Droga ku pełni. Dzieje muzyki wobec prawa tetraktysu. Rekonesans
The Road to Completeness. History of Music and the Law of the Tetractys. A Reconnaissance

Summary/Abstract: The four times of the day, the four seasons, the four parts of the world and the four winds, the four elements and the four tempers... According to Pythagoreans, numbers are crucial to the understanding of the structure of the universe. Chief among them is the number four. It has become the foundation of the so-called tetractys: a system derived from the first four cardinals, one that represents a particular and optimal whole. Its elements manifest themselves in many laws in the history of music. The development of the fundamental structures of the musical work in both its simultaneous and successive aspects has been surprisingly consistent in the history of European music, or world music as it came to be called. The history of musical texture (the simultaneous aspect) has been marked by a step-by-step transition from deeply medieval monophony of plainsong through the duophony of the organum phase and the triphony of the early Renaissance trecento to High Renaissance quadrophony (CATB) that has remained, to a great degree, the extant canon. All attempts to transcend the “magical” quadrophony proved to be more or less peripheral and received no historical perpetuation. A similar logic of development can be observed in the successive aspect of the structure of the musical work, i.e. in the development of musical form. Its history, too, sees first a growth in the number of movements in any given period’s typical genre, and then a perpetuation of a state that seems to have achieved a particular “completeness.” Works characteristic for a given phase of historical development came, first, in one movement; early Baroque introduced two (recitative and aria; prelude and fugue); then came three movements (Italian overture, concerto, aria da capo) and finally four (sonata, quartet, symphony etc.). Systems of more than four voices have not established themselves; despite attempts by Beethoven and Berlioz, five movements have not become the norm. Thus one might say that the quantitative development in the two aspects has been arrested at a “classical,” a “canonic” whole in accordance with the unwritten law of the tatractys. Assaults on the rule remained sporadic; unsupported, they only functioned as mere transgressions caused by “romantic” flamboyance and by peculiar excess of creative energy. This poses a number of questions without answers. Does not the music of the classical era, best embodied in the work of Haydn, Mozart and Beethoven, represent a particular and exceptional category in the history of Western (world) music, one that saw the realization of the “completeness” principle? Is it possible that a new completeness might manifest itself in the future, based on objective laws, as the basis of a new aesthetical canon? Finally: is the answer to those and other questions only relevant to the realm of culture, or is it also part of the objective laws of nature? Quite understandably, any attempt to discuss this problem must needs be treated as initial reconnaissance. It does not touch upon philosophy or, even less, any multifaceted and ever-recurring esoteric knowledge.

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