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    "Consecutive leaps must outline a triad" in the 16th century?

    An often-cited restriction in modern teaching of species counterpoint is that consecutive leaps in the same direction must outline a major or minor triad. Since we deal with the concept of the triad constantly, this is a convenient way to evaluate three consecutive pitches. At what point did this rule become codified with the term "triad" and how was it addressed before then? 

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    • 7 Comments sorted by Votes Date Added
    • A partial answer to your question may involve the "modern teaching of species counterpoint" versus the actual stylistic practice of the 16th century.  Gauldin's text (and others) do not use a CF/species approach, but rather, a "direct" approach to style emulation.  (There's a wonderful debate about that in the introduction to the Salzer/Schachter text.)  And Gauldin includes other possibilities regarding consecutive leaps in the same direction: 5th/4th combinations, such as C-G-C, or D-G-D, and D-A-C in Dorian (I've also seen A-E-G in Lassus, I think in both Aeolian and Dorian).

    • At the risk of stating the obvious, may I say that the D-a-c leap as a dorian mode signifier is so ingrained in chant that it is hardly surprising that it should take its place in C16th polyphony. So, by analogy, A-e-g, as a kind of aeolian analgoue.

    • As for other options, Soderlund's textbook gives a bit more detail than Gauldin (based on exhaustive analysis of Palestrina's music):

      Skips outlining the three notes of the major and minor triads... and the octave with intervening fourth or fifth all occur in the style, the latter ones occurring mostly in the bass parts.


      The ascending skip of a perfect fifth followed by minor third or, more rarely, by a major third is a favorite Dorian melodic idiom; the descending skip of a perfect fifth followed by a third is, on the other hand, quite infrequent.  In practically all cases the sum of the two intervals is that of a minor seventh, which may be noticed in another combination of the two intervals, namely, the descending minor third followed by the perfect fifth.

      Two perfect fifths or two perfect fourths in the same direction are permitted in long note values only; such occurrences, however, are quite rare.

      So, these other kinds of motions do occur, but only rarely or as a characteristic melodic idiom.  Some 16th-century theorists were concerned about modal characteristics, and leaping that outlined an octave (e.g., 5th+4th or 4th+5th) would typically emphasize characteristic tones in the mode or local harmonic progressions (e.g., idiomatic cadential motions).  I'm sure some 16th-century treatises have more hints about this, but given the solmization difficulties in navigating wider intervals that span multiple hexachords, other patterns would occur mostly in idiomatic passages (or cadential bass motion) which singers would be familiar with.

      As for the constraint about "major and minor" triads, that's just a consequence of avoiding diminished or augmented melodic intervals.  If you follow that principle and keep most of your leaping to thirds and fourths (much more common in Renaissance music than larger leaps, and larger leaps typically reverse direction), then you naturally end up with apparent "triadic" melodic motions, even if they weren't intended that way.

    • The concept of triad originated with Lippius in 1610: it is therefore most unlikely that, in the 16th century, consonant leaps would have been in any way codified in association with it. On the other hand, it must be realized that if two leaps in the same direction are to be consonant not only as dyads, but also that the third step be consonant with the first, the result necessarily is a triad, major or minor, in any of its inversions. But this does not appear to have been an important concern in 16th-century counterpoint, as the case of D–A–C shows.



    • Nicolas, that was my intuition as well. If each leap needs to be consonant and the interval from the first pitch to the third needs to be consonant, you naturally get what we'd call a triad.

       Perhaps it wasn't clear, but the subtext of the question mark in my title was that 16th-century composers  wouldn't have refered to triads. I didn't know if that way of thinking was a more recent anachronism or if that way of thinking about consecutive leaps (apart from the D-A-C idiom) began earlier. Thanks to everyone for the insight! 

    • This, in my opinion, has to do with the "modal" decision of the composer (Powers notwithstanding). Renaissance polyphonic compositions are essentially diatonic. At some point, conceptually at least in a first step of the act of composing, the composer choses a "reference note" (a "final", a "tonic") which in turn defines the diatonic scale ("the mode") in which the work will be written – say, C, for a composition in Ionian or transposed Lydian. This choice not only determines the scale, but also its articulation in 5th+4th, e.g. (G)–C–g–c etc. if the "tonic" is C. But the 5th of this articulation often is articulated in 3d+3d, e.g. C–E–g. This has little to do with triads, unless that it prepares the path for 17th-century triads.

      The image linked below shows the first points of imitation in Josquin's Ave Maria (adapted from my paper in Regards sur la tonalité, 2013). Josquin does not write leaps forming a triad, but the piece obviously is based on articulations suggesting a triad.


      [I don't know how to include the image here; it may eventually disappear from my website.]



    • Brian - if I understand your question now, you're wondering when counterpoint treatises/textbooks began talking about consecutive leaps in terms of triadic motion?

      If that's your main concern, I'd speculate that it's mostly a 20th-century phenomenon, perhaps post-Jeppesen and the major exhaustive studies done on Palestrina's style.  (Soderlund mentions the principle in the 1940s, for example.)  It might go back into the 19th century, but treatment of "modal counterpoint" then was quite a bit more loose and not generally based exclusively on true 16th-century style.  In such a hybrid modal/tonal species approach, it wouldn't be uncommon at all to see melodic patterns which outlined 7th chords or other less "triadic" combinations.  Even if you look at Fux in the 18th century, you'll see all sorts of weird combinations of leaps which don't outline a triad (particularly in white notes), some of which are significant departures from standard 16th-century style.

      In sum, if such a principle did exist historically, it probably referred to a style of species-type exercises which no longer were very Palestrina-like anyway.