268 



NOTCH NOTES. 



number became increased tenfold ; 1000 was also 

 expressed by C[3, as well as by M ; and for every 

 CD added, one at each end, the number was increased 

 tenfold. A horizontal line drawn over any figure, 

 increases it a thousand fold. 



Notation of the Greeks. These people had three 

 distinct notations, the most simple of which was, the 

 making the letters of their alphabet the representa- 

 tives of numbers : , I ; 0, 2 ; y, 3 ; and so on. 

 Another method was by means of six capital letters, 

 thus, I (<, for put), 1 ; n (<rivr), 5; A (Sw), 10; H 

 (iT), 100; X CtfX/a), 1000 ; M (pv ? ixs), 10,000; 

 and when the letter n enclosed any of these, except 

 I, it indicated the enclosed letter to be five times its 

 proper value, as stated above ; thus 



~~| represented 50 ; jifi 500 ; Mf] 5000 ; 



and so on. This notation was only used to represent 

 dates and similar cases : for arithmetical purposes 

 they had a more organized system, in which thirty-six 

 characters were employed; and by these any number, 

 not exceeding 100,000,000, might be expressed, 

 though, in the first instance, it appears that 10,000, 

 or a myriad, was the extent of their arithmetic. 



Our digits, . . 1, 2, 3, 4, 5, 6, 7, 8, 9, 



they expressed by . , /3, y, 3, t, <rr, , , 6. 



For our tens, as, . 10,20,30,10,50,60,70,80,90, 



they employed . /, *, A, p, v, g, /,''; 



for hundreds . . j , <r, r, t>, <p, %, *!/, a, 2) ; 



for thousands . . , /5, y, 5, , <r<r, , , 0, 

 i i i i i i iii 



that is, they had recourse again to the characters of 

 the simple units, which were distinguished by a small 

 iota or dash placed below them ; and, with these cha- 

 racters, a number under 10,000 was readily express- 

 ed; and this, as we have observed above, was for 

 some time the limit of their arithmetic. Afterwards 

 10,000, or a myriad, was represented by M, and any 

 number of myriads by M placed under the number of 

 them. Thus, 



a /} y 



M. M. M. 



represented 10,000 20,000 30,000, &c. 



The Notation of the Hebrews resembled, in a great 

 measure, that of the Greeks above described, only 

 substituting Hebrew letters for Greek, as far as thou- 

 sands ; and, for representing thousands, they had 

 again recourse to their simple units, distinguishing 

 them only by two dots, or acute accents ; thus, M , or 

 x, expressed 1000 ; s, 2000 ; V, 10,000; and so on. 

 For the Egyptian system of notation, see Hierogly- 

 phics. See also Symbols. 



NOTCH. See White Mountains. 



NOTE, BANK. See article Bank. 



NOTE, PROMISSORY. See Bill of Exchange. 



NOTES, in music ; the signs for tones (notee mu- 

 sic&). Even in the most remote antiquity, certain 

 letters of the alphabet were used as signs for musical 

 tones. According to some, the Hebrews made use 

 of accents for this purpose, as the modern Greeks still 

 do. The Greeks used different signs for vocal anc 

 instrumental music ; and, as they had not yet con- 

 ceived the idea of using the octave to express, by 

 means of a prefixed key, a number of the most diver- 

 sified tones in a similar manner, they must have re- 

 quired a great number of notes (said to have amountec 

 to 990 ; half for vocal tones, half for instruments) 

 As they used the alphabetical signs for notes, it be- 

 came necessary to employ the same letter in differen 

 positions, (inclining, inverted, &c.); thus r signified, in 

 different positions, seven different tones.. Accents also 

 were used, partly by themselves, partly added to letters 

 If a poem was to be sung, the letters which signifie 



he instrumental tone were placed first ; under these 

 he letters for the voice ; and under these the words. 

 As the syllables of the Greek language have mostly 

 i natural and distinct quantity (i. e. duration of time), 

 he Greek notes were not required to show the time, 

 and generally could be restricted to height, depth, and 

 nature of tone. In the case of the syllables called 

 common (short and long), there was a liability to mis- 

 take, and they were therefore marked with A if long, 

 and with B if short. The fifteen chief tones of the 

 reek system (extending from our A to a ; see the 

 article A) were first reduced to seven by pope Gre- 

 jory I., towards the end of the sixth century, and 

 marked with the seven first letters of the Roman 

 alphabet ; so that the capitals were used for the first 

 voice, the small letters for the higher octave, and the 

 double letters for the highest octave. Parallel lines 

 were soon invented, on which the letters were written. 

 These were used until the happy idea was conceived 

 of substituting for letters points with five lines, the 

 joints and rhombuses being placed as well between 

 ;he lines as on them. This invention is generally 

 ascribed to Guido of Arezzo. According to some, it 

 was known even in the tenth century. The letters 

 which had been formerly used as notes now became 

 clefs. Still the sign for the duration of a note was 

 wanting. The way of marking it was invented, 

 according to some, by a German of Cologne, of the 

 name of Franco, who lived towards the end of the 

 eleventh century. Others ascribe the invention, or, 

 at least, the improvement, to John de Murs (Jean de 

 Moeurs, or Meurs). The diminutio, or division of 

 one note into others of less value (for instance, the 

 division of a fourth into two eighths), and the use of 

 running notes, was invented first by Jean Mouton, 

 chapel-master to king Francis I., in the sixteenth 

 century. Since Rousseau, the designating of notes 

 by ciphers has been repeatedly proposed, and adopted 

 with great success in elementary schools; but, in 

 other respects, the old way of writing notes one of 

 the most ingenious contrivances ever produced, which 

 seems to have given to Leibnitz even the idea of a 

 pasigraphy (q. v.) or system of universal writing 

 has kept its ground. As to printing notes, two 

 periods are distinguished^the first when notes were 

 printed by plates, the second by movable types. 

 The first plates used for this purpose were of wood, 

 and the oldest known are of 1473. Books are known 

 of the time when this way of printing was not yet 

 quite perfected, in which notes were drawn by the 

 pen. Then the printing of notes by copper-plates was 

 invented. The cheaper way or printing from tin 

 plates, in which the notes are punched with steel 

 punches, did not become common till the middle of 

 the last century. As to the second period, the in- 

 ventor is uncertain. Some consider Ottavio Petrucci, 

 in the beginning of the sixteenth century, as such. 

 James Sanlecque (born at Chaulne, in Picardy, 

 1573), a celebrated type-founder at Paris, where he 

 died 1648, probably introduced the printing of notes 

 from types into France. Yet the art of printing with 

 them remained very imperfect, until the well-known 

 typographer Breitkopf, at Leipsic, carried the pro- 

 cess, in 1755, to such perfection, that he may fairly 

 be called the second inventor. Tauchnitz, of Leipsic, 

 first stereotyped notes. The process of lithography 

 is used at present. Great musicians can sometimes 

 compose with the pen in their hand, and without the 

 aid of the piano. They hear all the music in their 

 soul, as a picture stands, with all its hues and pro- 

 portions, before the mental eye of an artist, before he 

 touches the canvass. Many persons, however, who 

 play well extempore, are by no means able to com- 

 pose on paper ; and for them a machine would be 

 convenient, which could accompany the player's 



