History of Music Theory, Part Seven

During the period of the 14th and 15th centuries the practice of musica ficta - adding sharps or flats to notes to increase the contrapuntal effect of directionality and to accent closings (Which can properly be called cadences by this point) - had resulted in the theoretical completion of the chromatic octave. The result was not the twelve note chromatic octave with enharmonic equivalents whith which we are familiar, however. To the contrary, there were no enharmonic equivalents at all originally, which resulted in a seventeen note chromatic octave:


C

d-flat
c-sharp

D

e-flat
d-sharp

E
F

g-flat
f-sharp

G

a-flat
g-sharp

A

b-flat
a-sharp

B


This corresponds to natural vocal practice in which leading tones are raised and leaning tones are lowered slightly to add tension penultimate to the resolution effect. In fact, this practice can quite easily be heard today by listening to any good performance by a string quartet, so it's not just a phenomenon unique to the vocal idiom. Keep in mind though that theorists were still using their monochords and that they were dutifully marking these intervals off on them, and then they would have to rationalize the results to the Pythagorean tuning system's intervals that they were using. Obvously, this caused a lot of head scratching and endless mathematical calculations. One result of this was the discovery of the syntonic comma and it's precise enumeration as 81/80. This is the difference between two wholetones of 9/8 and the major third of 5/4. The point is, theorists were beginning to sense that another system of tuning or a system of temperament would be required for fixed-pitch instruments, since they accompanied singers with increasing frequency over the course of this period. Splitting all the black keys on a keyboard is possible, and that was tried on a few occasions in a limited fashion, but obviously that would not really be practical due to the resulting mechanical complexity and expense, not to mention performance difficulties.

Though credit for finding the theoretical derivation of major and minor thirds as imperfect consonances with the ratios of 5/4 and 6/5 as present in the natural harmonic overtone series was given to Bartolomeo Ramos de Pareja as written in his musica tractatus of 1482 for many years, they were actually properly described by Walter Odington circa two-hundred years earlier. Odington was very much a man of his age and thouroughly devout with respects to the Pythagorean tuning system however, so he basically noted that thirds sounded consonant when sung because singers adjusted them to conform to the simpler natural ratios and left it at that. In any event, it was not until the end of the fifteenth century that theorists generally started to recognize the rising to primacy of thirds and the resulting necessity for a corresponding change to the Pythagorean tuning system that had been in use for about a millennium.

The late fifteenth century was a kind of golden age for music theory, and theorists would often engage in public scholarly debates on the subject. They also circulated polemical pamphlets to defend their positions. Some of these debates were evidently quite heated exchanges, and the pamphlets no less so. I would have loved that age in that one respect, but since some of those men died of the bubonic plague, I think I'll accept my particular place in history with a cheerful disposition. Some of the players in the late fifteenth century era's hubbub were Bartolomeo Ramis, Giovanni Spataro, Nikolaus Bertius, Philippus de Caserta, Franchino Gafori, John Hothby, and of course, Johannes Tinctoris. Awesome names all, and fun to say as well.