As a medievalist, I am more and more inclined to avoid the term "triad" for music before around 1610-1612, when Lippius coined the term. However, what I would call a sonority combining a fifth, major third, and minor third (e.g. F3-A4-C4 or A3-C4-E4 - C4 is middle C, and higher numbers show higher octaves) would depend a great deal on the period. Especially before around 1450-1500, using the term "triad" can carry the implication of a stable sonority where we are dealing in fact with a mildly unstable one.
For music of the 13th-14th centuries, I would use a very convenient term of Jacobus of Liege, quinta fissa, or in English "split fifth," a sonority with an outer fifth "split" by the middle voice into a major third below and minor third above, or vice versa. Jacobus (c. 1325) prefers the former arrangement with major third below, but recognizes that the converse may occur, as in the opening of a motet he cites:
E4 C4 A3
The term quinta fissa or "split fifth" not only expresses a medieval viewpoint, but avoids the implications of a stable sonority which "triad" may carry. For example, the above sonority might often resolve:
E4 D4 E4 G4 C4 D4 C3 D4 A3 G3 or A3 G3
The first progression involves resolutions of the two mildly unstable thirds in this sonority by stepwise contrary motion (m3-5, M3-1), while the second involves a lower m3-5 resolution. Note that in the second case we resolve to a complete three-voice sonority analogous to the triad in later music as the most complex stable sonority: an octave "split" the the middle voice into lower fifth and upper fourth. Johannes de Grocheio (c. 1300) calls this trina harmoniae perfectio or "threefold perfection of harmony," and in English I call it a "trine."
Note also that a medieval Pythagorean tuning will bring out the active rather than restful quality of major and minor thirds, tuning them at 81:64 and 32:27 rather than 5:4 and 6:5. Thus the effect, although treated by composers and theorists as relatively "concordant" or "blending," is also somewhat tense, adding to the dynamic quality of resolutions to stable intervals and sonorities.
For the era of roughly 1200-1420, or Perotin to Ciconia and his contemporaries, say, this kind of approach may be best: We speak of stable trines, and mildly unstable sonorities including the quinta fissa or "split fifth," etc. For one approach to classifying 13th-century sonorities, see A Quick Guide to Combinations and Cadences.
While I might now be inclined to revise my use of continuo symbols to identity sonorities by their intervals above the lowest voice, this article should at least give an idea of what trinic harmony is about.
Around 1420-1500, the era from the young Dufay to Josquin, say, and including the particularly ambivalent music of Ockeghem (c. 1410?-1495), we are really in a period of transition from the trinic music of the Gothic to the tertian music of the 16th century. I'd be inclined to say that the early Dufay is still largely trinic, although the pervasive role of thirds and sixths between cadences suggests a new direction. In Ockeghem's style, sonorities with a third are pervasive but not quite conclusive, although maybe a bit before 1500, people like Josquin and Isaac start concluding pieces with sonorities including thirds.
For Ockeghem, perhaps I would describe the harmonic situation as "a saturated tertian sonority with the fifth and third above the bass."
For the 16th century, the term "triad" might not in itself be so inaccurate, because as Zarlino (1558) points out, the standard of complete harmony or harmonia perfetta is "the third plus fifth or sixth" above the bass. However, the term "triad" might imply a theory of inversion, which in fact Lippius introduces, while Zarlino takes a different approach to "relatedness" between tertian sonorities.
Thus for 16th-century pieces, I tend generally to follow Zarlino and speak of harmonia perfetta rather than "a triad." More specifically, Zarlino speaks of a fifth divided by a third voice into a major third below and minor third above as the "harmonic division of the fifth" (e.g. F3-A3-C4), and of the division with the minor third below and the major third above as the "arithmetic division" (e.g. A3-C4-E4). I find these terms natural for discussing fully Renaissance music.
The idea is that if we take three strings forming the harmonic division, the ratios of their lengths will form a harmonic ratio (15:12:10):
F3 A3 C4 15 12 10 3 2
That is, the ratios of the differences between the two pairs of adjacent terms (15-12):(12:10) or 3:2 will be equal to the ratio of the extreme terms (15:10 or 3:2).
In the arithmetic division, the differences between pairs of adjacent terms are identical, as in the string-ratios for the sonority with minor third below and major third above (6:5:4):
E3 G3 B3 6 5 4
Note that in addition to the harmonic and arithmetic divisions of the fifth, Zarlino discusses sonorities "with the sixth in place of the fifth," that is, with a third plus a sixth above the bass - and these are regarded as independent sonorities, not merely inversions of the form with the third and fifth. Also, Zarlino discusses forms with a sixth divided into a fourth below and a third above (e.g. G3-C4-E4), and he concludes that if the sixth and the upper third are major, this sonority might well be treated as a concord, although in practice it is treated more cautiously. (This raises the larger issue of the status of the fourth in Renaissance theory and practice, a sometimes disputed topic.)
Another 16th-century author who gives a system for describing sonorities is Tomás de Santa María, who identifies a sonority primarily by its outer interval, occurring in his four-voice examples between the bass and tiple or treble. This outer interval may permit various "differences," in which the middle parts serve to fill in the musical space in adding accompanying consonances. Santa Maria's system (1565) has been compared to later continuo. For example, here are three sonorities he regards as "of the first grade," that is, the most desirable to use in four-voice writing:
8 10 12 D4 A4 C5 A3 F4 A4 F3 C4 F4 D3 F3 F3
In the first difference, that of the octave, we have an ascending sequence of adjacent intervals third, third, and fourth. In the difference of the tenth, we have fifth, fourth, and third; in the difference of the twelfth, we have octave, third, and third.
Interestingly enough Santa Maria's "differences" of 1565 use the same approach of listing outer and adjacent intervals as Jacobus of Liege's "partitions" or "split" intervals of around 1325. We look at combinations as unions of intervals. However, this general approach produces different systems in the two eras, because of changes in musical style.
In Zarlino's terms, the three above most choice "differences" of the octave, tenth, and twelfth are all instances of harmonia perfetta: We have the third and fifth above the bass, or their octave extensions, present.
However, Zarlino's terminology allows us to make the further distinction that in the specific example above, the difference of the octave is an arithmetic division of the fifth, with the minor third below; the differences of the tenth and twelfth are here harmonic divisions, with the major third below.
Returing to the intermediate case of Ockeghem, I might lean toward the 16th-century terminology, even though it might be a bit "modernistic." Also, I might want to take a closer look at how someone like Ramos (1482) discusses these sonorities.
Incidentally, I'm tempted to comment that similarities in some of the sonorities of Ockeghem and Beethoven may reflect certain common rules and assumptions of style: For example, the use mostly of tertian sonorities (with thirds and sixths as favored intervals), and the general avoidance of parallel fifths and octaves. Also, some cadential patterns of the 15th and 16th century, very attractive for these styles, happened to be carried over into 18th-19th century styles.
Similarly, we can find sonorities such as G3-B3-D3-E4 both in late 16th-century music and in modern jazz. Thomas Morley (1597) describes this as taking "the fifth and sixth together," typically used as a cadential dissonance. In modern jazz, it is often stable and conclusive. However, if this combination were called in modern theory a "complete tetrad," I might be hesitant to apply this term to earlier music where it may be clearly unstable, or at any rate differently conceived.
In favoring medieval and Renaissance terms (or derivations) for early music analysis whenever practical, I don't want to exclude interesting cross-period comparisons, but only to bring the theoretical concepts of each period to the fore in discussing contemporaneous practice.
To some preliminary remarks on medieval chord structure
To Early Music FAQ.Margo Schulter