Whereas "harmony" was a word used, since ancient times, to mean a reconciliation of dissimilar or even opposing elements, "counterpoint" originated as a technical term of music composition. European monks in the Middle Ages used the term "points" to name the dark spots on a page indicating particular musical notes. If a talented monk could sing a second melody to decorate the melody of a Gregorian chant sung by the other monks, he was said to be placing points "against" points. In Latin, "against" was "contra," and so the phrase "punctus contra punctum" ("point against point") eventually turned into the word "counterpoint." When this art was taught to children, a master would give a student one melody—the "fixed song" or cantus firmus—and the child would improvise a second part, the counterpoint. Doing this was called "counterpointing."

At the elementary level one can think about counterpoint literally as points against points. Each tone in a reference or fixed voice will be matched with tones in other voices that go well together. This is not easy because when more than one new voice is added, the added voices themselves form counterpoint and their interactions need to be considered. A four-voice composition, for instance, involves six two-voice counterpoints, and a five-voice composition involves ten.

Organists and other accompanists of multi-part vocal and/or instrumental music worked out a shorthand to represent the different types of sonorities created by the singers and instrumentalists. We call this shorthand a "figured bass" or "thoroughbass." That is, a code of numbers attached to a bass line that continues all through a piece of music (basso continuo or generalbass or thoroughbass) indicates which tones are being sung or played. Over the period from about 1600 to 1700, thoroughbass developed into a way of thinking about counterpoint. Given a segment of a bass with a particular shape, musicians learned to associate it with a set of preferred counterpoints. In Italy, these specific shapes were termed bass "motions" (movimenti or moti del basso). In France they were called "marches harmoniques" (harmonic-contrapuntal progressions or sequences).

In the sixteenth-century counterpoint of Palestrina, the pope's chief musician at the Vatican, all but the briefest of tones were significant and related each to the next in sequence. As a result one can often predict what the next tone will be, but not what will be sung ten notes into the future. By contrast, in the music of Bach and Handel in the eighteenth century, a tone on the downbeat of one measure can relate to the tone on the downbeat of the next measure or even to two measures later. So there is a distinction between important, core tones and tones that are less important and more ornamental.

The first or Palestrina type counterpoint (the so-called prima prattica or "first practice") was often taught through what was called "species" counterpoint. "Species" meant "appearances or types" That is, a student would practice counterpoint with different types of rhythmic relationships between the fixed voice and the counterpoint. First species is a 1:1 relationship of durations. Second species is 2:1 (two counterpointing notes for each fixed note), and so forth. Species counterpoint was develoed in the 1600s in Italy, but received its most famous codification in Vienna in 1725 by Johann Joseph Fux, the emperor's chief musician.

The second type of counterpoint (seconda prattica) involved learning schematic collocations ("co-locations") of core tones in two voices, as well as what kind of ornamental tones can be used. This was also developed in Italy but remained relatively unknown outside of the conservatories.

Species counterpoint as taught by Fux in Vienna was directed towards a memory of the first practice, never reaching more modern styles. Counterpoint as taught in Italy covered the simple species briefly before proceeding to the main focus on contemporary style. The manuscripts presented on this website give a good cross-section of Italian and French methods.