chief function is to represent durations which cannot be represented by a single character, such as five eighth notes.

11.—In pianoforte music a note is very occasionally intended to be reiterated before the first iteration has ceased to sound. This is effected by allowing the key to rise sufficiently to release the hammer, but not sufficiently to reimpose the damper on the string. The second sound therefore overtakes the first. (It is comparatively easy on some pianos and very hard on others.) As the sound, though periodically reinforced, is continuous, the composer indicates his intention by a tie. There is nothing but one's judgment to distinguish this from the ordinary kind of tie. The chief indication is the employment of a tie where a single musical character would otherwise have been better. For instance, the following tied sixteenth notes from the Adagio of Beethoven's Sonata, Op. 106, could better have been represented by eighth notes, had it not been for the intention of overlapping iteration (Fig. 6).

Fig. 6.

The ties commencing in measure 134 of Beethoven's well-known Sonata Pastorale were evidently regarded by Cipriani Potter as of this order. As having been a personal friend of Beethoven's he was likely to know. (The great composer refers to him in corresponding with Ries in 1818.) The duration of these notes could not have been written otherwise than by means of ties. The above test is therefore inapplicable; this is evidently why, in the edition edited by Potter, they are marked with a tie plus a dot and horizontal stroke (Fig. 6a).

Fig. 6a.

Another indication is the tying of an unaccented note to an accented one, thus obliterating the accent if the tie be observed literally (instances occur in Chopin's Valse, Op. 31, No. 1). So much critical judgment, however, is required to distinguish this treatment from that proper to a tie, that composers would do well to adopt some such method as Cipriani Potter's to make their exact meaning clear.

This interpretation of a tie, according to which the notes, since they overlap, are just not separated, must not be confused with the mezzo-staccato touch, also indicated with a slur, but having dots also (in the case of a single note indicated by a stroke with a dot), and which means that the notes are to be just not joined. In legato, of course, they should be neither separated nor overlapping, but exactly contiguous.

12.—The commonest errors in simple time are not in regard to notes, but rests. This is because silence cannot be divided or syncopated, and therefore that would often be quite right as a representation of sound which is quite wrong as a representation of silence. Thus a beat should not be represented by two rests where one would do, though it might be by two notes (see a, Fig. 7). Nor one rest represent parts of two beats (see b, Fig. 7). Nor one rest represent an unaccented and an accented beat (see c, Fig. 7). In triple time it is better to avoid a single rest representing the latter and greater part of a measure (see d, Fig. 7), indeed, it may be said that half-note rests should not be used in triple time.

Fig. 7.

13.—But in compound time errors, if not more numerous in kind, are much more common anyway in regard to notes as distinct from rests. A note should never be written which represents a beat and part of another. The commonest violation of this principle—and it is very common—is in writing a dotted half note in six-eight time; this divides the measure into three thirds instead of two halves, by representing a beat-and-a-third and two thirds of a beat (see a, Fig. 8). A beat-and-a-third, if required, should be represented by a note of the value of a beat tied to one of the value of a third, never by a single note equalling both—a half note in this case (see b, Fig. 8). A similar principle applies to rests. A measure's silence should be represented by rests divisible into beats, not by rests which fuse a beat and part of the next (see c, Fig. 8). Two dotted quarter notes in twelve-sixteen time are not so bad as a dotted half note in six-eight time, as they correctly represent the division of the measure into two halves, but they misrepresent these halves as consisting of three sixths of a measure whereas they rhythmically consist of two quarters (see d, Fig. 8).

Fig. 8.

A twelve-sixteen measure of silence is much easier to write, since it can be done by a single whole note rest, which is also commonly used as a measure-rest, irrespective of the value of the measure. (Hence the German name taktpause.) The six-eight measure of silence (see c, Fig. 8) might also, of course, have been written in the above way, or by quarter, eighth, quarter, eighth rests in place of the dotted rests.

Placing of Notes.

14.—The characters which will correctly represent the given rhythm having been determined, the second point is the correct placing of them in the measure. Mentally, at least,