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Music from the Earliest Notations to the Sixteenth Century


CHAPTER 15 A Perfected Art
Richard Taruskin

All theory we have studied up to now has been discant theory, in which two voices (the “structural pair”) define harmonic norms and in which only perfect consonances enjoy full freedom of use. If nowhere else, composers of written music still honored this ranking of consonances at final cadences, where as we have seen, triads had to be purged of their thirds for full cadential finality. Zarlino was the first theorist to accept the triad as a full-fledged consonance. Not only did he accept it, he dubbed it the harmonia perfetta—the “perfect harmony.” He rationalized giving the triad this suggestive name not only on the basis of the sensory pleasure that triadic harmony evoked, nor on the basis of the affective qualities that he ascribed to it, although he was in fact the first to come right out and say that “when [in a triad] the major third is below [the minor] the harmony is gay, and when it is above, the harmony is sad.”7 Along with these factors Zarlino cited mathematical theory, so that he could maintain, like a good Aristotelian, that according to his rules reason held sway over sense. The “perfect harmony,” he asserted, was the product of the “perfect number,” which was six.

Just as Glareanus had come to terms with modern practice by adding two more finals to the Frankish four to account for contemporary melodic styles, Zarlino added two more integers to the Pythagorean four in order to generate the harmonies of contemporary music that he now wished to rationalize. The perfect Pythagorean harmonies could all be expressed as “superparticular” ratios of the integers from 1 to 4. That is, they could be expressed as fractions in which the numerator was one more than the denominator, thus: 2/1 = octave; 3/2 = fifth; 4/3 = fourth. But, said Zarlino, there is nothing special about the number four, and no reason why it should be taken as a limit.

Ah, but six! It is the perfect number because it is the first integer that is the sum of all the numbers of which it is a multiple. That is, one plus two plus three equal six, and one times two times three also equal six. So a harmony that would embody all the superparticular ratios between 1 and 6 would be a perfect harmony, and a music that employed such harmony would be a perfect music. In effect, that meant adding a major third (harmonic ratio 5:4) above the fourth and a minor third (ratio 6:5) above the major third, producing a very sonorous spacing of tones, a kind of ideal doubling of the triad in six voices (three roots, two fifths, one third), as shown in Ex. 15-1.

The Triad Comes of Age

ex. 15-1 Gioseffo Zarlino’s senaria (chord of six), based on C

Nowadays this configuration is recognizable as the beginning of the natural harmonic series (or “overtone” series), which since the eighteenth century has been the standard method of explaining the triad and asserting its “naturalness.” Zarlino, needless to say, would have jumped for joy to see this confirmation of his rational speculation in the realm of “natural philosophy.” But nobody knew about overtones as yet in the sixteenth century.

What people certainly did know is that when pitches were stacked up in this way they sounded good. In rich textures of five and six voices, which were increasingly common by the late sixteenth century, this ideal spacing and doubling was widely practiced, and compositions ended more and more frequently with full triads sonorously spaced. (See the end of Sennfl’s luxuriant parody of Josquin’s Ave Maria in Ex. 14-7 for an illustration of the practice in advance of the justification for it.) Now both of these harmonically enriching practices—larger vocal complements, triadic endings—had a properly “theoretical” support. They were among the finishing touches, so to speak, that defined the ars perfecta as the last word in harmony.


(7) Zarlino, The Art of Counterpoint, p. 70.

Citation (MLA):
Richard Taruskin. "Chapter 15 A Perfected Art." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 7 Oct. 2022. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-015003.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 15 A Perfected Art. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 7 Oct. 2022, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-015003.xml
Citation (Chicago):
Richard Taruskin. "Chapter 15 A Perfected Art." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 7 Oct. 2022, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-015003.xml