Or, the "business logic" of 15th century music composition. Still relevant if you want your music to sound like a 15th century chant (as corrupted by harmony or anything else you've studied or accidentally picked up) or want practice in melody writing, as the counterpoint is ideal when both lines are good and go well with one another. This can be difficult, and it is possible to write horrible sounding music that yet passes all the rules. Actual compositions may show various errors that a strict grader (e.g. a computer program) will fail. This is much like a grammar checker that I once fed some Tolkien to, and the checker was, like, "this is bad English, instead you should …". Maybe grammar checkers have improved since the early 1990s, or will they still ding Tolkien's prose as problematic? More useful might be to read and write enough prose or music, which worked well enough for many before (and after) grammarians and music theorists came along.
Traditionally there are "species" of counterpoint that isolate and simplify particular aspects; in theory this will help the student chunk the particulars of note-against-note, two notes against another note, four notes against another note, and suspensions where one note is held over another and sometimes resolved downwards, if dissonant. Once these are learned, to some degree, (Beethoven was not a good student) one can move on to free counterpoint which makes use of all the species, and more, in any voice, plus other complications not typically handled in counterpoint exercises: cadential formula, modern harmonics, etc. Think of counterpoint rules as training wheels: good reminders of where the ground is, for the inexperienced, but something to move past when no longer necessary. However, music is more abstract than a world coming up to hit you, so you may need to review the various rules now and then. One might also be a bit unsteady after getting back on a bike after a while.
There are various rules systems, akin to nets obnoxiously stretched across a tennis court, rules that allow or disallow various combinations of notes either horizontally or vertically. The fixed melodies (cantus firmus) supplied for education are often designed to create troublesome situations; one may need to backtrack and try something else if a hopeless situation is encountered, or a bottleneck may only allow one solution where normally a larger variety of options are possible. Have to angle the ball just right for it to bounce through. A student may improve their situation by noting that using "C" against "G" locks one to the notes C, E, and G in the additional voices, while using C against E allows the other voices the use of C, E, G, or A, as both and the first inversion of work with C and E. Other rule systems that allow such things as consonant fourths or second inversion chords which will offer more choices, as there one might employ 4-3 (F to E above C) in addition to the usual consonant 6-5 (A to G above C). Mozart was okay with the fourth being consonant, other people, not so much.
The rules are supposed to help create independent voices, that is, voices that do not parallel one another (except by 3rds or 6ths, but those not for too long) nor get tangled up and cross one another (except when they do). There are limits to voice independence; with four or more voices there will be less independence on account of there only being so many ways for multiple voices to move independently of one another. That is, with many voices some of the voices will need to directly parallel another voice, or go silent while the other voices play. With more voices various rules must be relaxed or ignored, as again there's only so many ways voices can be independent given the limited motions relative to another voice (move closer, away from, or to hold steady) and limited interval choices available. Also, too many voices risks the work collapsing to noise as there's too much going on, much like too much speech at a resturant does. And there is plenty of music where the voices do parallel one another to good effect, but that's not the point of counterpoint.
Some examples may help clarify these ramblings.
voice1 B4 A4 B4 A4
voice2 G4 F4 E4 D4A lot of bad here; from left to right there is a "parallel major 3rds" violation that creates a tritone effect (the first B4 with the F4 next below). Even worse is the parallel fifths (octaves are likewise bad) created by the <e b'> and <d a'> chords. Also there's another tritone problem (counterpoint really hates this interval) between the F4 in the lower voice and 2nd B4 in the upper voice.
The final lesson is to not repeat yourself too swiftly (the B4 A4 B4 A4), though there are musical forms where repetition, frequent and often, is the norm. Counterpoint does see repetitions, though if close together the repeition will be in a different voice, and otherwise there will typically be some amount of different material before the next repetition in the same voice.
To correct the above, in a fully worked example of Fux's 1st species counterpoint in two parts, one solution might be:
voice1 A4 D4 G4 A4 B4 C5 C5 D5 A4 C5 D5
voice2 D4 F4 E4 D4 G4 F4 A4 G4 F4 E4 D4This has more leaps in it than I might normally use. Note how the voices tend to move by contrary or oblique motion, and where parallel motion is used (twice) it is to the interval of a 3rd; a 6th would also be okay.
A4 C5 A4 E4
Counterpoint frowns on successive leaps, especially those that do not outline a triad, among other complications. A leap may give the impression that a new voice has started, and too many leaps is not so much melodic as bouncing around, a feature that can be found in various music forms. Not so much in counterpoint. When to leap is also important; some counterpoint rules frown on leaping up from an accented or strong position, that is on the 1st or 3rd beat of a four-note measure. The 2nd and 4th beats are weaker, and is also where more dissonant notes are allowed. A rules system will usually have some arbitrary limit on leaps, which may give the impression that "leaps bad". A look at a random motet—"Beatus Vir", part of twelve motes by Lassus—shows various successive leaps, two or even three in a row. Moreover, these leaps are used in each voice, with the alternate voice using the same or a similar leap set a short time later. The leaps thus form a distinctive motif, and are used multiple times (but not close together, in the same voice). A too simple rules system here risks marking the work as bad simply because too many leaps were used, and may not judge how skillfully the leaps were used.
Lassus also wrote shorter compositions on days the Duke would hunt. It may not take a leap to see why keeping the Duke too long pewed might be bad.
Given a computerized grading system, a student may want to hack around and see exactly what can be gotten away with. For example, in 3rd species (quarter note against whole note) rests are allowed, so can they be sprinkled in to good effect in the middle of the voices? Also, can where the counterpoint is done be varied, rather than confining the quarter notes to only one voice? These sorts of experiments may yield good results and bring the student closer to the practice of free counterpoint, even if strictly illegal as the counterpoint is "supposed" to confine itself to a single voice in a training exercise. Why not pull micro-Kobayashi Marus when you can? (Because it may irk your instructors who may not be so willing to advance someone who is clearly not a good culture fit, or you may spend too long yelling at the rules system over something you see as being perfectly cromulent.)
=> fux-1st-species-2parts.midi
What's the harmony here? I haven't a clue, and it's more or less irrelevant to the counterpoint process.
=> fux-3parts-G.midi | counterpoint2.mp3
=> https://www.cpdl.org/wiki/index.php/Twelve_Two-Part_Motets_(Orlando_di_Lasso) This content has been proxied by September (ba2dc).Proxy Information
text/gemini