# 1911 Encyclopædia Britannica/Counterpoint

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​COUNTERPOINT (Lat. contrapunctus, “point counter point,” “note against note”), in music, the art happily defined by Sir Frederick Gore Ouseley as that “of combining” melodies: this should imply that good counterpoint is the production of beautiful harmony by a combination of well-characterized melodies. The individual audibility of the melodies is a matter of which current criticism enormously overrates the importance. What is always important is the peculiar life breathed into harmony by contrapuntal organization. Both historically and aesthetically “counterpoint” and “harmony” are inextricably blended; for nearly every harmonic fact is in its origin a phenomenon of counterpoint. And if in later musical developments it becomes possible to treat chords as, so to speak, harmonic lumps with a meaning independent of counterpoint, this does not mean that they have really changed their nature; but it shows a difference between modern and earlier music precisely similar to that between modern English, in which metaphorical and abstract expressions are so constantly used that they have become a mere shorthand for the literal and concrete expression, and classical Greek, where metaphors and abstractions can appear only as elaborate similes or explicit philosophical ideas. The laws of counterpoint are, then, laws of harmony with the addition of such laws of melody as are not already produced by the interaction of harmonic and melodic principles. In so far as the laws of counterpoint are derived from purely harmonic principles, that is to say, derived from the properties of concord and discord, their origin and development are discussed in the article Harmony. In so far as they depend entirely on melody they are too minute and changeable to admit of general discussion; and in so far as they show the interaction of melodic and harmonic principles it is more convenient to discuss them under the head of harmony, because they appear in such momentary phenomena as are more easily regarded as successions of chords than as principles of design. All that remains, then, for the present article is the explanation of certain technical terms.
1. Canto Fermo (i.e. plain chant) is a melody in long notes given to one voice while others accompany it with quicker counterpoints (the term “counterpoint” in this connexion meaning accompanying melodies). In the simplest cases the Canto Fermo has notes of equal length and is unbroken in flow. When it is broken up and its rhythm diversified, the gradations between counterpoint on a Canto Fermo and ordinary forms of polyphony, or indeed any kind of melody with an elaborate accompaniment, are infinite and insensible.
2. Double Counterpoint is a combination of melodies so designed that either can be taken above or below the other. When this change of position is effected by merely altering the octave of either or both melodies (with or without transposition of the whole combination to another key), the artistic value of the device is simply that of the raising of the lower melody to the surface. The harmonic scheme remains the same, except in so far as some of the chords are not in their fundamental position, while others, not originally fundamental, have become so. But double counterpoint may be in other intervals than the octave; that is to say, while one of the parts remains stationary, the other may be transposed above or below it by some interval other than an octave, thus producing an entirely different set of harmonies.
Double Counterpoint in the 12th has thus been made a powerful means of expression and variety. The artistic value of this device depends not only on the beauty and novelty of the second scheme of harmony obtained, but also on the change of melodic expression produced by transferring one of the melodies to another position in the scale. Two of the most striking illustrations of this effect are to be found in the last chorus of Brahms’s Triumphlied and in the fourth of his variations on a theme by Haydn.
Double Counterpoint in the 10th has, in addition to this, the property that the inverted melody can be given in the new and in the original positions simultaneously.
Double counterpoint in other intervals than the octave, 10th and 12th, is rare, but the general principle and motives for it remain the same under all conditions. The two subjects of the Confiteor in Bach’s B minor Mass are in double counterpoint in the octave, 11th and 13th. And Beethoven’s Mass in D is full of pieces of double counterpoint in the inversions of which a few notes are displaced so as to produce momentary double counterpoint in unusual intervals, obviously with the intention of varying the harmony. Technical treatises are silent as to this purpose, and leave the student in the belief that the classical composers used these devices, if at all, in a manner as meaningless as the examples in the treatises.
3. Triple, Quadruple and Multiple Counterpoint.—When more than two melodies are designed so as to combine in interchangeable positions, it becomes increasingly difficult to avoid chords and progressions of which some inversions are incorrect. In triple counterpoint this difficulty is not so great; although a complete triad is dangerous, as it is apt to invert as a “6/4” which requires careful handling. On the other hand, in triple counterpoint the necessity for strictness is at its greatest, because there are only six possible inversions, and in a long polyphonic work most of these will be required. Moreover, the artistic value of the device is at its highest in three-part polyphonic harmony, which, whether invertible or not, is always a fine test of artistic economy, while the inversions are as evident to the ear, especially where the top part is concerned, as those in double counterpoint. Triple counterpoint (and a fortiori multiple counterpoint) is normally possible only at the octave; for it will be found that if three parts are designed to invert in some other interval this will involve two of them inverting in a third interval which will give rise to incalculable difficulty. This makes the fourth of Brahms’s variations on a theme of Haydn almost miraculous. The plaintive expression of the whole variation is largely due to the fact that the flowing semiquaver counterpoint below the main theme is on each repeat inverted in the 12th, with the result that its chief emphasis falls upon the most plaintive parts of the scale. But in the first eight bars of the second part of the variation a third contrapuntal voice appears, and this too is afterwards inverted in the 12th, with perfectly natural and smooth effect. But this involves the inversion of two of the counterpoints with each other in the 9th, a kind of double counterpoint which is almost impossible. The case is unique, but it admirably illustrates the difference between artistic and merely academic mastery of technical resource.
Quadruple Counterpoint is not rare with Bach. It would be more difficult than triple, but for the fact that of its twenty-four possible inversions not more than four or five need be correct. Quintuple counterpoint is admirably illustrated in the finale of Mozart’s Jupiter Symphony, in which everything in the successive statement and gradual development of the five themes conspires ​to give the utmost effect to their combination in the coda. Of course Mozart has not room for more than five of the 120 possible combinations, and from these he selects such as bring fresh themes into the outside parts, which are the most clearly audible. Sextuple Counterpoint may be found in Bach’s great double chorus, Nun ist das Heil, and in the finale of his concerto for three claviers in C, and probably in other places.
4. Added Thirds and Sixths.—An easy and effective imitation of triple and quadruple counterpoint, embodying much of the artistic value of inversion, is found in the numerous combinations of themes in thirds and sixths which arise from an extension of the principle which we mentioned in connexion with double counterpoint in the 10th, namely, the possibility of performing it in its original and inverted positions simultaneously. The Pleni sunt coeli of Bach’s B minor Mass is written in this kind of transformation of double into quadruple counterpoint; and the artistic value of the device is perhaps never so magnificently realized as in the place, at bar 84, where the trumpet doubles the bass three octaves and a third above while the alto and second tenor have the counter subjects in close thirds in the middle.
Almost all other contrapuntal devices are derived from the principle of the canon and are discussed in the article Contrapuntal Forms.
As a training in musical grammar and style, the rhythms of 16th-century polyphony were early codified into “the five species of counterpoint” (with various other species now forgotten) and practised by students of composition. The classical treatise on which Haydn and Beethoven were trained was Fux’s Gradus ad Parnassum (1725). This was superseded in the 19th century by Cherubini’s, the first of a long series of attempts to bring up to date as a dead language what should be studied in its original and living form.  (D. F. T.)