The difference between the ancient strictness and modern laxity in plain counterpoint chiefly relates to the admission of consecutive octaves and fifths by contrary motion, even between extreme parts, and the doctrine of false relations, especially that of the tritone. Plain counterpoint, however, is most useful as a study, whereby facility may be acquired in conquering difficulties arising from the various motions of the different parts in a piece of music. It is obvious, therefore, that the more stringent rules should be observed by students with a view to this particular object, and that therefore they are enforced in the best text-books.
Plain counterpoint is generally divided into five species. The first is called 'note against note.'
The second species is called 'two notes to one.'
The third species is called 'four notes to one.'
The fourth is called 'syncopated counterpoint.'
The 'fifth species is called 'florid counterpoint,' and is a combination or rather alternation of the last three, with certain ornamental variations peculiar to itself.
Plain counterpoint may be in any number of parts, and the canto fermo may be assigned to the upper, middle, or lowest parts, according to circumstances.
Double counterpoint is when two or more melodies are so constructed that either of them may form a correct bass to the others; and when the various melodies may, by transposition, be placed in any relative order of acuteness, without infringing the laws of harmony. These transpositions may be such as to produce counterpoints at the octave, tenth, twelfth, or any other interval, but the most usual is double counterpoint at the octave.
Examples of various double counterpoints—
The above is a specimen of double counterpoint at the octave.
The next species is at the tenth, on a Canto fermo.