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.

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.

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

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.

Positional Estimation Within a Latent Space Model for Networks

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 24-33 ◽  
Author(s):  
Susan Shortreed ◽  
Mark S. Handcock ◽  
Peter Hoff
Keyword(s):  
Random Effects ◽  
Network Data ◽  
Random Effects Models ◽  
Space Model ◽  
Network Analyses ◽  
Recent Advances ◽  
Latent Space ◽  
Latent Space Model ◽  
Modeling Data

Recent advances in latent space and related random effects models hold much promise for representing network data. The inherent dependency between ties in a network makes modeling data of this type difficult. In this article we consider a recently developed latent space model that is particularly appropriate for the visualization of networks. We suggest a new estimator of the latent positions and perform two network analyses, comparing four alternative estimators. We demonstrate a method of checking the validity of the positional estimates. These estimators are implemented via a package in the freeware statistical language R. The package allows researchers to efficiently fit the latent space model to data and to visualize the results.

Information space model in tasks of distributed mobile objects managing

2019 ◽  
Vol 2019 (47) ◽  
pp. 80-86
Author(s):  
V.O. Filatov ◽  
◽  
A.L. Yerokhin ◽  
O.V. Zolotukhin ◽  
M.S. Kudryavtseva ◽  
...  
Keyword(s):  
Information Space ◽  
Space Model ◽  
Mobile Objects

Pencarian File Gambar Berdasarkan Dominasi Warna

2011 ◽  
Vol 2 (1) ◽  
Author(s):  
Vina Chovan Epifania ◽  
Eko Sediyono
Keyword(s):  
Digital Image ◽  
Retrieval System ◽  
Color Image ◽  
Color Space ◽  
Image Data ◽  
Image Search ◽  
Test Results ◽  
Application Form ◽  
Space Model ◽  
Image File

Abstract. Image File Searching Based on Color Domination. One characteristic of an image that can be used in image searching process is the composition of the colors. Color is a trait that is easily seen by man in the picture. The use of color as a searching parameter can provide a solution in an easier searching for images stored in computer memory. Color images have RGB values that can be computed and converted into HSL color space model. Use of HSL images model is very easy because it can be calculated using a percent, so that in each pixel of the image can be grouped and named, this can give a dominant values of the colors contained in one image. By obtaining these values, the image search can be done quickly just by using these values to a retrieval system image file. This article discusses the use of the HSL color space model to facilitate the searching for a digital image in the digital image data warehouse. From the test results of the application form, a searching is faster by using the colors specified by the user. Obstacles encountered were still searching with a choice of 15 basic colors available, with a limit of 33% dominance of the color image search was not found. This is due to the dominant color in each image has the most dominant value below 33%.   Keywords: RGB, HSL, image searching Abstrak. Salah satu ciri gambar yang dapat dipergunakan dalam proses pencarian gambar adalah komposisi warna. Warna adalah ciri yang mudah dilihat oleh manusia dalam citra gambar. Penggunaan warna sebagai parameter pencarian dapat memberikan solusi dalam memudahkan pencarian gambar yang tersimpan dalam memori komputer. Warna gambar memiliki nilai RGB yang dapat dihitung dan dikonversi ke dalam model HSL color space. Penggunaan model gambar HSL sangat mudah karena dapat dihitung dengan menggunakan persen, sehingga dalam setiap piksel gambar dapat dikelompokan dan diberi nama, hal ini dapat memberikan suatu nilai dominan dari warna yang terdapat dalam satu gambar. Dengan diperolehnya nilai tersebut, pencarian gambar dapat dilakukan dengan cepat hanya dengan menggunakan nilai tersebut pada sistem pencarian file gambar. Artikel ini membahas tentang penggunaan model HSL color space untuk mempermudah pencarian suatu gambar digital didalam gudang data gambar digital. Dari hasil uji aplikasi yang sudah dibuat, diperoleh pencarian yang lebih cepat dengan menggunakan pilihan warna yang ditentukan sendiri oleh pengguna. Kendala yang masih dijumpai adalah pencarian dengan pilihan 15 warna dasar yang tersedia, dengan batas dominasi warna 33% tidak ditemukan gambar yang dicari. Hal ini disebabkan warna dominan disetiap gambar kebanyakan memiliki nilai dominan di bawah 33%. Kata Kunci: RGB, HSL, pencarian gambar

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