1) The Mathematics of Music (120 pages) (Athens 1982)
It is a small monograph , that describes mathematics that are used to understand music. The mathematics range from those of the physics of acoustics of musical sound, to those that describe the combinatorics of musicology of ancient Greek, and modern Western musical systems , and finally to those that are often used by composers to control the morphology of their compositions. The mathematics involved are today incorporated in the design of hardware and software for music. They are both quantitative and qualitative techniques.
2)Examples of application of Universal Algebra and Categories to the musicology of ancient Greek, Byzantine ,modern European tonal and atonal systems.(Samos,1993)
This paper was presented in a Conference and presentation of Music compositions by various, University Departments, of Music and Computer Science, during July 1992 at Delphi in Greece. The main idea of the author is to show, how mathematical concepts like categories and Omega algebras, that have been applied successfully in describing Relational Data Bases , can also be applied in describing in a unified way older and new musical systems.
3) Rhythmic, pattern variations, of melodies by transformations derived from the symmetries groups of platonic Polyhedra. (2002-)
This is a composition technique to produce rhythmic variations of melodies new or old that we love, where the melodic pattern of the melody remains the same but the rhythmic pattern changes. The first ideas about it came to me through the years from 1985 , then 1993 and then again 2002. It is attractive to me as it combines disciplines like geometry and algebra, music, computers , dice and randomness and animations. We may apply it, for example, with groups of transformations that are derived from the symmetries of the cube or the dodecahedron etc. The composition may be interactive with the audience through the dice for the variations. Stochastic freedom, melodic stability and rhythmic changes combine in a a result that pleases. It can even be used to vary the ring tone melodies when they become boring. The composition system can be developed in software with sound and animations. The same idea can be applied in rewriting systems of phrases that change their meaning, by permutations of their words, in producing a love poem in dialogue form.
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