Non-Contextual JQZ Transformations

Characterisation of the Degree of Musical Non-Markovianity

“…They are used both as an aid for musical analysis, and to investigate some aspects of samples of compositions (Mazzola, 2007;Mazzola, 2002). In particular, these methods have been applied to analyse: musical theory in a geometrical way (M. et al, 2006); gesture in music (Mazzola & Andreatta, 2007;Mannone, 2018a;Arias, 2018); counterpoint; interpretation; harmony (Mazzola, 2002); common patterns in sound amplitude (Mendes et al, 2011); chord-sequences and voice-leading in the light of topology (Tymoczko, 2006;Tymoczko, 2020); and symmetries between chords in lattices called Tonnetze (Amiot, 2017;Jedrzejewski, 2019b). Formal tools also include using the abstract power of category theory in order to formalise musical structures, including relationships within music theory and between music theory and musical performance (Popoff et al, 2019;Mannone, 2018b;Mazzola, 2002;Mannone, 2018a;Arias, 2018;Jedrzejewski, 2019a).…”

Скрытые фигуры и потаенная геометрия в Прелюдии А. Н. Скрябина op. 74 № 1

“…The succession of harmonic functions of a composition will, therefore, be represented by a set of figures that will develop and follow one another within the octahedron depending upon the harmonic functions of the piece. For example, the first eight bars of Mozart's Piano Sonata K 282 6 In Example 5, the penultimate bar contains the symbol ('DD') that indicates the dominant of the dominant. 8 At this point it is possible to show the chain of the harmonic succession of the piece inside the octahedron and see which geometrical figures are created.…”