FIG. 15-2 Gioseffo Zarlino, anonymous portrait at the Civico Museo Bibliografico Musicale, Bologna.
The really valuable fruit of Zarlino’s rationalized empiricism was his recognition of harmony, as it
actually functioned in “early modern” music, as being worthy of theoretical attention, and his ingenuity in
devising a rationale for it. For a long time now—at least since the beginning of the fifteenth century, and
most likely before that in unwritten repertories—the triad, first imported into continental music from
England, had been the de facto normative consonance for all European polyphonic music. Before Zarlino,
however, no theorist had recognized it as an entity, given it a name, or legitimized its use.
THE TRIAD COMES OF AGE
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