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Species counterpoint

Species counterpoint is a type of so called strict counterpoint, developed as a pedagogical tool, in which a student progresses through several "species" of increasing complexity, always working a very plain given part in the cantus firmus (Latin for "fixed melody"). The student gradually attains the ability to write free counterpoint (that is, less rigorously constrained counterpoint, usually without a cantus firmus) according to the rules at the given time.The idea is at least as old as 1532, when Giovanni Maria Lanfraco described a similar concept in his Scintille di musica. The late 16th century Venetian theorist Zarlino elaborated on the idea in his influential Le institutioni harmoniche, and it was first presented in a codified form in 1619 by Lodovico Zacconi in his Prattica di musica. Zacconi, unlike later theorists, included a few extra contrapuntal techniques as species, for example invertible counterpoint. By far the most famous pedagogue to use the term, and the one who made it famous, was Johann Fux. In 1725 he published Gradus ad Parnassum, a work intended to help teach students how to compose, using counterpoint (specifically, the contrapuntal style as practised by Palestrina in the late 16th century) as the principal technique. As the basis for his simplified and often over-restrictive codification of Palestrina's practice, Fux described five species:

• Note against note
• Two notes against one
• Four (extended by others to include three, or six...) notes against one
• Notes offset against each other (as suspensions)
• All the first four species together, as "florid" counterpoint

A succession of later theorists imitated Fux's seminal work quite closely, but often with some small and idiosyncratic modifications in the rules. A good example is Luigi Cherubini.

Considerations for all species of counterpoint

Students of species counterpoint usually practice writing counterpoint in all the modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian and Aeolian). The following rules apply to melodic writing in each species, for each part:

• The final must be approached by step. If the final is approached from below, the leading tone must be raised, except in the case of the Phrygian mode. Thus, in the Dorian mode on D, a C# is necessary at the cadence.

• Permitted melodic intervals are the perfect fourth, fifth, and octave, as well as the major and minor second, major and minor third, and ascending minor sixth. When the ascending minor sixth is used it must be immediately followed by motion downwards.

• If writing two skips in the same direction (something which must be done only rarely) the second must be smaller than the first, and the interval between the first and the third note may not be dissonant.

• If writing a skip in one direction, it is best to proceed after the skip with motion in the other direction.

• The interval of a tritone in three notes is to be avoided (for example, an ascending melodic motion F - A - B natural), as is the interval of a seventh in three notes.

And, in all species, the following rules apply concerning the combination of the parts:

• The counterpoint must begin and end on a perfect consonance.
• Contrary motion should predominate.
• The interval of a tenth should not be exceeded between two adjacent parts, unless by necessity.

First species

In first species counterpoint, each note in every added part (parts being also referred to as lines or voices) sounds against one note in the cantus firmus. Notes in all parts are sounded simultaneously, and move against each other simultaneously. The species is said to be expanded if any of the added notes is broken up (simply repeated).
In the present context, a "step" is a melodic interval of a half or whole step. A "skip" is an interval of a third or fourth. (See Steps and skips.) An interval of a fifth or larger is referred to as a "leap".
A few further rules given by Fux, by study of the Palestrina style, and usually given in the works of later counterpoint pedagogues, are as follows. Some are vague, and since good judgement and taste have been regarded by contrapuntists as more important than strict observance of mechanical rules, there are many more cautions than prohibitions. But some are closer to being mandatory, and are accepted by most authorities.

• Begin and end on either the unison, octave, or fifth, unless the added part is underneath, in which case begin and end only on unison or octave.

• Use no unisons except at the beginning or end.

• Avoid parallel fifths or octaves between any two parts; and avoid "hidden" parallel fifths or octaves: that is, movement by similar motion to a perfect fifth or octave, unless one part (sometimes restricted to the higher of the parts) moves by step.

• Avoid moving in parallel fourths. (In practice Palestrina and others frequently allowed themselves such progressions, especially if they do not involve the lowest of the parts.)

• Avoid moving in parallel thirds or sixths for very long.

• Attempt to keep two adjacent parts within a tenth of each other, unless an exceptionally pleasing line can be written by moving outside of that range.

• Avoid having both parts move in the same direction by skip.
• Attempt to have as much contrary motion as possible.

In the following example in two parts, the cantus firmus is the lower part. (The same cantus firmus is used for later examples also. Each is in the Dorian mode.)

"First Species" counterpoint

Second species counterpoint

In second species counterpoint, two notes in each of the added parts work against each longer note in the given part. The species is said to be expanded if one of these two shorter notes differs in length from the other.
Additional considerations in second species counterpoint are as follows, and are in addition to the considerations for first species:

1. It is permissible to begin on an upbeat, leaving a half-rest in the added voice.

2. The accented beat must have only consonance (perfect or imperfect). The unaccented beat may have dissonance, but only as a passing tone, i.e. it must be approached and left by step in the same direction.

3. Avoid the interval of the unison except at the beginning or end of the example, except that it may occur on the unaccented portion of the bar.
4. Use caution with successive accented perfect fifths or octaves. They must not be used as part of a sequential pattern.

"Second Species" counterpoint

Third species

In third species counterpoint, four (or three, etc.) notes move against each longer note in the given part. As with second species, it is called expanded if the shorter notes vary in length among themselves.

"Third Species" counterpoint

Fourth species

In fourth species counterpoint, some notes are sustained or suspended in an added part while notes move against them in the given part, often creating a dissonance on the beat, followed by the suspended note then changing (and "catching up") to create a subsequent consonance with the note in the given part as it continues to sound. As before, fourth species counterpoint is said to be expanded when the added-part notes vary in length among themselves. The technique requires chains of notes sustained across the boundaries determined by beat, and so creates syncopation.

"Fourth Species" counterpoint

Florid counterpoint

In fifth species counterpoint, sometimes called florid counterpoint, the other four species of counterpoint are combined within the added parts. In the example, the first and second bars are second species, the third bar is third species, and the fourth and fifth bars are third and embellished fourth species.

"Florid" counterpoint

General notes

It is a common and pedantic misconception that counterpoint is defined by these five species, and therefore anything that does not follow the strict rules of the five species is not "proper" counterpoint. This is not true; although much contrapuntal music of the common practice period adheres to the spirit of the rules, and often to the letter of them, the exceptions are many. Fux's book and its concept of "species" was purely a method of teaching counterpoint, not a definitive or rigidly prescriptive set of rules for it. He arrived at his method of teaching by examining the works of Giovanni Pierluigi da Palestrina, an important late 16th-century composer who in Fux's time was held in the highest esteem as a contrapuntist. Works in the contrapuntal style of the 16th century—the "prima pratica" or "stile antico," as it was called by later composers—were often said by Fux's contemporaries to be in "Palestrina style." Indeed, Fux's treatise is a compendium of Palestrina's actual techniques, simplified and regularised for pedagogical use (and so permitting fewer liberties than occurred in actual practice).

Contrapuntal derivations

Since the Renaissance period in European music, much music which is considered contrapuntal has been written in imitative counterpoint. In imitative counterpoint, two or more voices enter at different times, and (especially when entering) each voice repeats some version of the same melodic element. The fantasia, the ricercar, and later, the fugue (the contrapuntal form par excellence) all feature imitative counterpoint, which also frequently appears in choral works such as motets and madrigals. Imitative counterpoint has spawned a number of devices that composers have turned to in order to give their works both mathematical rigor and expressive range. Some of these devices include:

• Melodic inversion: The inverse of a given fragment of melody is the fragment turned upside down – so if the original fragment has a rising major third, the inverted fragment has a falling major (or perhaps minor) third, etc. (Compare, in twelve tone technique, the inversion of the tone row, which is the so-called prime series turned upside down.) (Note: in invertible counterpoint, including double and triple counterpoint, the term inversion is used in a different sense altogether. At least one pair of parts is switched, so that the one that was higher becomes lower. See Inversion in counterpoint; it is not a kind of imitation, but a rearrangement of the parts.)

• Retrograde refers to the contrapuntal device whereby notes in an imitative voice sound backwards in relation to their order in the original.

• Retrograde inversion is where the imitative voice sounds notes both backwards and upside down.

• Augmentation is when in one of the parts in imitative counterpoint the notes are extended in duration compared to the rate at which they were sounded when introduced.

• Diminution is when in one of the parts in imitative counterpoint the notes are reduced in duration compared to the rate at which they were sounded when introduced.

Dissonant counterpoint

Dissonant counterpoint was first theorized by Charles Seeger as "at first purely a school-room discipline," consisting of species counterpoint but with all the traditional rules reversed. First species counterpoint is required to be all dissonances, establishing "dissonance, rather than consonance, as the rule," and consonances are "resolved" through a skip, not step. He wrote that "the effect of this discipline" was "one of purification." Other aspects of composition, such as rhythm, could be "dissonated" by applying the same principle.

Seeger was not the first to employ dissonant counterpoint, but was the first to theorize and promote it. Other composers who have used dissonant counterpoint, if not in the exact manner prescribed by Charles Seeger, include Ruth Crawford-Seeger, Carl Ruggles, Dane Rudhyar, and Arnold Schoenberg.