An introduction to hierarchised tiles
Alice Rixte
Université de Bordeaux
13th of November, 2023
Sound and Fury of Modeling, Arpino Winter School
What is musical structure ?
William E. Thomson, Functional Ambiguity in Musical Structures, 1983
Musical structure [...] refers to the way
elements are organized into patterns of coherence, the perceptual act of small events joining to create large events.
Morris R. Cohen, A preface to logic, 1944
Anything acquires meaning if it is connected with, or indicates, or refers to, something beyond itself, so that its full nature points to and is revealed in that connection.
Structure could then be
1. A hierarchy
Atoms are combined together to form patterns, themself combined into metapaterns more and more complex.
2. An articulation of this hierarchy
The different components should be compared and related one to the other
Outline
1. The hierarchy of patterns
- Level 0 (atoms) : music note, letter, pixel …
- Level 1 (patterns of atoms) : bar, word …
- Level 2 (patterns of patterns of atoms) : phrase, sentence …
- Level 3 (patterns of patterns of patterns of atoms) : section, paragraph …
- …
Outline
They allow to express similarity between patterns
- Shifting
- Symmetries
- Scaling
- …
Outline
3. How to construct patterns
- A musical composition procesxs
- Algebraic operations over patterns
- Programmation language
1. The hierarchy of patterns