Calculating Tonal Tension

1996 ◽  
Vol 13 (3) ◽  
pp. 319-363 ◽  
Author(s):  
Fred Lerdahl
Keyword(s):  
Voice Leading ◽  
Hierarchical Approach ◽  
Directed Motion ◽  
Tonal Music ◽  
Generative Theory ◽  
Tonal Pitch ◽  
Pitch Space

The prolongational component in A Generative Theory of Tonal Music assigns tensing and relaxing patterns to tonal sequences but does not adequately describe degrees of harmonic and melodic tension. This paper offers solutions to the problem, first by adapting the distance algorithm from the theory of tonal pitch space for the purpose of quantifying sequential and hierarchical harmonic tension. The method is illustrated for the beginning of the Mozart Sonata, K. 282, with emphasis on the hierarchical approach. The paper then turns to melodic tension in the context of the anchoring of dissonance. Interrelated attraction algorithms are proposed that incorporate the factors of stability, proximity, and directed motion. A distinction is developed between the tension of distance and the tension of attraction. The attraction and distance algorithms are combined in a view of harmony as voice leading, leading to a second analysis of the opening phrase of the Mozart in terms of voiceleading motion. Connections with recent theoretical and psychological work are discussed.

Genesis and Architecture of the GTTM Project

2009 ◽  
Vol 26 (3) ◽  
pp. 187-194 ◽  
Author(s):  
Fred Lerdahl
Keyword(s):  
Theory Construction ◽  
Tonal Music ◽  
Generative Theory ◽  
Tonal Pitch ◽  
Pitch Space

I EXAMINE THE INTELLECTUAL AND MUSIC-THEORETIC origins of A Generative Theory of Tonal Music (Lerdahl & Jackendoff, 1983) and review the crucial steps in theory construction that led to its overall architecture. This leads to a discussion of how shortcomings in GTTM motivated developments in Tonal Pitch Space (Lerdahl, 2001). I conclude with a diagram that encompasses the major components of the expanded GTTM/TPS theory.

Modal Pitch Space — A Theoretical and Analytical Study

2003 ◽  
Vol 7 (1) ◽  
pp. 57-86 ◽  
Author(s):  
Costas Tsougras
Keyword(s):  
Analytical Study ◽  
Tonal Music ◽  
Generative Theory ◽  
Tonal Space ◽  
The Stability ◽  
Tonal Pitch ◽  
Melodic Motion ◽  
Algebraic Representations ◽  
Pitch Space ◽  
Modal Music

This paper presents an approach to the pitch space of the seven diatonic modes. The proposed theory is an expansion of Fred Lerdahl's tonal pitch space model; its purpose is a more accurate description of the situations involved in the analysis of diatonic modal music. The original methodology and set of algebraic calculating formulae is retained, but it is applied on modal instead of tonal space, on the basis that the latter is a subset of the former. In connection to Fred Lerdahl's theory, melodic motion, chord attraction and various cadence types are described within the modal context. Apart from the calculation of the pitch and the chordal and regional space algebraic representations, geometrical representations of all three levels of the modal pitch space are also included. Finally, the stability conditions arising from the new model are used as criteria to build the time span reduction and prolongational reduction parts of the Generative Theory of Tonal Music (GTTM) analysis of modal music. Two short GTTM analyses of 20th century modal music are being presented to illustrate the new model's analytical use.

Perceptions of Musical Dimensions in Beethoven's Waldsiein Sonata: An Application of Tonal Pitch Space Theory

2003 ◽  
Vol 7 (1) ◽  
pp. 7-34 ◽  
Author(s):  
Nicholas A. Smith ◽  
Lolal Cuddy
Keyword(s):  
Random Order ◽  
Temporal Orientation ◽  
Voice Leading ◽  
Space Theory ◽  
Piano Sonata ◽  
Time Points ◽  
Piano Students ◽  
Key Space ◽  
Tonal Pitch ◽  
Pitch Space

This study conducted a perceptual analysis of an excerpt from Beethoven's Waldstein piano sonata in four experiments. The experiments were followed by an application of Lerdahl's (2001) Tonal Pitch Space theory, or TPS, to perceptual judgments of musical tension over the course of the excerpt. In the experiments, data were obtained for each of 15 time points corresponding to the 15 successive sonorities in the excerpt. Listeners in the first three experiments were piano students who learned and performed the excerpt before participating in the experimental tasks. In Experiment 1, judgments of phrase structure permitted examination of the perceptual segmentation of the excerpt. In Experiment 2, probe-tone ratings (Krumhansl and Kessler, 1982) were used to derive both a measure of perceived distance traveled in key space as well as a measure of temporal orientation — the degree to which listening at each time point was retrospective or prospective. In Experiment 3, a tension contour over the 15 time points was derived from listeners' continuous responding to perceived tension throughout the excerpt. In Experiment 4, judgments of consonance/dissonance for each sonority, isolated from context and presented in random order in a randomly selected transposition, were obtained from piano students unfamiliar with the excerpt. Strong correspondences were found between the perceptual measures and related music-theoretic predictors generated from TPS. The tension contour was regressed on TPS predictors. Both sensitivity to hierarchical structure and expectancies arising from voice leading, as well as the overall melodic contour, significantly contributed to the prediction of perceived tension.

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

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1291
Author(s):  
María Navarro-Cáceres ◽  
Marcelo Caetano ◽  
Gilberto Bernardes ◽  
Mercedes Sánchez-Barba ◽  
Javier Merchán Sánchez-Jara
Keyword(s):  
State Of The Art ◽  
Objective Measure ◽  
Global Changes ◽  
Voice Leading ◽  
Relative Importance ◽  
Tonal Music ◽  
Harmonic Motion ◽  
Proposed Model ◽  
Interval Space ◽  
Over Time

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.

Modeling Tonal Tension

2007 ◽  
Vol 24 (4) ◽  
pp. 329-366 ◽  
Author(s):  
Fred Lerdahl ◽  
Carol L. Krumhansl
Keyword(s):  
Tonal Music ◽  
Space Model ◽  
Attraction Model ◽  
Cognitive Principles ◽  
Data Point ◽  
Pitch Space

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.

Tonalité immanenté, tonalite manlfestee Quelques ré flexions à propos de Tonal Pitch Space de Fred Lerdahl

2003 ◽  
Vol 7 (1) ◽  
pp. 87-100 ◽  
Author(s):  
Nicolas Meeùs
Keyword(s):  
Tonal Pitch ◽  
Pitch Space

La théorie de Tonal Pitch Space, contrairement à d'autres theories spatiales de la tonalité, est une théorie du systeme tonal plutôt que du discours tonal. L'espace décrit et les distances qu'on peut y mesurer sont precompositionnelles; les contraintes de type fonctionnel qui peuvent regir les deplacements” dans l'espace ne sont pas reellement considerees parce qu'elles n'appartiennent pas au niveau du systeme immanent. D'autres theories au contraire, notamment les theories transformationnelles, privilegient la description des mouvements et des transformations et n'utilisent l'espace tonal que comme visualisation des contraintes auxquelles ils sont soumis. Ces deux types de description doivent Stre considers comme complementaires.

Parsing of Melody: Quantification and Testing of the Local Grouping Rules of Lerdahl and Jackendoff's A Generative Theory of Tonal Music

2004 ◽  
Vol 21 (4) ◽  
pp. 499-543 ◽  
Author(s):  
Bradley W. Frankland ◽  
Annabel J. Cohen
Keyword(s):  
Multiple Regression ◽  
Musical Training ◽  
Length Change ◽  
Tonal Music ◽  
Nursery Rhyme ◽  
Generative Theory ◽  
Wide Range ◽  
Identical Manner ◽  
Repeated Experiment ◽  
Local Grouping

In two experiments, the empirical parsing of melodies was compared with predictions derived from four grouping preference rules of A Generative Theory of Tonal Music (F. Lerdahl & R. Jackendoff, 1983). In Experiment 1 (n = 123), listeners representing a wide range of musical training heard two familiar nursery-rhyme melodies and one unfamiliar tonal melody, each presented three times. During each repetition, listeners indicated the location of boundaries between units by pressing a key. Experiment 2 (n = 33) repeated Experiment 1 with different stimuli: one familiar and one unfamiliar nursery-rhyme melody, and one unfamiliar, tonal melody from the classical repertoire. In all melodies of both experiments, there was good within-subject consistency of boundary placement across the three repetitions (mean r = .54). Consistencies between Repetitions 2 and 3 were even higher (mean r = .63). Hence, Repetitions 2 and 3 were collapsed. After collapsing, there was high between-subjects similarity in boundary placement for each melody (mean r = .62), implying that all participants parsed the melodies in essentially the same (though not identical) manner. A role for musical training in parsing appeared only for the unfamiliar, classical melody of Experiment 2. The empirical parsing profiles were compared with the quantified predictions of Grouping Preference Rules 2a (the Rest aspect of Slur/Rest), 2b (Attack-point), 3a (Register change), and 3d (Length change). Based on correlational analyses, only Attack-point (mean r = .80) and Rest (mean r = .54) were necessary to explain the parsings of participants. Little role was seen for Register change (mean r = .14) or Length change (mean r = ––.09). Solutions based on multiple regression further reduced the role for Register and Length change. Generally, results provided some support for aspects of A Generative Theory of Tonal Music, while implying that some alterations might be useful.

A Generative Theory of Tonal Music

1985 ◽  
Vol 4 (3) ◽  
pp. 292
Author(s):  
David Harvey ◽  
Fred Lerdahl ◽  
Ray Jackendoff
Keyword(s):  
Tonal Music ◽  
Generative Theory
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