principles aesthetically indistinguishable from some types of
variation-form inevitably arose in the polyphonic treatment
of Gregorian hymns verse by verse. Accordingly, the hymns
and Magnificats of Palestrina might without great extravagance
be described as contrapuntal sets of variations on ecclesiastical
tunes, like very free examples of the type shown later in
extreme simplicity and formality by Haydn's variations on
his Austrian national anthem in the “ Emperor ” quartet
(Op. 76, No. 3).
Already in the 16th century instrumental music was assuming such independence as it could attain by means of a primitive variation-form, growing partly out of the habit of playing vocal madrigals on the virginals or similar keyed instruments, or singing the top part as a solo to an instrumental accompaniment, with an overwhelming weight of ornaments beneath which the original madrigal was quite unrecognizable. (See, for example, the “diminutions ” given in the 3oth volume of Breitkopf & Hartel's complete edition of Palestrina's works.) A favourite plan, of which numerous examples may be found in the Fitzwilliam Virginal Book, was to put together several popular or original tunes, with an ornamental variation sandwiched between each. Sometimes, however, sets of variations on a single tune were produced, with essentially modern effect, as in Byrd's variations on “The Carman's Whistle." Such variations were naturally grouped in order of increasing complexity and brilliance. Some of the keyboard passages in which the early English variation-writers indulged are of extraordinary difficulty, even from the standpoint of modern pianoforte technique.
In the 17th century a highly artistic form of variation arose, very favourable to the earliest composers of the transition period, because of the simplicity of its principle, which relieved the composer of all the graver problems of formal organization. This was the ground-bass, a single phrase placed in the bass and repeating itself as long as the composer had fresh harmonies and superstructure with which to vary it. In typical examples the ground-bass was derived from the dance forms of the passacaglia and the chaconne, which in classical music resembled each other in being in slow time, and did not otherwise differ markedly, except that in the passacaglia the theme could' be transferred now and then to the treble or to an inner part, a purely natural aesthetic resource which makes no radical difference to the art-form. The genius of Purcell was cruelly hampered by the lack of possibilities for organizing large musical forms in his time, and nothing is more significant than the avidity with which he seizes upon the ground-bass as a means of giving coherence to his ideas. By the time of Bach and Handel a lighter type of variation work, less capable of high organization, and more like Byrd's variations on “ The Carman's Whistle, ” had arisen. Bach's Aria variata alla maniera Italiana is an instance of this; and so is the air et doubles that appears now and then in Handel's instrumental works. The principle of this form is simply to take a symmetrical melody (generally in binary form) and embroider it. Such variations are called doubles whenever each variation divides the rhythm systematically into quicker notes than the one before. The most familiar example is that known as “ The Harmonious Blacksmith ” in Handel's E major suite. Sometimes the air itself was stated in a tangle of ornamentation, while the doubles made it float in a simplified form over an accompaniment of increasingly rapid flow. (See, for example, Handel's D minor suite and the little set in B flat on a theme afterwards varied in the noblest modern style by Brahms.)
But Bach had' meanwhile applied the principle of the ground bass to variations on a complete symmetrical movement in binary form. His Air and 30 Variations, commonly known as the “Goldberg ” variations, is (with the exception of Beethoven's 33 Verdnderzmgen on a waltz by Diabelli) not only the most gigantic set of variations in the world, but one of the three largest compositions in any form ever written for a single instrument. Of course in so large a work the conception of the ground-bass, as a clearly recognizable theme repeated with no more than slight ornament, would be inadequate whatever the variety of the superstructure: but so steady is the drift of Bach's bass that he is enabled to represent it by countless alternative harmonies and analogous chromatic progressions, without weakening its individuality. The grouping of the thirty variations is extremely subtle in balance and climax, the more so because there are no means within the terms of Bach's art for making a free coda to the work, his ground-bass being both too long and too purely a bass to be taken as the theme of a fugue, like that in his great passacaglia for organ. Yet Bach contrives to round off the work perfectly by the simple direction aria da capo at the end. There is no question of retaining or varying the melody of the aria, which indeed is so ornamental as to be pointless and unrecognizable as a basis for variations; nor could it, like the above-mentioned Italian examples of Handel, be simplified, since most of its ornaments are integral parts of the phrases.
The next chapter in the history of the variation form is intimately connected with the sonata style. A set of variations used as a movement for a sonata inevitably tends to be variations on the melody. The sonata style implies the identification of themes by their melodies rather than by their texture, the very term “ theme ” being primarily used in a melodic connotation (see MELODY). Hence a set of exclusively harmonic variations would not be in the sonata style. Now, most of the best sets of variations by Mozart and Haydn are movements in their sonata works; and this should always be remembered in discussing the tendency of their treatment of the form. Few of their independent sets are of any importance, since most are very early works, or were Written for pupils, or intended as encore pieces for concerts. Haydn shows a great fondness for a special form which, even if earlier specimens can be found, he may properly be said to have invented. It consists of alternating variations on two themes, the first a highly organized complete binary melody, and the other a shorter binary melody, often beginning with the same figure as the first, but clearly contrasted with it, inasmuch as, whichever theme is in the major, the other is in the minor. The first theme usually returns as if it were going to be unvaried, but its first repeat is an ornamental variation. The form is rarely worked out far enough to include more than one variation of the second theme; but the effect is always that of a happy blend of a clearly marked variation form with a more contrasted scheme a little more highly organized than the roundand-round symmetry of a minuet and trio, but not so elaborate as a rondo. The only later example exactly corresponding to Haydn's form is the first allegretto of Beethoven's pianoforte trio in E flat, Op. 70, No. 2; although, with a wider range of key, a free application of the principle of alternating themes is magnificently illustrated by the slow movement of his C minor symphony.
Beethoven in his last works invented another variation-form on two themes, in which the first theme is very free in structure and the second theme is a more rigid melody in a different key and time. The examples of this are the slow movement of the oth Symphony and the Lydian figured chorale in the A minor quartet. A fine later development of this is the slow movement of Brahms's F major string quintet, Op. 88, in which the alternation of the two keys gives rise, in the last line of the movement, to one of the most astonishing and subtle dramatic strokes in all music.
In sonata works, Beethoven's examples of the normal variation form based on a single theme are as wonderful as may be expected from him; but nothing is more significant than his strict adherence in sonata works to the melodic principle of variation. He uses the form as an unsurpassable means of obtaining repose in slow movements. The extreme case of this is the slow movement of the sonata, Op. S7 (commonly called Appassionata), which is described in the article on Sonata Forms. In this and in many other instances, his method is aesthetically that of the air et doubles, as being the simplest possible means
