Understanding the Two Great Temperaments: Equal and Meantone
1965; SAGE Publishing; Volume: 13; Issue: 3 Linguagem: Inglês
10.2307/3343668
ISSN1945-0095
Autores Tópico(s)Musicology and Musical Analysis
ResumoPYTHAGORAS, Ptolemy, Baethius, and (in more modern times) Mersenne, and Heltnholtz are names of some of world-famous mathematicians who have concerned themselves with problem of musical intonation. This problem is basically one of finding intermediate values between 1 and 2 or, in other words, divisions of octave (represented by 1:2) for twelve or more tones. Since this is strictly a matter of measurement alld nothing else, mathematics, pure or geometrical, is proper tool. Yet, fundamental as it is, among musicians, subject is one of least understood. VVith regard to this laclz of knowledge, musician should not too breezily ask, So what? for such a blind spot actually retards or limits musical progress in all areas. For example, string players practice intonation from necessity. One would think that this very freedom makes urgent formulation of principles that should govern free intonation; still, unbelievable as it may seem, nothing of sort is generally recognized; hence, string intonation (in its highest, artistic aspects) remains a mystique! In this instance, piano keyboard is not aslswer, for tuning of piano is accomplished by means of extremely artificial and, in case of Efths and fourths, extremely minute distortions that can not apply to string intonation, unless one intends to employ piano as a constant guide, which practice, artis tically, is usually viewed askance. There is saying that, to be in tune, piano must be tuned slightly out-of-tune. However we interpret degree of compromise involved in tuning piano, there is no question but that keyboard is abode of temperament. Therefore, as an introduction to subject of intonation, purpose of this article will be to offer some of general principles that underlie art of compromise. What is can be understood, although actual tuning of piano remains a task for piano technician. Another apology for this article will be attempted presentation of not one but both of great temperamentsqual and meantone. While everyone is intimately acquainted with aural effects of equal temperament, fewer know of alternate that has, at least, an historical importance. This other system, which goes by name of the meantone temperament or, more specifically, Aron's meantone temperament has certain properties that are foreign to those of equal temperament.l Because meantone is diSerent and has historical validity, there is, today, an mcreasing effort to revive a tonal scheme of high sophistication. As a
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