1.1 Systematic Musicology: Discipline and Field of Research
The term systematic musicology denotes a scientific discipline as well as a large and interdisciplinary area of research. While the academic discipline of systematic musicology was established only in the 20th century in universities, research in this field dates back far into history. In this chapter, a brief account of several stages in the historical development of research pertaining to systematic musicology will be given. It goes without saying that, within the frame of a chapter, this account cannot even attempt to cover every relevant fact and person. The focus here is on selected areas where certain problems have either been approached for the first time, or where a theoretical and methodological framework has gained the role of a paradigm for some period (as, for example, Gestalt theory or musical semiotics; see below). Moreover, there are problems that tend to resist a final solution (which seems a condition typical for science at large []).
Historical developments for some subfields of systematic musicology have been covered in comprehensive works (such as music theory in the ten vols of the Geschichte der Musiktheorie [] provides a systematic overview that covers much of the research in musicology and neighboring disciplines from the 19th century to about 197080.
1.2 Beginnings of Music Theory in Greek Antiquity
Scholars of Greek antiquity conducted a huge amount of research on the fundamentals of tone systems and scales using an approach that combined mathematical reasoning with observation and measurement (see [].
Greek mathematics and music theory rested on numbers representing both ideal magnitudes and measurable quantities. Ratios of whole numbers in general were used to establish intervals and scales. Pairs of ratios form proportions like
known as a Pythagorean Tetraktys, which contains the intervals of the octave 12, the fifth 23, the fourth 34, and the whole tone 89. Ratios considered as fundamental for harmony could either contain multiples of a basic number like (21, 31, 41), or be formed according to
(the class of superparticular intervals 32, 43, 54, 65, 76, 87, 98, ). In addition, there were so-called superpartientes (ratios of the form
like 53 considered in particular by a range of medieval scholars []), who opposed empiricism, in fact let Socrates refer to the Pythagoreans as people who torture strings by working on their tension with tuning pegs. Archytas it seems already distinguished between the arithmetic, the geometric and the harmonic division (that can be applied either to an interval defined by numbers or to sectioning a line or string of given length). Though observation was used as a method for scientific investigations, mathematical reasoning among the Pythagoreans was regarded superior for its logical coherence and general applicability.
Since there evidently was music performed in various contexts in Greek societies (as many paintings and engravings demonstrate), the question of course is to what extent fundamental structures described by theorists (such as different divisions of the tetrachords, see Sect. ]) gives many hints that musical practice at his time did not (or perhaps no longer) conform in every respect to norms and models that had been set up mainly by the Pythagorean school. One of the fundamental objections Aristoxenus made is that musical experience based on performance and listening may differ from, or may even contradict, certain models and propositions developed from arithmetic.
Much of classical Greek music theory survived in writings of the Hellenistic period, in particular in the works of Claudius Ptolemaeus and Nicomachus of Gerasa (both lived in the 2nd century []). Phenomena of polyphonic music such as the organum were treated in writings on music theory as early as the musica enchiriadis (9th century).
1.3 From the Middle Ages to the Renaissance and Beyond: Developments in Music Theory and Growth of Empiricism
While much of medieval music theory reflects its Pythagorean origin and background, issues relevant to musical practice and organology gained increasing importance. One area where a transition from basically mathematical to empirically validated approaches can be shown is the mensuration of organ pipes [, Part III, Chap. 32], one in fact can derive the major and the minor chord from the operations Zarlino proposes for the two divisions of the fifth, and later theorists like Rameau and Riemann therefore saw Zarlino's ideas as decisive steps on the way to modern tonality. As a matter of fact, Zarlino elaborated vertical harmony in his own polyphonic works ( Modulationes sex vocum , 1566).
In the 16th century, progress was also made in musical acoustics when Fracastoro (1546) correctly explained the nature of resonance in strings (while the phenomenon as such, i.e., sympathetic vibration, was known long before [, T. III, pp. 126f.] reports, in Italy organization of a range of string, woodwind and brass instruments into a Chorus instrumentalis alternating or playing together with the Chorus vocalis (in concert-like form) was part of musical practice.