominent, it is likely to establish a second tonal center to which later intonations are related. Thus the rhythmic structure of a melodic phrase interacts with pitch choices in performance.

Rameau's Nouvelle Méthode

DISCUSSIONS OF THE THEORETICAL SYSTEM of Jean-Philippe Rameau (I16831764) are ordinarily concerned with the origin and significance of the basse fondamentale and related concepts and with Rameau's scientific or Cartesian bias, which served to attract the attention of the philosophes and Encyclopedists. Such discussions often pay insufficient attention to the fact that one of the principal sources of Rameau's system, and probably the main reason for its endurance, was his activity as a composer, performer, and teacher. His stated purpose was always to simplify and thus improve harmonic practice in conformance with the natural, scientific procedures and principles that he had discovered. Traditional methods of continuo realization required an abundance of chords, chord progressions, and rules-rules of doubling, voice leading, and dissonance treatment. But the principle of the fundamental bass-the succession of chord roots-was supposed to make possible a simpler, more natural, and therefore better method of learning keyboard accompaniment and composition. The fundamental bass principle told the performer or composer the key or tonal center of the piece of music, the various keys through which it passed, the functions of the chords, the harmonic rhythm, the lengths of the phrases, and the location of the cadences. In i732 Rameau published a short treatise entitled Dissertation sur les diffdrentes me'thodes d'accompagnement pour le clavecin ou pour l'orgue; avec le plan d'une nouvelle me'thode, ftablie sure une me'chanique des doigts, que fournit la succession fondamentale de l'harmonie : et d l'aide de laquelle on peut devenir sfavant compositeur, & habile accompagnateur, meme sans sfavoir lire la musique1 (Dissertation on the different methods of accompaniment for the harpsichord or organ, with the plan for a new method, based on a fingering technique furnished by the fundamental succession of the harmony, and with the aid of which one can become a knowledgeable composer and skillful accompanist, even without knowing how to read music). By this time his theories were generally known, mainly from the Traite de l'harmonie (1722) and the Nouveau Systkme (1726). He was now fifty years old and was living in Paris. Although not yet known as a dramatic composer (the opera

Some Thoughts on "Universals" in World Music

and our own that captured our interest in the first place and we, as well as the next man, respond to the unique, the fascinating, the exotic. It follows naturally that much of our discourse is devoted to the differences between musics, but we spend so much of our time on these differences, brought to us from every corner of the world, and sometimes from our own backyards, that we can't help wondering if there are not also great overruling similarities. The plenary session on at the November, 1970, annual meeting of the Society was an attempt to consider these similarities in the broadest perspective. We are drawn together at our various kinds of meetings because we share an interest and we do not doubt for a moment that this interest is music, however it is defined and whatever the culture from which it derives. One of the odd things about us is how heterogeneous we are as a Society: we are made up of anthropologists, ethnologists, folklorists, dancers, dance ethnographers, linguists, sociologists, and I haven't even begun to enumerate the musicians and the scholars of music among us, who constitute the greater part of our numbers. When we are assembled, it sometimes occurs to us to ask what we really have in common. If there are elements of music that are found everywhere, then these are what we share. A sharpened awareness of such elements could be valuable in helping us understand ourselves as a group. Let me venture the opinion, first, that there are probably no absolute universals in music. I say this simply on the grounds of human variability and complexity. Any student of man must know that somewhere, someone is doing something that he calls music but nobody else would give it that name. That one exception would be enough to eliminate the possibility of a real universal. But I think there are plenty of near-universals and, even though such a term contradicts itself, a near-universal is near enough for our purposes. I will be satisfied if nearly everybody does it. I will just mention some of these and then go on to the one that interests me the most. Almost everywhere there is some sense of the tonic, some kind of a tonal center in music. Almost everywhere music establishes a tendency. It seems to be going somewhere, whatever its terms are, and the joy

Modality in Spanish Renaissance Vihuela Music and Archaic Chilean Folksongs: A Comparative Study

monophonic criterion--involving endings, ranges, octave species, and cadences-borrowed from plainsong and applied to the modal recognition of the upper voice or the tenor; and 2) a new empirical polyphonic criterion, not considered in theoretical writings as belonging to the realms of modality but evident in the written and unwritten accidentals added mostly in connection with the rules of consonance.2 In fact, Renaissance musical idioms employed a new transitional polyphonic mode of which the main identifiable features are: a) Addition of written and unwritten accidentals. Alternative use of a sharp or flat seventh degree.3 Conflicting or partial key signatures.4 b) Change in modal preferences. In theory, expansion of the eight modes to twelve; in practice, reduction of the eight modes and predominance of two. c) Relative ambiguity of tonal centers; emphasis on modal degrees.5 Emergence of tonal transposition. The Spanish vihuela repertory, which flourished most brilliantly during the sixteenth century, provides an ideal source for the study of modality. If compared with the less precise polyphonic scores, the vihuela tablatures based on chromatic frets offer a reliable notation. A recent study by the present writer (Grebe 1966) of a specific part of the vihuela repertory indicates the existence of several innovations in its modal language: the sharp reduction of modal preferences, the growth of transpositions, the large quantity of accidentals, and other features anticipating the transitional idiom of the early Baroque. Vihuela music expresses the native Spanish character better than sacred vocal polyphony. Its repertory was developed by native court minstrels and instrumentalists whose links with the traditional ballad jongleur are shown in the frequent borrowings of folk melodies be

Patterns of Ratio Relationships in Melody

Musicians selected their preferred tunings for specific melodies, using an instrument that allows choice of intonation. In this critical listening situation, their choices were found to represent a number of variations on a principle of organization by simple whole-number ratios to tonal centers. Even without modulation, these melodic choices shift away from direct relation to the tonic to relation to other tonal centers. These acting tonal centers stand in small-whole-number ratios to other centers, which in turn have the same class of relation to the tonic. The instances presented do not match any known scale; they indicate structural importance for variant tunings of the same note, and for what is here called “extended reference,” a tendency to avoid direct relationship to the tonic until resolution is desired. Thus, they indicate that tuning preferences are the result of the operation of structural principles embodied in a melody rather than in a scale.

The Polyphonic Magnificat of the Renaissance as a Design in Tonal Centers

The Polyphonic Magnificat of the Renaissance as a Design in Tonal Centers

The Polyphonic Magnificat of the Renaissance as a Design in Tonal Centers

The Polyphonic Magnificat of the Renaissance as a Design in Tonal Centers