5: Patterns / Form / Process
In this topic we will consider applications of musical ‘patterning’ – palindromes, rotation, reflection and inversion – as structural determinants, with particular reference to Webern’s Symphonie, op. 21. The use of the Fibonacci Sequence and the Golden Section as structural ‘generators’ will be examined through a consideration of Claude Debussy’s La fille aux cheveux de lin. |
We will next consider the notion of form as process, and of ‘forming’ in music. Several examples will be examined, which have in common the principle of the organic generation of form from fundamental components. Stockhausen’s , Varèse’s crystal analogies, Steve Reich’s process music, and computer-based algorithmic composition will be investigated alongside more traditional methods of forming in music. |
Class Documents
|
Audio & Visual
|
Articles
Symmetry
|
Symmetry in Webern’s Music
- Starr, M – Webern’s Palindrome
- Kabbash, P – Aggregate-Derived Symmetry in Webern’s Early Works
- Lynn, D – 12-Tone Symmetry: Webern’s Thematic Sketches for the Sinfonie, Op. 21, Second Movement
- Archibald, B – Some Thoughts on Symmetry in Early Webern: Op. 5, No. 2
- Bailey, K – Symmetry as Nemesis: Webern and the First Movement of the Concerto, Opus 24
- Johnson, P – Symmetrical Sets in Webern’s Op. 10, No. 4
- Bailey, K – Webern’s Opus 21: Creativity in Tradition
- Clifford, R – Multi-Level Symmetries in Webern’s Op. 11, No. 1
|
The Golden Section and the Fibonacci Series
- Crilly, D – Form and Forming in Music. In musicology, architectural and mathematical correlations have been observed in studies of the nature of musical form, whilst Schopenhauer restated the Pythagorean view that the universality of music resembles geometrical figures and numbers. Stravinsky suggested that we could not better define the sensation produced by music than by saying that it is identical with that evoked by the contemplation of the interplay of architectural forms. This paper considers the perception of architectural form in music and reveals Debussy’s use of Golden Section as a structural determinant in his prelude La fille aux cheveux de lin for piano.
- Murzi, M – Logical Positivism
- Kramer, J.D. – The Fibonacci Series in Twentieth-Century Music
- Markowsky, G. – Misconceptions about the Golden Ratio
|
Crystal Form
|
Moment Form
|
Process and Algorithmic Composition
|
Internet Sites
- Leonardo of Pisa: Bunny Rabbits to Bull Markets
- Fibonacci Numbers and the Golden Section
- Bibliography of sources related to the Golden Section in Music
- Terry Riley’s In C courtesy of Other Minds.
- There is a wealth of material available concerning medieval isorhythmic motets, arguably the earliest examples of algorithmic composition. See, for example, the Wikipedia article (yes, some Wikipedia articles are good!) on Dufay’s Nuper Rosarum Flores, which contains a good illustration of Dufay’s use of isorhythm. Compare this with the modern score realisation by Moriwaki Michio.
- Bach’s Musical Offering provides many examples of the canon. This site contains a animation of the famous Canon 1 a 2, a ‘crab canon’.
- An implementation of Mozart’s famous Musical Dice Game.
- Random Round: An interactive version of Percy Grainger’s experiment with random composition, written in 1912.
- Algorithmic.net provides a comprehensive research resource for computer aided algorithmic music composition, including over one-thousand research listings, over one hundred system listings, cross referenced links to research, links to software downloads and documentation, and web-based tools for searching and filtering the complete lexicon.
|
Every present moment counts as well as no moment at all; a given moment is not merely regarded as the consequence of the previous one and the prelude to the coming one, but as
something individual, independent and centered in itself, capable of existing on its own. An instant does not need to be just a particle of measured duration. This concentration on the present moment – on every present moment – can make a vertical cut, as it were, across horizontal time perception, extending out to a timelessness I call eternity. This is not an eternity that begins at the end of time, but an eternity that is present in every moment. I am speaking about musical forms in which apparently no less is being undertaken than the explosion – yes – even more, the overcoming of the concept of duration. (Stockhausen, 1962)
Let's Get in Touch