Marek Zabka | Comenius University (original) (raw)
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Papers by Marek Zabka
Lecture Notes in Computer Science, 2011
Recently, an interaction between the mathematical discipline of combinatorics on words and musica... more Recently, an interaction between the mathematical discipline of combinatorics on words and musical scale theory has led to various interesting results. So far, the focus was mainly on scales generated by a single interval. The paper proposes an extension of word scale theory to tone systems of higher dimensions, i.e. generated by more than one interval. It is shown that the number of specific varieties for any non-zero generic interval in n-dimensional comma-demarcated generated tone systems is between 2 and 2 n. Therefore, generating patterns in two-dimensional systems are words over a four-letter alphabet. A concept of quasi pairwise well-formed words is introduced as a weakening of Clampitt's pairwise well-formedness. The main result of the paper is that a four-letter word is a generating pattern in a comma-demarcated two-dimensional system if and only if it is quasi pairwise well-formed.
The paper focuses on mathematical aspects of harmonies in extended just intonation and their rela... more The paper focuses on mathematical aspects of harmonies in extended just intonation and their relations. The first part lays down a theoretical framework for the investigation of structural features of such harmonies. Among other aspects, it addresses symmetry, inversion, and multiplication of harmonies. The second part explores transformational relations among harmonies of the same type, while the approach is intrinsically dualistic. Riemann-Klumpenhouwer’s concepts of Schritts and Wechsels are generalized for ‘harmony spaces’ in extended just intonation. This enables a deeper analysis of harmonic ‘neighborhoods.’ Finally, a graphical representation of the complete neighborhood of a harmony, called ‘neighborhood network,’ is presented along with several simpler and more complex examples.
Mathematica Slovaca
ABSTRACT
Journal of Music Theory, 2014
Lecture Notes in Computer Science, 2013
Journal of Mathematics and Music, 2013
Lecture Notes in Computer Science, 2011
Recently, an interaction between the mathematical discipline of combinatorics on words and musica... more Recently, an interaction between the mathematical discipline of combinatorics on words and musical scale theory has led to various interesting results. So far, the focus was mainly on scales generated by a single interval. The paper proposes an extension of word scale theory to tone systems of higher dimensions, i.e. generated by more than one interval. It is shown that the number of specific varieties for any non-zero generic interval in n-dimensional comma-demarcated generated tone systems is between 2 and 2 n. Therefore, generating patterns in two-dimensional systems are words over a four-letter alphabet. A concept of quasi pairwise well-formed words is introduced as a weakening of Clampitt's pairwise well-formedness. The main result of the paper is that a four-letter word is a generating pattern in a comma-demarcated two-dimensional system if and only if it is quasi pairwise well-formed.
The paper focuses on mathematical aspects of harmonies in extended just intonation and their rela... more The paper focuses on mathematical aspects of harmonies in extended just intonation and their relations. The first part lays down a theoretical framework for the investigation of structural features of such harmonies. Among other aspects, it addresses symmetry, inversion, and multiplication of harmonies. The second part explores transformational relations among harmonies of the same type, while the approach is intrinsically dualistic. Riemann-Klumpenhouwer’s concepts of Schritts and Wechsels are generalized for ‘harmony spaces’ in extended just intonation. This enables a deeper analysis of harmonic ‘neighborhoods.’ Finally, a graphical representation of the complete neighborhood of a harmony, called ‘neighborhood network,’ is presented along with several simpler and more complex examples.
Mathematica Slovaca
ABSTRACT
Journal of Music Theory, 2014
Lecture Notes in Computer Science, 2013
Journal of Mathematics and Music, 2013