D I E 



Diesis. . r . t . 



— v— »'' substitutes — and — for the fractions of 2 and m, of the 



T s u 



temperament of the fifth, in any proposed regular sys- 

 tem ; each of such tempered fifths being therefore, V— . 



r t 



— 2— — m. And he finds 



s u 



104s— 2r 9u—2t 

 In cor. 12. T= £-f-2f.f m. 



739 



D J E 



T 46s-|-5r „ 4«4- 



Incor. 11. L= -^ 2 +f +^lX 



* u 



St 



5u—7i 



s 



, 58s— 7r 

 In cor. 10. /= s +f + 



12r— 12s 

 In cov. 9. D= 



S T 2< 



70s— 19r 6m— 19* 



d =~l s+f + -U — m - 



The minor limma or /, expressing the value of aflat 

 and a s/zarp throughout the scale, the greater diesis D, 

 expressing the interval between the sharps and the ad- 

 jacent flats of whole notes, or such as are unusually 

 said to be whole tones asunder, as between C$ and !)[>, 

 D* and Eb, Ft and Gb, G* and A\>, A* and Bb, &c. 

 and the lesser diesis (now for the first time published) 

 ct, expressing the interval between adjacent fiats and 

 sharps of half notes, or where the half notes of the scale 

 fall, as between E>& and F[>, B$ and C\>, Sec. We will 

 endeavour to explain this, by stating, as an example, 

 the notes of a scale of 24 notes, such as Mr David 

 Loeschman's patent organs and piano-fortes are capable 

 of giving in any proposed temperament, from the Phil, 

 Mag. voLxxxix. p. 418, viz. 



D:cis 



Djezan. 



C, C$ Db, CM D, D# Eb, E Fb, E& F, F$ Gb, F%% G, G& Afc A Bbb, A% Bb, Bcb, B&c 

 / D d D / D * D d D I D d D I D I D d D I D d D 



The upper line representing the notes, and the lower 53m will result. Mr Loeschman prefers the mean tone 



one the intervals between every two adjacent ones system for his instruments, wherein every major third is 

 above. 



By counting up the lower ones, it will be seen, that perfect, and — = — and— =— . See Mr Farey's 2nd 

 the octave is in this case made up thus, viz. VIII= * 4 u 4 



7/+ 12D + 5d ; and so it will be found by multiplying Scholium in the volume first above quoted, which nunv 



the formulas above by these numbers respectively, and bers substituted in the formulas above, give 

 adding the products together, viz. that 6l22-|-12f-f- 



, 232 — 77 „ 20—7 



I = 1 2-j-f-l — 4— m, •s.ZQ'Z+i+Qm, the sharp andflat of this syrtem; 



132 — 48 12—4 



D= — J 2 -f — j— m, =212 +2m, the greater Enharmonic Diesis; and 



280—209 ' 24—19 „ 



d = 4 2+f+ — ^— m, = l7| r 24-f-f-l|m ) the lesser Enharmonic Diesis, as have been 



mentioned above. 



On instruments which have only 12 notes hi the oc- 

 tave, {as is the case on all common organs,) or 14, 16, 

 &c. notes, when tuned to this scale, any of the inter- 

 vals required may be found by help of the above Table, 

 and values of I, D, and ct ; thus, if the interval between 

 C and D be sought, it is Z-f-2D-f-d, which will easily 

 be found =98i2-f2f+8im; if between C and E, it is 

 3Z+3D + d, = 1972 + 4f+ 17m, or III, as it should 

 be. 



DIESIS Trientalis of Aristoxenus, in his genus 

 chromatic molle, is stated to be four thirtieths of the 

 minor fourth, (and was supposed to be equal to the 

 third part of a tone, whence the name,) or^- x 4th,= 

 33.8l626s-f.f-f- 3m, or 33|f2+|f-f-244m, and its log. 

 =.9833415,0179- It falls short of -f T, by rather more 

 than f 2, or .200522. 



DIESIS Trientalis of Euclid, is one third of the ma- 

 jor tone or fT, = 2 -1- V9 = 34.61 67792 -f-f-f- 3m, or 

 34f2+|f-f3m, and its log. =.9829491,5919 ; it is = 

 .056641 x VIII,=3.l6047xc. 



DIESIS Triple Enharmonic, (or 3 £) has a ratio 

 1 9*53 125 5 9 



2fi91,\52 > ox W*> = 62 - 858201 s + f + 5f» or 632 + 6m; 

 its common log. .9691000,3008, its Euler's log. = 

 .1026459, its schisma log. =63.047178, and its comma 

 log.=5. 7274715. The following equations will shew 

 some others of its relations to the other intervals, in 

 Plate XXX. Vol. III. viz. 3£=S + R, =3C + 3€, = 

 6€-f-32, = 6c— 32,=2/— 2, =6S— 3t, =3T— 68, =3t 

 — 6S,=P+p— R, = 3 6ths— 6III, =3VIII— 9 III, by 



either of which last it may be tuned by perfect inter- 

 vals. (?) 



DIERVILLA, a genus of plants of the class Pen- 

 tandria, and order Monogynia. See Botany, p. 176. 



DIET. See Aliments. 



DIEU, Isle de. See Vendee La. 



DIEUZE, a town of France, in the department of 

 La Meurthe. It is situated on the river Seille, be- 

 tween Metz and Saverne, and has four convents and 

 two hospitals. It is remarkable for its dyeworks, its 

 manufactories of saltpetre, of hosiery and cotton goods, 

 but particularly for its salt pits, which furnish annually 

 280,000 quintals of salt. The salt springs have existed 

 since the beginning of the 1 1th century, and are the most 

 considerable in Lorraine, both for their strength and 

 copiousness. One hundred pounds of water furnishes 

 16 pounds of salt. The superfluous water is conducted 

 by a canal to the salt- work of Moyenvic. The little 

 river called the Spin, separates the salt works of Dieuze 

 from the town. Population 3344. See Peuchet's 

 Diet. Commercantc. Herbin Statistique de France-, and 

 Reichard's Guide des Voyageurs en Europe, (j) 



DJEZAN Ras, Ghezan, or Gezan, is a seaport town 

 of Arabia, in the principality of Abu Arisch, and the 

 Province of Yemen. It is situated on the Red Sea, 

 which forms one side of a large bay. The town is 

 built with straw and mud, and carries on a considera- 

 ble trade in senna, which grows in the adjacent coun- 

 try, and in coffee, which is brought from the mountains 

 of Haschid-u-Bekil. The trade in coffee, however, 



