Simply put, it is just “note against note” as that is what the original Latin means. But in a world where a typical musical texture might be somebody singing a blues or gospel-derived tune over a drum machine with some guitar strums, further clarification might be in order. We are used to listening to accompanied melody, or sometimes the accompanied form of chanting known as ‘rap’. But in any case, just one melody at a time. Counterpoint began with the organum of Léonin and Perotin who were working at the Cathedral of Notre Dame in Paris in the 12th and 13th centuries. Before that, pretty much all music everywhere was melody with or without some form of accompaniment—usually a drone. There was a big repertoire of Gregorian chant that was used in every church. Léonin and Perotin’s contribution was to write down some ways of decorating that chant. The idea was that the people singing the chant would stretch each syllable out for a long time, while another singer would sing a different melody in quick notes over top. This was quite an exciting idea. It immediately led to the idea or problem of harmony. Put simply, some notes sound very smooth and natural together (the 4th, 5th and octave) while others sound more complex (3rds and 6ths) and still others quite stressful or ‘dissonant’ (2nds, 7ths and tritones). So there had to be ways of putting notes together that took into account these differences. This was the first time in music history that we have real evidence of harmony, by the way. Here is a little alleluia by Léonin:
Things progressed step by step from there. From one voice singing quicker notes over another voice singing long notes (called a cantus firmus) to two quicker voices was not a big step. The rules of harmony were pretty simple at the beginning as well: you had to start with a consonance (the smooth natural sounding combinations or intervals) and end with a consonance and use a consonance on stressed syllables and in between you could use the other notes. One day, some brilliant fellow came up with the idea of canon. Take one of those melodies and sing it against itself! Perhaps it was discovered by accident when Brother Wilbur came in late one day, but it sounded good anyway. You have to be careful writing a canon, because the melody has to be written just right to combine with itself and obey the rules of harmony. Here is Bach showing off by writing a 'Crab' canon, meaning not only that the top voice and the bottom voice are the same, but that they are reversals of one another. The bottom voice is the top voice backwards. The whole piece is a palindrome:
Of course, soon after it was realized that you could combine the idea of quick notes over top of slow ones and the idea of canon. What if you wrote a canon that would work if one of the voices always had notes twice as long as the other? There is even a name for it: canon per augmentationem.
This is Bach really showing off! Ok, the first voice plays a melody. After four measures the second voice enters playing the same melody BUT down a 4th, in note-values twice as long AND in contrary motion, meaning everywhere the first voice went up, this voice goes down--inverted in other words. In Latin this is a canon per augmentationem in contrario motu. Just for laughs, in the second half, from about 1'50, the two voices switch--now the lower voice starts and the upper voice comes in four measures later, up a 5th, in note-values twice as long and in contrary motion. Whew!
Another brilliant idea was to realize that a canon was nothing but one voice imitating another and you didn’t have to stick to whole melodies—you could just imitate short phrases. Well, that led to being able to tie together the whole texture of a piece with those short phrases, echoing around among the voices. And sure, you could to all those tricky canon things as well including imitating or answering the short melody with itself in longer notes, or upside down or even backwards. A piece that does this kind of thing was a specialty of J. S. Bach and is called a fugue and I've posted a few of those. You can have a fugue on one theme or on two or more, called a ‘double fugue’.
Counterpoint developed a set of rules that help the voices to remain distinct from one another. For example, it is better for the voices to move in different directions—this is called ‘contrary motion’. Some movement in the same direction sounds good, such as in 3rds and 6ths, but one of the big sins is moving in 5ths in the same direction, the dreaded parallel 5ths! One of the best tricks in the counterpoint biz is ‘invertible counterpoint’. Say you write a melody, then you write another melody to go with it. If you are careful to write them in such a way that they will also work together if you flip them, then you have invertible counterpoint. Bach could do this in his sleep with a quill pen. You see, the problem is when you flip—invert—the melodies, the intervals change. One way, the interval might work, but it might not the other way. Unless you’re careful. But if you can do it, it is a very neat thing.
It's not Justin Bieber!