D I A 



729 



D I A 



Diarbekr which the Pacha and his officers reside. The river 

 II Tigris, which in spring rises to a great height, is cross- 



Diaschisma. e( j D y a bridge- of twelve arches, situated about half a 

 """"V""" mile below the town. Mr Kinneir describes Diarbekr 

 as having a grand appearance when viewed from a dis- 

 tance. " The elevation of the surrounding mountains," 

 says he, " the windings of the Tigris, and height of the 

 walls and towers, with the cupolas of the mosques, give 

 it an air of grandeur, far above that of any other city 

 which I have visited in this quarter of the world." The 

 inhabitants manufacture cotton, silk, copper, and iron, 

 and export it to Bagdad and Constantinople ; but they 

 are principally employed in dressing, tanning, and dye- 

 ing goat skins, commonly called Turkey leather. Great 

 numbers of pilgrims frequent this city, and at some dis- 

 tance from the town there is a large village with a ca- 

 ravansera, where the caravans that go to or from Persia, 

 find a cheaper accommodation than in the caravanseras 

 within the town. 



Diarbekr is said to have been founded by Taimuras. 

 The Emperor Constans strengthened it with fortifica- 

 tions, and it was then regarded as the strongest place 

 in Mesopotamia. In A. D. 359, however, it was taken 

 by Sapor D'Ulaktaf, and in 505 by Cobades his de- 

 scendant. The Arabs, the Silguckians, and the Atta- 

 beks, had it successively in their possession. It was 

 pillaged in 1393 by Timour, became an independent 

 state under the princes of the Black Ram, and was at 

 last taken by Selim the First, from Shah Ismael Sefi. 



The population of Diarbekr is reckoned at30,000 souls, 

 the greater part of whom are Turks, and the rest Ar- 

 menians, Curds, Jacobites, and Catholics. The men are 

 affable and courteous, and the women enjoy a great de- 

 gree of liberty, and live in terms of intimacy with the 

 Christian women. Distance from Merdin 60 miles; 

 from Orfa 287 ; and from Malatea 172|. The position 

 of this city as ascertained by Mr Simon, is in East Long. 

 39° 52', and North Lat. 37° 55' 30". See Macdonald 

 Kinneir's Geographical Memoir of the Persian Empire, 

 p. 332—335. (*■) 



DIARRHOEA. See Medicine. 



DIASCHISMA, in Music, (£) an interval so named 

 by Pythorus, the remainder when a limma is taken 

 from an apotome. By some it is called the ancient 

 eomma, and the comma syntonum. It was the comma 

 maximum of Boethius ; the comma ditonicum of Koll- 

 man, and his major comma; the quint wolf of Earl 

 Stanhope. It has also been called the tonemajor wolf, 

 and is the least sum of the quint temperaments and 

 wolves in a douzeave. 



m ..,,.,. . 524,288 



The ratio of the diaschisma is -— -— : 



531,441 



2 ij> 



the compo- 



nent primes of which are — ; its common logarithm is 



.9941148,6098, and its reciprocal .0058851,3902; in 

 the Binary logarithms of Euler, or decimals of the oc- 

 tave, it is =.019550; in major comma logarithms, 

 1.0908429 ; in schismas, 12.007862405; in Farey's No- 

 tation, which we have chosen as a common scale or 

 measure of intervals, it is = 122 + m. In tunable in- 

 tervals, it is 5 V — 7 4ths, and may be correctly obtained 

 on an organ, by tuning upwards five perfect major 

 fifths, and downwards seven perfect minor fourths, 

 either successively or alternately, as is most convenient, 

 when the last sound will stand in relation to the first, 

 as diaschisma. None of the 59 notes on Mr Liston's 

 enharmonic organ are thus related to each other, al- 

 though 13 intervals between adjacent notes thereon, 

 VOL. VII. part II. 



differ from it only one schisma, and 26 others only two Piasehieriia. 

 schismas, respectively. See Philosophical Magazine, S """Y~"""' 

 vol. xxxix. p. 419- 



The following equations, in terms of the several in- 

 tervals, in Plate XXX. Vol. II. exhibit the relation of 

 the diaschisma to each of the 30 intervals less than the 

 least concord, respectively, and to several of the con- 

 chords, viz. 



A = 2 + c 



= 22 -f€ 



= 122 + m 



<i = P— L d=3c — 



£ 



<i= 5T — 2 4ths 



= 3- y, = 4C 



/ 



= 6T - VIII 



b D — r = T — 



2L 



= 5V _7 4ths 



= 2 — D - f— 



2€ 



= 12V — 7VIII 



= 2P— T = 2£ — 



3€ 



= 12 4ths— 5VIH 



= 2c — € =3/-r 



4£ 





<*= 2 + /c + R 



d = 



: 62 + f+ R 



= 22 + J€+R 





:112 + f-f-Fj 



= 32 + ^ + R 





:112 + Sf + d 



= 42 + r -f- R 







d = 12d + 36f —11m 



d= 57 + C D 



— € + r — f 





= / + 2- D 



B <p -f- 2S — f 





= S + 2 — it 



= c + x — r 





= / + 2Z— * 



b w + 2 — i€ 





= /+ 2- £ 



= D + 22 — i€ 





= rf + 2— / 



= 5T + 22 — /c 





= 2£ +22— f 



= D + 32 — /c 





— p + § —26 



= *■ + r — R 





= :/+; §- l 



= D + *— R 





= S + 2— L 



— e, + 2 — -e 





= S + 2— S 



= 2m + 222 — € 





= § + 2c — S 



= 2m + 232 — c 





— J + 3c — S 



= 4£ + 52— 7c 





— T + 2 — t 



= £ + /c— D 





= T + 2— T 

 = 2P + c — T 



<J=2€— m— 82 d= S- 



-<p- 



-42 d= T— 2/— 2£ 



= D— f— 22 = S— 



• r — 



-2c =2T— 2t— € 



= ,r_ r — 2 =2S— 



■ r — 



- P =3T— 2"t— 2S 



= „._f_32 = L— 



■ r — 



- / =3T— 3t— £ 



- £ — C— 2 = S— 



■/- 



- € =4T— 4t— / 



= £_ m _9s = S — S — 



■2€ = T— 2L— c 



= £-R— * 







= / — c — r 







— ct be any small fraction of the diaschisma, or pow- 



t 



er of its numeral ratio, 

 1055729 XM— -7 153X* 



whose index is — ; then will 

 u 



be equal to its numeral ratio 

 1055729 xu +7153X2 

 extremely near. 



, t , , , • 2104305 



If, for example, - = \, the theorem gives us , 



as the approximate ratio of the half diaschisma or schis- 

 ma of Galileo and Glareanus ; and its logarithm will 

 be found to differ only 1 in the eighth place of decimals 

 from the true log of ^d\ This interval is=5.996068s 

 +m, or 6 + 2^m, and is=2|T — 4th. (5) 



DIASCHISMA of Boethius, is an interval, descri- 

 bed as the half the limma, or |L, which has by some 

 writers also been called the Half Diesis, or Minor Se- 

 mitone. Its approximate ratio is 44tt> fotmd by a ge- 

 neral theorem ) XT + T J"~; T ^"~ XT ?, , wherein N and D 

 (N + D)m + (D — sS)t 



denotes the numerator and denominator of a small frac- 

 4 z 



