The term originates from the Latin punctus contra punctum meaning "point against point", i.e. The internal structures that create each of the voices separately must contribute to the emergent structure of the polyphony, which in turn must reinforce and comment on the structures of the individual voices. In particular, Mazzola's model gives a structural (and not psychological) foundation of forbidden parallels of fifths and the dissonant fourth.
Octavio Agustin has extended the model to microtonal contexts.
There are many examples of song melodies that sound well together when performed simultaneously.
For example, "Frère Jacques" and "Three Blind Mice" combine euphoniously when sung together.
Concerning the common practice era, alterations to the melodic rules were introduced to enable the function of certain harmonic forms.
The combination of these melodies produced the basic harmonic structure, the figured bass.Some examples of related compositional techniques include: the round (familiar in folk traditions), the canon, and perhaps the most complex contrapuntal convention: the fugue.All of these are examples of imitative counterpoint.A further example of fluid counterpoint in late Beethoven may be found in the first orchestral variation on the "Ode to Joy" theme in the last movement of Beethoven's Symphony No. The famous theme is heard on the violas and cellos, while "the basses add a bass-line whose sheer unpredictability gives the impression that it is being spontaneously improvised.Meantime a solo bassoon adds a counterpoint that has a similarly impromptu quality." In the Prelude to Richard Wagner's opera Die Meistersinger von Nürnberg, three themes from the opera are combined simultaneously.Since all notes in First species counterpoint are whole notes, rhythmic independence is not available.In the present context, a "step" is a melodic interval of a half or whole step. (See Steps and skips.) An interval of a fifth or larger is referred to as a "leap".The student gradually attains the ability to write free counterpoint (that is, less rigorously constrained counterpoint, usually without a cantus firmus) according to the given rules at the time.The idea is at least as old as 1532, when Giovanni Maria Lanfranco described a similar concept in his Scintille di musica (Brescia, 1533).Each is in the Dorian mode.) In second species counterpoint, two notes in each of the added parts work against each longer note in the given part.In third species counterpoint, four (or three, etc.) notes move against each longer note in the given part.