Tonal Tension Research Articles

TenseMusic: An automatic prediction model for musical tension.

The perception of tension and release dynamics constitutes one of the essential aspects of music listening. However, modeling musical tension to predict perception of listeners has been a challenge to researchers. Seminal work demonstrated that tension is reported consistently by listeners and can be accurately predicted from a discrete set of musical features, combining them into a weighted sum of slopes reflecting their combined dynamics over time. However, previous modeling approaches lack an automatic pipeline for feature extraction that would make them widely accessible to researchers in the field. Here, we present TenseMusic: an open-source automatic predictive tension model that operates with a musical audio as the only input. Using state-of-the-art music information retrieval (MIR) methods, it automatically extracts a set of six features (i.e., loudness, pitch height, tonal tension, roughness, tempo, and onset frequency) to use as predictors for musical tension. The algorithm was optimized using Lasso regression to best predict behavioral tension ratings collected on 38 Western classical musical pieces. Its performance was then tested by assessing the correlation between the predicted tension and unseen continuous behavioral tension ratings yielding large mean correlations between ratings and predictions approximating r = .60 across all pieces. We hope that providing the research community with this well-validated open-source tool for predicting musical tension will motivate further work in music cognition and contribute to elucidate the neural and cognitive correlates of tension dynamics for various musical genres and cultures.

A Computational Model of Tonal Tension Profile of Chord Progressions in the Tonal Interval Space.

In tonal music, musical tension is strongly associated with musical expression, particularly with expectations and emotions. Most listeners are able to perceive musical tension subjectively, yet musical tension is difficult to be measured objectively, as it is connected with musical parameters such as rhythm, dynamics, melody, harmony, and timbre. Musical tension specifically associated with melodic and harmonic motion is called tonal tension. In this article, we are interested in perceived changes of tonal tension over time for chord progressions, dubbed tonal tension profiles. We propose an objective measure capable of capturing tension profile according to different tonal music parameters, namely, tonal distance, dissonance, voice leading, and hierarchical tension. We performed two experiments to validate the proposed model of tonal tension profile and compared against Lerdahl’s model and MorpheuS across 12 chord progressions. Our results show that the considered four tonal parameters contribute differently to the perception of tonal tension. In our model, their relative importance adopts the following weights, summing to unity: dissonance (0.402), hierarchical tension (0.246), tonal distance (0.202), and voice leading (0.193). The assumption that listeners perceive global changes in tonal tension as prototypical profiles is strongly suggested in our results, which outperform the state-of-the-art models.

Assistive Model to Generate Chord Progressions Using Genetic Programming with Artificial Immune Properties

In Western tonal music, tension in chord progressions plays an important role in defining the path that a musical composition should follow. The creation of chord progressions that reflects such tension profiles can be challenging for novice composers, as it depends on many subjective factors, and also is regulated by multiple theoretical principles. This work presents ChordAIS-Gen, a tool to assist the users to generate chord progressions that comply with a concrete tension profile. We propose an objective measure capable of capturing the tension profile of a chord progression according to different tonal music parameters, namely, consonance, hierarchical tension, voice leading and perceptual distance. This measure is optimized into a Genetic Program algorithm mixed with an Artificial Immune System called Opt-aiNet. Opt-aiNet is capable of finding multiple optima in parallel, resulting in multiple candidate solutions for the next chord in a sequence. To validate the objective function, we performed a listening test to evaluate the perceptual quality of the candidate solutions proposed by our system. Most listeners rated the chord progressions proposed by ChordAIS-Gen as better candidates than the progressions discarded. Thus, we propose to use the objective values as a proxy for the perceptual evaluation of chord progressions and compare the performance of ChordAIS-Gen with chord progressions generators.

MorpheuS: Generating Structured Music with Constrained Patterns and Tension

Automatic music generation systems have gained in popularity and sophistication as advances in cloud computing have enabled large-scale complex computations such as deep models and optimization algorithms on personal devices. Yet, they still face an important challenge, that of long-term structure, which is key to conveying a sense of musical coherence. We present the MorpheuS music generation system designed to tackle this problem. MorpheuS' novel framework has the ability to generate polyphonic pieces with a given tension profile and long- and short-term repeated pattern structures. A mathematical model for tonal tension quantifies the tension profile and state-of-the-art pattern detection algorithms extract repeated patterns in a template piece. An efficient optimization metaheuristic, variable neighborhood search, generates music by assigning pitches that best fit the prescribed tension profile to the template rhythm while hard constraining long-term structure through the detected patterns. This ability to generate affective music with specific tension profile and long-term structure is particularly useful in a game or film music context. Music generated by the MorpheuS system has been performed live in concerts.

Analysis of Musical Expression Using Tonal Tension and Attraction Models

Musical Expression is constructed from repetition of tension and relaxation made from the chord progression, melodic motion and progression, beat structure, rhythmic structure, etc. In addition, musical expression is affected by some kinds of attraction between each adjacent pairs of events of chords. In this article, using the tonal tension and attraction models, some analyses of musical expression for actual performances by top-class pianists are shown. In these analyses, the multiple regression analysis with Akaike Information Criterion is used.

Implicit Absolute Pitch Representation Affects Basic Tonal Perception

It is undisputed that the cognition of tonal music is primarily established by pitch relationships set within a tonal scheme such as a major or minor key. The corresponding notion—that absolute pitch and absolute key are largely inconsequential for tonal cognition—thus seems inevitable. Here, we challenge the latter notion, presenting data suggesting that absolute pitch and absolute key significantly modify listeners’ judgments of tonal fit and tonal tension. In two experiments extending the probe tone technique (as applied in Krumhansl & Kessler, 1982) participants heard a brief tonal context (a major triad in Experiment 1, a harmonic progression in Experiment 2) followed by individual probe tones, and rated how well each probe fitted the preceding context, as well as the musical tension conveyed by each probe. Two maximally distant key contexts, G major and D♭ major, were used in both experiments and in both tasks. Ratings revealed significant absolute pitch effects in both tasks, though in different ways. In the tonal fit task, diatonic pitches in G major were rated higher than those in D♭ major; in contrast, chromatic pitches were rated higher in D♭ major, compared to G. In the tension task, overall ratings were significantly higher for D♭ major contexts than for G major context (Experiment 1). Importantly, these effects reflect the occurrence frequency of pitch classes and keys in the tonal repertory: frequent pitch classes were rated as better fits than rarer ones, and a rarer key (D♭) rated tenser than a frequently-occurring key (G). Absolute pitch effects were most strongly manifested by participants without formal training, for whom the relative pitch effects of the tonal hierarchy were weak, and were stronger when tonal context was weaker (Experiment 1 as compared to Experiment 2). Results suggest that implicit absolute pitch perception, reflecting key and pitch class occurrence frequency, significantly affects tonal music processing; such absolute pitch effects may be activated principally when tonal perception or tonal cues are lacking.

Harmonic Structure Predicts the Enjoyment of Uplifting Trance Music.

An empirical investigation of how local harmonic structures (e.g., chord progressions) contribute to the experience and enjoyment of uplifting trance (UT) music is presented. The connection between rhythmic and percussive elements and resulting trance-like states has been highlighted by musicologists, but no research, to our knowledge, has explored whether repeated harmonic elements influence affective responses in listeners of trance music. Two alternative hypotheses are discussed, the first highlighting the direct relationship between repetition/complexity and enjoyment, and the second based on the theoretical inverted-U relationship described by the Wundt curve. We investigate the connection between harmonic structure and subjective enjoyment through interdisciplinary behavioral and computational methods: First we discuss an experiment in which listeners provided enjoyment ratings for computer-generated UT anthems with varying levels of harmonic repetition and complexity. The anthems were generated using a statistical model trained on a corpus of 100 uplifting trance anthems created for this purpose, and harmonic structure was constrained by imposing particular repetition structures (semiotic patterns defining the order of chords in the sequence) on a professional UT music production template. Second, the relationship between harmonic structure and enjoyment is further explored using two computational approaches, one based on average Information Content, and another that measures average tonal tension between chords. The results of the listening experiment indicate that harmonic repetition does in fact contribute to the enjoyment of uplifting trance music. More compelling evidence was found for the second hypothesis discussed above, however some maximally repetitive structures were also preferred. Both computational models provide evidence for a Wundt-type relationship between complexity and enjoyment. By systematically manipulating the structure of chord progressions, we have discovered specific harmonic contexts in which repetitive or complex structure contribute to the enjoyment of uplifting trance music.

VOICE‐LEADING ENERGETICS IN WAGNER'S ‘TRISTAN IDIOM’

ABSTRACTRecent theories of musical energetics have typically given tonality – often a powerfully synthetic, prolongational monotonality – a decisive role in accounting for sensations of musical tension, force and attraction. Though well‐suited to music of the common practice, these models fare less well in certain repertoires of the later nineteenth century, where tonal centres are often fleeting and traditional syntax is weakened or even annulled—as is often the case in Wagner's late music, where dissonant tertian tetrachords are combined in new and sometimes confounding ways.This study offers a new perspective on tonal tension and relaxation in such passages – which I call Wagner's ‘Tristan idiom’ – by focusing on voice‐leading contour. Taking a broad cue from Ernst Kurth, it asks what might be gained by bracketing questions of chord identity and structure to focus instead on the voice leading that produces and interconnects them. Using a tool called kinetic displacement metrics (KDMs), it assigns emergent psychokinetic tension values to chord pairs based on the directions that their voices move, both in pitch‐ and pitch‐class space. Of special interest throughout is a phenomenon I call ‘directional variance’, where opposing contours in a single passage (between abstract and real voice leading, for example, or between the harmonic layer and the melodic one) seem to have psychodramatic relevance for the stage action.After a brief exposition of the theory and its uses (and limitations), with brief examples from all of Wagner's post‐Lohengrin operas, it then moves to a series of longer vignettes on excerpts from Tristan und Isolde: the opening of the Act I Prelude, the closing of the same, and the entirety of the Act III Prelude.

Of Non-vital Interest: Art, Mimicry, and the Phenomenon of Life

My aim in this essay is to explore certain parallels—concerning anthropomorphism—in the work of Roger Caillois, Hans Jonas, Theodor Adorno and Sigmund Freud. Both Caillois (a thinker closely connected to French Surrealism and an important source for Jacques Lacan) and Jonas (philosopher and one-time student of Heidegger) take issue with the ban on anthropomorphism—an anathema that is the legacy of Western science. Part of the thesis in Jonas’ major work, The Phenomenon of Life, is that freedom is not exclusively a human quality but a potential within the simplest organic forms, even within inorganic matter. Anthropomorphism may be the legacy of a primitive stage in human development in which the whole of creation was endowed with a soul, but this attitude, Jonas argues, is the more natural one. Whereas in the early phases of humanity death was the stranger in a world that was fundamentally alive, modern thinking made life the riddle within a world of neutral matter and mechanistic principles. Freud’s own theory of the death-drive (“an urge inherent in organic life to restore an earlier state of things which the living entity has been obliged to abandon under the pressure of external disturbing forces”) seems quite consistent with the primacy of death over life instituted by modern thought. I have a general interest in comparing Freud’s theory of the death drive, the aim of which is the restoration of an original equilibrium, with music, whose traditional structure (via the cadence) is to relieve tonal tension through a restoration of the keynote (Grundton). This bears upon the problem of anthropomorphism in that “classical” music since the seventeenth century has cast expression in terms of simulated human emotions: we hear music and perceive love, longing or fear, not to mention (in the case of pastorale) the “cheer” of birdsong or the “rage” of a thunderstorm. Adorno’s critique of this tradition, in which true expression is replaced by mere images of expression, theorizes what he calls a “tendency of the material,” extolling the composer whose sheer mastery of technique enables the material to go where it “wants” to go. What Adorno means by “material” is not merely the inventory of sounds available to the musician but the historical experience sedimented within musical convention. Nonetheless, I would like to attempt an argument whose parameters are Adorno’s “tendency of the material” and Jonas’ idea that freedom must be conceived as a “genuine potency” within physical substance.

Cognitive Models of Tonal Tension

Cognitive Models of Tonal Tension

Emotional processing in music: Study in affective responses to tonal modulation in controlled harmonic progressions and real music.

The pitch material of virtually all the musics of the world is organized into tonal hierarchies in which the pitch classes of a tonal scale divide the octave into (typically) five to seven steps of a tonal scale, with a stable home base in the tonic pitch, and a variety of tonal functions and tendencies assigned to the remaining pitch classes (Dowling & Harwood, 1986). In western music, the tonal hierarchy is organized in terms of two principal modes, major and minor, defined in terms of tonal scales of seven pitch classes (Krumhansl, 1990). The seven pitch classes of a mode are selected from the set of 12 logarithmically equal steps (semitones) into which the octave has been divided by the system of equaltempered tuning adopted in Europe beginning in the early 18th century (Robinson & Needham, 1962). All the intervals defined by a mode are defined in terms of numbers of semitones, so any of the 12 possible pitch classes can be chosen as the tonic pitch of a musical (e.g., C major or E minor). Hence, a melody played in one key can be shifted to another key without distorting its melodic intervals. This system makes possible a shift of keys within a piece, which is called modulation.Tonal modulation involves a shift of tonal center within the same musical composition, involving a transition to a different key (tonality) with a new scale of pitch classes. Modulation is one of the main structural and expressive aspects of music in the European musical tradition. Relationships among tonalities are described in terms of the circle of fifths (Diletsky, 1677; see Figure 1). The circle of fifths arises because you can start with any pitch class and go up or down by 7 semitones (a musical fifth) and arrive at a tonal center whose major scale differs from the original scale by just one altered pitch. In Figure 1, this is illustrated by going from C up a fifth to G. The key of G major has one altered pitch (F#) with respect to the key of C major. The second example in Figure 1 shows what happens if we go up clockwise by five fifths around the circle, landing on B and adding five sharps (#) to alter the pitches of the scale. The more steps (in the shortest direction) between two pitches on the circle of fifths, the more differences between the two pitch sets that define the tonalities represented by these letters. Modulations can thus vary in the distance over which they travel in tonal space from one key to another. The greater the distance, the more complicated and surprising they are likely to be.Modulations can also vary in the relationships between the original and target modes. Each of the 12 available steps around the circle of fifths can be the center for two tonalities, one in a major mode and another in a minor mode, so that there are four possible modal relationships involved in modulations: Major- Major, Major-minor, minor-Major, and minor-minor. The major mode is generally characterized as happy, and the minor mode as sad. The affective influence of the major and minor modes has been thoroughly investigated (Gagnon & Peretz, 2003; Halpern, Martin, & Reed, 2008; Hevner, 1935; Kastner & Crowder, 1990; Panksepp & Bekkedal, 1997; Webster & Weir, 2005).Previous studies have demonstrated that listeners are able to track modulations in that their cognitive responses in terms of tonal-hierarchy profiles and ratings of tonal distance or tension are differentially affected (Firmino, Bueno, & Bigand, 2009; Krumhansl & Kessler, 1982; Lerdahl & Krumhansl, 2007; Thompson & Cuddy, 1989, 1992; Toiviainen & Krumhansl, 2003). The process of following the reorientation of a tonal center is guided by musical expectations and by perceived tonal tension (Lerdahl & Krumhansl, 2007; Meyer, 1956). In modulation, the degree of the perceived change in tonal tension increases with key distance (Bigand & Parncutt, 1999; Firmino et al., 2009) and is greater with clockwise (vs. …

Modeling Tonal Tension

THIS STUDY PRESENTS AND TESTS a theory of tonal tension (Lerdahl, 2001). The model has four components: prolongational structure, a pitch-space model, a surfacetension model, and an attraction model. These components combine to predict the rise and fall in tension in the course of listening to a tonal passage or piece. We first apply the theory to predict tension patterns in Classical diatonic music and then extend the theory to chromatic tonal music. In the experimental tasks, listeners record their experience of tension for the excerpts. Comparisons between predictions and data point to alternative analyses within the constraints of the theory. We conclude with a discussion of the underlying perceptual and cognitive principles engaged by the theory's components.

Overview of the KTH rule system for musical performance

The KTH rule system models performance principles used by musicians when performing a musical score, within the realm of Western classical, jazz and popular music. An overview is given of the major rules involving phrasing, micro-level timing, metrical patterns and grooves, articulation, tonal tension, intonation, ensemble timing, and performance noise. By using selections of rules and rule quantities, semantic descriptions such as emotional expressions can be modeled. A recent real-time implementation provides the means for controlling the expressive character of the music. The communicative purpose and meaning of the resulting performance variations are discussed as well as limitations and future improvements.