Proj. no. 5126 of the Scientific Grant Agency VEGA,
(at the Ministry of Slovak Rep. and Slovak Acad. Sci.)

PROJECT LEADER -- PRINCIPAL INVESTIGATOR:
RNDr. Ján HALUŠKA, CSc.
Senior research fellow, Mathematical Institute, Slovak Academy of Sciences (abbreviation: MI)
jhaluska@mail.saske.sk

SCIENTIFIC CO-WORKERS
                 1998
Prof. RNDr. Beloslav RIECAN, DrSc.; MI
Peter ŠIDLÍK, Ph.D.; Acad. Music and Drama - Dept. Music Theory (abbreviation: MT)
RNDr. Emília HALUŠKOVÁ, CSc.; MI
Doc. PhDr. Zuzana MARTINÁKOVÁ, CSc.; MT
RNDr. Gejza WIMMER, CSc.; MI
PhDr. Eva FERKOVÁ, CSc.; MT
                  1999
RNDr. Jarmila HEDLÍKOVÁ, CSc., MI
RNDr. Miloslav DUCHON, DrSc., MI
RNDr. Emília HALUŠKOVÁ, CSc., MI
Doc. RNDr. Gejza WIMMER, CSc.; MI
Doc. PhDr. Zuzana MARTINÁKOVÁ, CSc, MT
RNDr. Olga KULCSÁROVÁ, CSc., University of P. J. Šafárik

DURATION OF THE PROJECT:
JAN 1998 -- DEC 2000

SCIENTIFIC GOALS OF THE PROJECT:
The goals of the project are to achieve new results concerning objects and structures which appear in the mathematical theory of music.

COMPENDIUM OF SCIENTIFIC PROJECT:
At the present we can find papers about mathematics and music in every branch of mathematics and also music. With the treatment in production of electronic music key instruments, there is an objective pressure to systematize the dispersed results into one theory, usually called now as the Mathematical Music Theory. Tone system is a subset of the positive real halfline equipped with the usual multiplicative structure. The tone system problems were ones of those sources which founded Mathematics as Science (among them, e.g. Pythagorean Tuning) and also many branches of Mathematics during the history (e.g. Partial Differential Equations, Harmonic Analysis, etc.).

The analogous mathematical project was not solved in Slovakia up to now. But there is a great tradition of the highest world level given by J. M. Petzval work in this area.

According to the actual state of science, the principal investigator published papers concerning this topic for some years. There are developed own methods to solve problem (11 papers were published or submitted as scientific publications, some further papers are devoted to professional public). The results have been presented at the international conferences (algebra, real functions, fuzzy theory, music-theoretical conferences), in the Slovak-Czech WORKSHOP MATHEMATICS AND MUSIC and they were the substantial part of the specialized invited session Fuzzy Principles of Music on the 7th World Congress IFSA, Prague, 1997.

COOPERATIONS:

We intend to continue the coperation within the

WORKSHOPS  MATHEMATICS AND MUSIC
16 years of duration, the  organizers of the workshop: Mathematical Institute of the Slovak Scademy of Sciences, (Bratislava and Kosice) and Music Faculty of the University of Arts and Drama (Bratislava).