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A pictorial method of representing sounds to the ear through the medium of the eye. It is probable that the earliest attempts at notation were made by the Hindus and Chinese, from whom the legacy was transferred to Greece. The exact nature of the Greek notation is a subject of dispute, different explanations assigning 1680, 1620, 990, or 138 signals to their alphabetical method of delineation. To Boethius we owe the certainty that the Greek notation was not adopted by the Latins, although it is not certain whether he was the first to apply the fifteen letters of the Roman alphabet to the scale of sounds included within the two octaves, or whether he was only the first to make record of that application. The reduction of the scale to the octave is ascribed to St Gregory, as also the naming of the seven notes, but it is not safe to assume that such an ascription is accurate or final. Indications of a scheme of notation based, not on the alphabet, but on the use of dashes, hooks, curves, dots and strokes are found to exist as early as the 6th century, while specimens in illustration of this different method do not appear until the 8th. The origin of these signs, known as neumes (veuµaTa, or nods), is the full stop (punctus ), the comma (virga ), and the mound or undulating line (clivus ), the first indicating a short sound, the second a long sound, and the third a group of two notes. The musical intervals were suggested by the distance of these signals from the words of the text. The variety of neumes employed at different times, and the fluctuations due to handwriting, have made them extremely difficult to decipher. In the 10th century a marked advance is shown by the use of a red line traced horizontally above the text to give the singer a fixed note (F = fa), thus helping him to approximate the intervals. To this was added a second line in yellow (for C=ut), and finally a staff arose from the further addition of two black lines over these. The difficulty of the subject is complicated for the student by the fact that an incredible variety of notations coexisted at one period, all more or less representing attempts in the direction of the modern system. A variety of experiments resulted in the assignment of the four-lined staff to sacred music and of the five-lined staff to secular music. The yellow and red colours were replaced by the use of the letters F and C (fa and ut) on the lines. This use of letters to indicate clef is forestalled in a manuscript of Guido of Arezzo's Micrologus, dating from the 12th century, in which is the famous hymn to St John, printed with neumes on a staff of three lines (see Guido Of Arezzo). The use of letters for indicating clefs has survived to the present day, our clef signatures being modified forms of the letters C, F and G, which have passed through a multitude of shapes. Before the 12th century there is no trace of a measured notation (i.e. of a numerical time division separating the component parts of a piece of music). It is at the time of Franco of Cologne 2 that measured music takes its rise, together with the black notation in place of neumes, which disappeared altogether by the end of the 14th century. Writing four hundred years after St Gregory, Cottonius complains bitterly of the defects in the system of neumes: "The same marks which Master Trudo sang as thirds, were sung as fourths by Master Albinus; while Master Salomo asserts that fifths are the notes meant, so at last there were as many methods of singing as teachers of the art." Possibly the reckless multiplication of lines in the staff may have contributed to the obscurity of which Cottonius complains. In the black notation, which led to the modern system, the square note with a tail ( 1 ) is the long sound; the square note 2 The principles of Franco are found in the treatises of Walter Odington, a monk of Evesham who became archbishop of Canterbury in 1228.

without a tail (u) is the breve; and the lozenge shape 0) is the semibreve. In a later development there were added the double n and the minum (i). The breve, according to Franco of Cologne, was the unit of measure. The development of a fixed time division was further continued by Philippe de Vitry. It has been noted with well-founded astonishment that at this time the double time (i.e. two to the bar) was unknown, in spite of this being the time used in marching and also illustrated in the process of breathing. Triple time (i.e. three to the bar) was regarded as the most perfect because it was indivisible. It was as if there lay some mysterious enchantment in a number that could not be divided into equal portions without the fraction. "Triple time," says Jean de Muris, "is called perfect, according to Franco, a man of much skill in his art, because it hath its name from the Blessed Trinity which is pure and true perfection." Vitry championed the rights of imperfect time and invented signs to distinguish the two. The perfect circle 0 represented the perfect or triple time; the half circle C the imperfect or double-time. This C has survived in modern notation to indicate four-time, which is twice double-time; when crossed it means double-time. The method of dividing into perfect and imperfect was described as prolation. The addition of a point to the circle or semi-circle (0. c) indicated major prolation; its absence, minor prolation. The substitution of white for black notation began with the first year of the 14th century and was fully established in the 15th century.

It has already been shown how the earlier form of alphabetical notation was gradually superseded by one based on the attempt to represent the relative height and depth of sounds pictorially. The alphabetical nomenclature, however, became inextricably associated with the pictorial system. The two conceptions reinforced each other; and from the hexachordal scale, endowed with the solmization of ut, re, mi, fa, sol, la - which was a device for identifying notes by their names when talked of, rather than by their positions when seen on a page of music - arose the use of what are now known as accidentals. Of these it may here be said that the flat originated from the necessity of sinking the B of the scale in order to form a hexachord on the note F in such a way as to cause the semitone to fall in the right place - which in the case of all hexachords was between the third and fourth notes. This softened B was written in a rounded form thus: b ( rotundum ), while the original B remained square thus: h (quadrum). The original conception of the sharp was to cross or lattice the square B, by which it was shown that it was neither to be softened nor to remain unchanged. The flat, which originated in the Toth century, appears to have been of far earlier date than the sharp, the invention of which has been ascribed to Josquin Des Pres (1450-1521). The B-sharp was called B cancellatum, the cross being formed thus. The use of key signatures constructed out of these signs of sharp and flat was of comparatively late introduction. The key signature states at the beginning of a piece of music the sharps and flats which it contains within the scale in which it is written. It is a device to avoid repeating the sign of sharp and flat with every fresh occasion of their occurring. The exact distinction between what were accidental sharps or flats, and what were sharps or flats in the key, was still undetermined in the time of Handel, who wrote the Suite in E containing the "Harmonious Blacksmith" with three sharps instead of four. The double bb (sometimes written h or /3 ) and the double sharp x (sometimes written (, 'N or #) are conventions of a much later date; called into existence by the demands ofmodern music, - while the sign of natural (E) is the outcome of the original B quadra= tion or square B b.

The systems known as Tonic Sol Fa and the Galin-ParisCheve methods do not belong to the subject of notation, as they are ingenious mechanical substitutes for the experimentally developed systems analysed above. The basis of these substitutes is the reference of all notes to key relationship and not to pitch.

Authorities.-E. David and M. Lussy, Histoire de la notation musicale (Paris, 1882)

H. Riemann, Notenschrift and Notendruck (1896); C. F. Abdy Williams, The Story of Notation (1903); Robert Eitner, Bibliographie der musik. Sammelwerke des 16. and 17. Jahrhunderts (Berlin, 1877); Friedrich Chrysander, "Abriss einer Geschichte des Musikdrucks vom 15.-19. Jahrh.," Allgemeine musikalische Zeitung (Leipzig, 1879, Nos. 11-16); W. H. James Weale, A Descriptive Catalogue of Rare Manuscripts and Printed Works, chiefly Liturgical (Historical Music Loan Exhibition, Albert Hall, London, January-October, 1885); (London, 1886); W. Barclay Squire, "Notes on Early Music Printing," in the Zeitschrift bibliographica, p. IX. S. 99-122 (London, 1896); Grove's Diet. of Music.