scholarly journals Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes

Author(s):  
Louis Bigo ◽  
Moreno Andreatta ◽  
Jean-Louis Giavitto ◽  
Olivier Michel ◽  
Antoine Spicher
2015 ◽  
Vol 39 (3) ◽  
pp. 9-24 ◽  
Author(s):  
Louis Bigo ◽  
Daniele Ghisi ◽  
Antoine Spicher ◽  
Moreno Andreatta

In this article, we present a set of musical transformations based on the representations of chord spaces derived from the Tonnetz. These chord spaces are formalized as simplicial complexes. A musical composition is represented in such a space by a trajectory. Spatial transformations are applied on these trajectories and induce a transformation of the original composition. These concepts are implemented in two applications, the software HexaChord and the Max object bach.tonnetz, dedicated to music analysis and composition, respectively.


10.37236/1245 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Art M. Duval

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the $h$-triangle, a doubly-indexed generalization of the $h$-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generalize the Cohen-Macaulay conditions for pure complexes, so that a nonpure shellable complex is sequentially Cohen-Macaulay. We show that algebraic shifting preserves the $h$-triangle of a simplicial complex $K$ if and only if $K$ is sequentially Cohen-Macaulay. This generalizes a result of Kalai's for the pure case. Immediate consequences include that nonpure shellable complexes and sequentially Cohen-Macaulay complexes have the same set of possible $h$-triangles.


2020 ◽  
pp. 102986492097214
Author(s):  
Aurélien Bertiaux ◽  
François Gabrielli ◽  
Mathieu Giraud ◽  
Florence Levé

Learning to write music in the staff notation used in Western classical music is part of a musician’s training. However, writing music by hand is rarely taught formally, and many musicians are not aware of the characteristics of their musical handwriting. As with any symbolic expression, musical handwriting is related to the underlying cognition of the musical structures being depicted. Trained musicians read, think, and play music with high-level structures in mind. It seems natural that they would also write music by hand with these structures in mind. Moreover, improving our understanding of handwriting may help to improve both optical music recognition and music notation and composition interfaces. We investigated associations between music training and experience, and the way people write music by hand. We made video recordings of participants’ hands while they were copying or freely writing music, and analysed the sequence in which they wrote the elements contained in the musical score. The results confirmed experienced musicians wrote faster than beginners, were more likely to write chords from bottom to top, and they tended to write the note heads first, in a flowing fashion, and only afterwards use stems and beams to emphasize grouping, and add expressive markings.


2021 ◽  
Vol 31 (4) ◽  
pp. 041102
Author(s):  
Y. Lee ◽  
J. Lee ◽  
S. M. Oh ◽  
D. Lee ◽  
B. Kahng
Keyword(s):  

2012 ◽  
Vol 231 (2) ◽  
pp. 843-854
Author(s):  
Benson Farb ◽  
Amir Mohammadi
Keyword(s):  

2017 ◽  
Vol 86 (10) ◽  
pp. 2167-2181 ◽  
Author(s):  
Seunghwan Chang ◽  
Jong Yoon Hyun

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