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by any specific sign, since an experienced performer can always judge from the nature of the passage. As a rule, it may be said that whenever two tied notes are written for which a single longer note might have been substituted repetition is indicated—for the use of the tie proper is to express a note-value which cannot be represented by a single note, e.g. five quavers. Thus Ex. 1, which is an instance in point, might, if no repetition had been required, have been written in quavers, as in Ex. 2.

Beethoven. Sonata, op. 106. Adagio.

Another instance of the employment of this close repetition sometimes occurs when an unaccented note is tied to an accented one, as in Ex. 3. Here the rhythm would be entirely lost if the tied notes were sustained instead of repeated

Chopin. Valse, op. 31, no. 1.

In the same sense it seems quite possible that the subject of the scherzo of Beethoven's Sonata for piano and violoncello, op. 69, and other similar phrases, may have been intended to be played with repetition; and in support of this view it may be mentioned that an edition exists of the Sonata Pastorale, op. 28, by Cipriani Potter, who had opportunities of hearing Beethoven and becoming acquainted with his intentions, in which the analogous passage in the first movement is printed with what is evidently meant for a sign of separation between the tied notes, thus—

[ F. T. ]

TIEDGE, Christoph August, born 1752, died March 8, 1841; a German elegiac poet and friend of Beethoven's, who in Rhineland dialect always called him 'Tiedsche,' and who set some lines to Hope—'an die Hofihung'—from his largest and best poem, 'Urania,' to music twice, once in E♭, op. 32, and again in G, op. 94. Both are for voice and piano; the former dates from 1808, the latter from 1816. Tiedge's name occurs in the correspondence between Beethoven and Amalie Sebald, and there is a most interesting letter from Beethoven to him of Sept. II, 1811, betokening great intimacy. (Thayer, iii. 179, 213, etc.)

[ G. ]

TIERCE, i.e. Tiers, third. I. A name given to the interval of the Third, whether Major or Minor.

II. The fourth of the series of natural harmonics, being the Major Third in the third octave above the ground-tone or prime; its vibrations are five times as numerous as those of its prime.

III. An open metal organ stop of the same pitch as the similarly-named harmonic; i.e. if the note CC is held down and the Tierce-stop drawn, the E above middle C will be heard. That such a stop can only be used in combination with certain other harmonics, and then but sparingly, will be evident when it is remembered that if C, E, and G be held down there will be heard at the same time G sharp and B. Hence, the Tierce when found in a modern organ is generally incorporated as a rank of the Sesquialtera or Mixture, in which case it is of course combined with other harmonics, its near relations. Some organ-builders, however, altogether exclude it. A serious difficulty is now met with, if a Tierce be introduced; it is this modern organs are tuned to 'equal temperament,' whereas the Tierce (whether a separate stop or a rank) certainly ought to be tuned to its prime in 'just intonation,' in which case tempered and natural thirds would be heard simultaneously when the Tierce is used. Much difference of opinion exists as to the utility or effect of this stop.

[ J. S. ]

TIERCE DE PICARDIE. In Polyphonic Music, it is essential that every Composition should end with a Major Third, even though the Third of the Mode in which it is written should be Minor. The Third, thus made Major by an Accidental Sharp or Natural, is called the 'Tierce de Picardie.' It is not very easy to arrive at the origin of the term; though it may perhaps be accounted for by the proximity of Picardy to Flanders, in which country the characteristic Interval was in common use, at a very early period. Rousseau's explanation of the term (Dictionnaire, 'Tierce') is a very strange one, viz. that it was given 'in joke, because the use of the interval on a final chord is an old one in church music, and therefore frequent in Picardy, where there is music in many cathedrals and other churches'!

[ W. S. R. ]

TIERSCH, Otto, born Sept. 1, 1838, at Kalbsrieth in Thuringia, received instruction from Töpfer of Weimar, Billermann, Marx, and Erk; was then teacher in Stern's Conservatorium, and is now teacher of singing to the city of Berlin. His writings are practical, and concern themselves much with an endeavour to make the modern discoveries of Helmholtz and others, in acoustics, available in teaching singing. The principal are as follows, 'System und Method der Harmonielehre' (1868); 'Elementarbuch der musikalischen Harmonie und Modulationslehre' (1874); 'Kurzes praktisches generalbass Harmonielehre' (1876); the same for Counterpoint and Imitation (1879). The article on 'Harmonielehre' in Mendel's Lexicon is by him.

[ G. ]