Tonal Pitch Space

1988 ◽  
Vol 5 (3) ◽  
pp. 315-349 ◽  
Author(s):  
Fred Lerdahl
Keyword(s):  
Experimental Data ◽  
Music Psychology ◽  
Tonal Pitch ◽  
Pitch Space

Models of pitch space have been developed in music psychology to account for perceived proximity among pitches, chords, or regions. This article introduces a different model that (1) treats pitches, chords, and regions within one framework, (2) correlates with the experimental data, and (3) connects in interesting ways with a variety of music theories.

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.

Travelling Through Pitch Space Speeds up Musical Time

2009 ◽  
Vol 26 (3) ◽  
pp. 205-209 ◽  
Author(s):  
ÉÉrico Artioli Firmino ◽  
Joséé Lino Oliveira Bueno ◽  
Emmanuel Bigand
Keyword(s):  
Time Estimation ◽  
Time Interval ◽  
Space Theory ◽  
Harmonic Structure ◽  
Musical Time ◽  
Chord Sequence ◽  
Tonal Pitch ◽  
Pitch Space

SEVERAL MODELS OF TIME ESTIMATION HAVE BEEN developed in psychology; a few have been applied to music. In the present study, we assess the influence of the distances travelled through pitch space on retrospective time estimation. Participants listened to an isochronous chord sequence of 20-s duration. They were unexpectedly asked to reproduce the time interval of the sequence. The harmonic structure of the stimulus was manipulated so that the sequence either remained in the same key (CC) or travelled through a closely related key (CFC) or distant key (CGbC). Estimated times were shortened when the sequence modulated to a very distant key. This finding is discussed in light of Lerdahl's Tonal Pitch Space Theory (2001), Firmino and Bueno's Expected Development Fraction Model (in press), and models of time estimation.

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.

A Perceptual Experiment on Harmonic Tension and Melodic Attraction in Lerdahl's Tonal Pitch Space

2003 ◽  
Vol 7 (1) ◽  
pp. 35-55 ◽  
Author(s):  
Diego Vega
Keyword(s):  
Inverse Relationship ◽  
Influential Factor ◽  
Piano Sonata ◽  
Harmonic Reduction ◽  
High Tension ◽  
Theoretical Predictions ◽  
Anchoring Strength ◽  
Tonal Pitch ◽  
High Attraction ◽  
Pitch Space

The experiment reported here provides a comparison between listeners' judgments and theoretical predictions on harmonic tension and melodic attraction using Lerdahl's (2001) Tonal Pitch Space theory. A harmonic reduction of measures 1 to 8 from the first movement of Mozart's Piano Sonata, K282 was used for the experiment. The listeners heard the 24 sequential chord pairs from the harmonic reduction and were asked, first, to judge how strongly the two chords were attached to each other and, second, if there was an increase, decrease or no-change in tension in the progression from one chord to the next. The results from the experiment showed a significant correlation between theoretical predictions and listeners' tension judgments. However, a low correlation between Lerdahl's model and the attraction judgments demonstrated that distance in semitones is a more influential factor than anchoring strength in the perception of melodic attraction. This conclusion followed from the high attraction ratings given to repeated chords or adjacent chords in which the bass is repeated or progresses by step. The most interesting result of this experiment, consistent with the theory, is the demonstration that listeners perceive an inverse relationship between tension and attraction. In other words, listeners give high-tension ratings to points of low melodic attraction and vice versa, even when they judge each factor separately. Although we obtained a convergence of results between predictions and listeners' tension judgments and demonstrated a perceptual inverse relationship between tension and attraction, further tests are needed to determine how distance in semitones and anchoring strength combine to give a measure of melodic attraction.

Lerdahl's tonal pitch space model and associated metric spaces

2010 ◽  
Vol 4 (3) ◽  
pp. 121-131 ◽  
Author(s):  
Richard R. Randall ◽  
Bilal Khan
Keyword(s):  
Metric Spaces ◽  
Space Model ◽  
Tonal Pitch ◽  
Pitch Space

Tonal Pitch Space and the (neo-)Riemannian Tonnetz

2011 ◽  
pp. 321-348 ◽  
Author(s):  
Richard Cohn
Keyword(s):  
Hybrid Model ◽  
Hierarchical Model ◽  
Spatial Model ◽  
Spatial Models ◽  
Key Space ◽  
Tonal Pitch ◽  
Analytical Tools ◽  
Pitch Space

This article reexamines the Tonnetz as an analytical apparatus. Drawing on Fred Lerdahl's Tonal Pitch Space, which is critical of the homology of tone, chord, and key space posited by the Riemannian Tonnentz, the article proposes a hybrid spatial model that draws on both the Riemannian tradition and Lerdahl's hierarchical model. The pragmatic solution presented in this article allows for communication, reinterpretation, and relocation between tempered and unbounded spaces of tones, key spaces, and diatonic spaces or regions of triads, through the graphic metaphors of the Tonnetz and its allied spatial models. Apart from providing a pragmatic solution, the article also illustrates the hybrid model in analyses of Schumann, Wagner, and Chopin, with the view of suggesting further explorations and applications of these analytical tools.

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.

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