Counterpoint

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Counterpoint

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.

Introduction

Counterpoint is a method of composing music. It is a set of "rules" that are traditionally followed in order to write music for two or more voices. It is organized into "types" of counterpoint known as species. They go in order from most restrictive to the least. The more voices there are in a musical score, the more freedom the voices have (less rules to follow).

History

Much of the credit for the formation and organization of the rules of counterpoint is given to a single man by the name of Joseph Fux. His classic and groundbreaking work on counterpoint, Gradus ad parnassum, is regarded as the most important contribution to the advancement of the theories of counterpoint. It has been historically proven that great composers such as Haydn, Mozart, as well as Beethoven worked from the same book (giving much to say concerning the usefulness and importance of this method.)

Consonant Intervals

Consonant intervals in counterpoint are:

Perfect unison (Prime)
Third
Perfect Fifth
Sixth
Octave

The inversion of the perfect 5th is not consonant.

Dissonant Intervals

Dissonant intervals in counterpoint are:

Second
Fourth
TRITONE - diminished fifth or augmented fourth
Seventh

First Species

The first species of counterpoint is the most simple, being that of one note placed against one note (that is, if the cantus fimus is quarter notes, the counterpoint will also be in quarter notes).

There are two ultimate rules of counterpoint that should be observed in first species counterpoint and are almost never broken in any counterpoint with two voices.

When progressing into a perfect consonance, oblique motion or contrary motion may be used.
When progressing into a imperfect consonance, any motion might be used (however, parallel motion may only be used when progressing from imperfect to imperfect).

The Definition of Motions

Motion, with regards to counterpoint, is the relationship between two notes in different voices and how they "move", with reference to each other, as the score progresses.

Motion where one voice does not move and the other does is called oblique motion.
Motion where one voice moves up and the other down, or vice versa is called contrary motion.
Motion where both voices move up or down in the same interval is called parallel motion.
Motion where both voices move down, or both up (but not necessarily by the same interval) is called similar motion.

Parallel motion may be considered a special case of similar motion.

The Definition of Consonances

A consonance is any interval considered harmonious by tonal standards (the third, sixth, fifth, octave, and unison). (Note that the unison may not be used except in beginning a counterpoint below the cantus firmus.)
- a Perfect Consonance is any consonant interval that cannot be major or minor. These are the Perfect Fifth, Perfect Octave, and Perfect Unison (and any variation of these such as the fifteenth).

Special Note: In traditional counterpoint, the fourth is not considered a consonance because of the potential dissonance that can result if both fourth and third or fourth and fifth are utilized with a bass line in three or four voice counterpoint; however, in the less strict counterpoint of more vertical music, fourths are very frequently utilized as consonances. In the case of any exercises in counterpoint, it would be prudent to consider the fourth as a dissonance.

an Imperfect Consonance is any consonant interval that can be either major or minor. These are the major and minor third, sixth and tenth.

A dissonance is any interval that is considered to be unpleasant to the ear or unstable by tonal standards (these are the second, tritone, seventh, and augmented or diminished intervals)

Linear Nature of Counterpoint

Good counterpoint must be multiple melodies set against each other. As such, both melodies must be well written, with mostly stepwise motion and a high or low point that is reached as a "goal" of the melody. In general, large skips should not be made over the bar line or onto a strong beat. There are many other rules that will not be described in particular detail here.

Chordal Nature of Counterpoint

It is important for counterpoint to make harmonic sense in addition to melodic sense. The first and last chords must be the tonic chord of the key, and it is important for the cadence to make sense (usually the dominant or subdominant chord of the key).

Archaic vs. Modern

Fifths are more utilized in archaic style as a perfect consonance. In modern style, fifths are less utilized in favor of imperfect consonances, because these emphasize the tonality of the implied chord (major or minor)

Use of Leaps

According to Fux, leaps of seventh or any diminished or augmented intervals should be avoided. The melodic direction should change after a leap greater than a third.

Cadences

'in archaic style': If the counterpoint is in the upper voice, the cadence should involve a major sixth resolving to a perfect consonance. If the counterpoint is in the lower voice, the cadence should be a minor third resolving to a perfect consonance.

'in modern style': A V or IV chord must resolve to a I chord.

References

Chapter 8 of Music In Theory and Practice by Benward and Saker

Second Species

In Second Species counterpoint, two tones are used against each note of the melody. It is important to note where one places the consonant and dissonant tones.

Accented beats on the counterpoint should create consonant intervals. The exceptions for this are that the perfect unison should only fall on unaccented beats until the last note of the song and the octave should be used sparingly on accented beats.

Dissonant tones can be used on the weak beats provided that it is used as a passing tone.

A rest may be used in place of the first beat for the counterpoint. This is the only place a rest is allowed. In this case, the unaccented beat must have a perfect consonant interval. If the cantus firmus is above, this would refer only to the octave or the prime. If below, it refers to the octave, the prime, and the fifth.

It is often best to start by writing the cadence first.

Cadences

When writing the cadence in second species counterpoint, you have to think about whether you are writing your counterpoint above or below the Cantus Firmus.

Writing cadences above the Cantus Firmus

If your Cantus firmus ends in 2-1, then your counterpoint will end with (6-7)-8. Often the 5 will proceed the 6.

If your Cantus Firmus ends in 7-8, then your counterpoint will end with (2-5)-P

Writing cadences below the Cantus Firmus

If the cadence of the Cantus Firmus is 7-8 then the counterpoint will end with (5-2)-1.

If the cadence of the Cantus Firmus is 2-1 then the counterpoint will end with (6-7)-8.

NOTE: Numbers in () show that they are half the duration of the others.

Forms

Cadence and Neo-Harmony

You probably worked out, the image up there is an example of counterpoint. Well, counterpoint is ruled by one major thing - cadence. A cadence is a series of intervals that end a section of music. However, cadences can be made to clash, and create what is known as a 'dissonated cadential trill'. There are several types of cadence.

1. Perfect Authentic Cadence. This is chords V to I (e.g.: in C it would be G chord to C chord)

3. Imperfect Authentic Cadence. Similar to a PAC, but the V chord can be a diminished vii in first inversion, or the V or I chords ar inverted.

5. Half cadence: any cadence ending on V, whether preceded by ii, IV, or I, or any other chord. Because it sounds incomplete or "suspended", half cadence is considered a weak cadence - the weakest cadence, in fact. A progression of a diminished second in first inversion to V is considered the Phrygian Half Cadence.

6. Plagal cadence: IV to I, also known as the "Amen Cadence" because of its frequent appearance in hymns.

7. Deceptive (or interrupted) cadence: V to any chord except I (typically vi or VI). This is considered a weak cadence because of the "hanging" (suspended) feel it invokes.

Cadences can also be classified by their rhythmic position. A masculine cadence occurs on a strong position, typically the downbeat of a measure. A feminine cadence occurs in a metrically weak position, for instance, after a long appoggiatura (see also feminine ending). Masculine cadences are considered stronger and are generally of greater structural significance. (To avoid offending those sensitive to sex stereotypes, the Society for Music Theory endorses the terms "metrically accented" and "metrically unaccented cadence" in their Guidelines for Nonsexist Language.) Likewise, cadences can be classified as either transient (a pause, like a comma in a sentence, which implies that the piece will go on after a brief lift in the voice) and terminal (more conclusive, like the period or other terminal punctuation, which implies that, at least for the time being, we are done). Most transient cadences are half cadences (which stop momentarily on a dominant chord), though IAC or deceptive cadences are also usually transient, as well as Phrygian cadences. Terminal cadences are usually PAC or sometimes plagal ("Amen") cadences.

Neo-Harmony. You may think it means 'new harmony', which technically it should. However, it in fact represents a certain sequence of notes. It is a sequence in which a certain mode, melody or key is hinted at, but then turned into something else.