HISTORY OF MUSICAL SCALES. 425 



famous Al Farul)i.^ who died 950 A. D.. is tiie short-necked tanhonr 

 of Baodiid, usually having two strings: on this a fret was first placed 

 at one-eighth the length of the string from the upper end, and this 

 space then divided into tive equal parts. As the compass on each string 

 was but little over a whole tone, each step was about a quarter-tone. 

 These ligatures or frets are called •'heathen '' or "pagan," and the tunes 

 played on them '"heathen airs," clearly indicating that there was a 

 scale native to the people whom the ]\lohanmiedan armies had con- 

 quered, a scale utterl}^ different from either that of the lute or the 

 tanhouroi Khorassan, with their resemblances to Greek scales. Three 

 hundred years later, or about 1250 A. D., Safi-ed-din.' a famous musi- 

 cian of Bagdad, wrote for his pupil, the son of the Vizier, a Treatise 

 on Musical Ratios. He based them on string lengths, and in discussing 

 instruments gives a figure of the frets on the neck of the lute, and it is 

 noteworthy that these are equally spaced over a distance of a quarter 

 length of the string. Further, he explains how of the ten frets in this 

 short distance, located b^- various rules, five were fixed by arithmetical 

 bisection or halving of the space between two frets alread}^ fixed; one 

 of these, midway between what we should call D and E, if the open 

 string gives C, was called the "Persian middle," and was very much 

 in use in his time. Safi-ed-din^ further describes, in two connections, 

 a division of the Fourth, like the Greek one already quoted, where the 

 string lengths are 12, 11, 10, 9, saying it is consonant and much used; 

 in fact it is preferred to one that is substantialh' like the theoretical 

 diatonic scale; still it should be added that when he comes to arrange 

 intervals to make up tw^o octaves he puts our arrangement along with 

 the most agreeable half dozen genera. 



4. In India there has been in modern times a curious reversion from 

 an elaborate historical scale of twenty-two steps to the octave, of which 

 no modern Hindu or European knows the theor}', to an equal linear 

 division;* one-half of the string on the sitar is bisected; the first or 

 end quarter-length is then divided into nine parts, each marked 1)y a 

 fret, and the second quarter-length into thirteen parts similarly 

 marked. Out of the twenty-three tones within the octave the player 

 selects a limited number, five, six, or seven, rarely eight, for any par- 

 ticular tune. Most of the notes used are found on calculation to be 

 deceptively close to the notes of our chromatic scale, and so may be 

 easily confounded with them })v European hearers. 



5. This arithmetical division has been advocated b}^ European 



' Land's translation in Travaux de la 6'' session du Congres internationale des Orien- 

 Talistes u Leide, 1883, pp. 107-114. 



'^Carra de Vaux'.s translation in Journal Asiatique, XVIII, 1891, p. 330. 



='Idem, pp. 308-317. 



*Tagore, Musical Scales of the Hindu^^, Calcutta, 1884, supplement. Partly quoted 

 by C. R. Day, IMusic ... of Southern India, 1891, and Ellis, Journal Society of Arts, 

 XXXIII, 1885, 1). .102. 



NAT MUS 1900- 30 



