Explikace pojmu tónové skupiny v teorii množin
| Title in English | The Concept of Tone Group Explicated whithin the Set Theory |
|---|---|
| Authors | |
| Year of publication | 2005 |
| Type | Article in Periodical |
| Magazine / Source | Acta Musicologica |
| MU Faculty or unit | |
| Citation | |
| Web | http://acta.musicologica.cz/05-02/0502s03.html |
| Field | Art, architecture, cultural heritage |
| Keywords | tone groups; application of set theory; musical theory; musicology |
| Description | In 1971 Alois Piňos published a book Tónové skupiny (Tone Groups) which is an exhaustive study in general music theory. In present paper I explicate main concepts of his book in terms of set theory. According to first hypothesis the tone group is mere set of tones. However during the inquiry of s.c. representative of tone groups (tone groups in narrower sense) it can be found that they are not only mere sets because Piňos has taken into account the fact of tone heights. Thus tone group must be concieved as ordered set, i.e. a set consisting of the set of tones and the set of higher-than relation (this relation orders the set of tones). Then I define a concept of intervalic group to show how much of Piňos original definition of tone group representative is adopted from intervalic understanding of music. Complementary to intervalic group and its representative I define other than Piňos' representative of tone group which is independent of intervalic concieving of music. However Piňos' defintion of representative of tone group that is 'mixed' from that ideal definition of representative of tone goup and definition of representative of intervalic group seems to be more useful for musicology because it counts with heights of tones. |