cular case, by the way, is perhaps the earliest instance of the occurrence of the always-misunderstood direction, 'Minuetto Da Capo.' By the time of Haydn the term Trio is firmly established, and even in his earliest works (such as the first quartets) there are two minuets, each with a trio. Haydn also experimented in using keys for the trio a little more remote from the tonic than those already mentioned, even anticipating Beethoven's favourite use of the major key a third below. These innovations become almost necessary in the modern striving for new forms of contrast. Beethoven affords perhaps the only instances (in Symphonies Nos. 4 and 7) of a scherzo and trio twice repeated, but Schumann was fond of writing two trios to his, having adopted the device in three of his symphonies, besides his Pianoforte Quintet and Quartet. Not that he was the first to write a second trio—a plan which has since found many followers; there is at least one instance in Bach (Concerto in F for strings and wind) where the minuet has three trios, and another in Mozart (Divertimento in D for ditto) of two minuets, one with three trios and another with two. Schumann was so given to dividing his pieces up and enclosing the several sections in double bars, that he seems occasionally in the pianoforte works to lose himself in a chain of trios, as for instance, in the 'Blumenstück,' 'Humoreske,' and 'Novelletten.' In his six Intermezzi (op. 4), he adopted the more rational term 'Alternativo' for his subordinate sections, while in the F♯ minor Sonata the middle part of the Scherzo is itself called an Intermezzo, this title signifying its entire want of relationship to the rest of the movement, which is no small part of its charm. A trio, as well as a subordinate section in a rondo, etc., which presents a change from tonic major to minor or the reverse, is sometimes simply headed 'Minore' or 'Maggiore' as the case may be. This is common in Haydn and not infrequent in Beethoven (PF. Sonata in E♭, op. 7; in E major, op. 15, etc). Schumann, Raff, and other modern composers, have also occasionally given this heading. In modern music, though the trio exists, it is often taken as an understood thing and not specially so entitled. (Chopin, Sonata in B minor, Grieg in E minor, etc, and see Beethoven, 9th Symphony.)
Speaking generally we may say that the most obvious key for the trio of a minuet, scherzo, march, etc., written in a major key, is the subdominant, as it stands in place of a third subject, the main movement having appropriated the tonic and dominant keys. But where, as in modern marches, there are more trios than one, and still another key has to be sought, the relationship of the key a third above or below—distant but still real—is turned to account. Military marches and most dances intended to be danced to are written with a separate trio, or trios, so that they can be repeated as often as necessary, but in concert pieces (such as Weber's Invitation à la Valse, the marches by Mendelssohn and others) the sections answering to trio are not often so designated, the piece being written out in extenso.
TRIPLET (Fr. Triolet; Ital. Terzina; Ger. Triole). In modern notation each note is equal to two of the next lower denomination, and the division of a note into three is not provided for, although in the ancient 'measured music' it was the rule. [See Dot, vol. i. p. 455.] On this account notes worth one third of the next longer kind have to be written as halves, and are then grouped in threes by means of curved lines, with the figure 3 usually placed over the middle note as an additional distinction. Such a group is called a Triplet, and is executed at a slightly increased speed, so that the three triplet-notes are equal to two ordinary notes of the same species: for example—
Beethoven. Sonata, op. 2. no. 1.
Triplets may be formed of notes of any kind, and also of rests, or of notes and rests together.
Beethoven. Sonata, op. 22.
So also a group of two notes, one twice the length of the other, is read as the equivalent of a triplet, provided it is marked with the distinctive figure 3.
Schumann. Trio, op. 63.
In instrumental music, when the fingering is marked, there is some risk of the figure 3 of a triplet being confounded with the indication for the third finger. To obviate this, the two figures are always printed in different type, or, better still, the triplet figure is enclosed in brackets, thus (3). This plan, which has recently been rather extensively adopted, appears to have been first introduced by Moscheles, in his edition of Beethoven, published by Cramer & Co.
Groups of a similar nature to triplets, but consisting of an arbitrary number of notes, are also frequently met with in instrumental music. These groups, which are sometimes called quintolets, sextolets, etc., according to the number of notes they contain, always have their number written above them, as an indication that they are played at a different (usually a quicker) rate from ordinary notes of the same form. Their proper speed is found by referring them to ordinary groups of the same kind of notes; thus,
