EIGHTH. 



in dia- 



Eighth. 56703153: in the new notation of Farey, it is 565S 

 v ' +llf+49m (see Plate XXX. of Vol. II.); it is 

 equal in concordant elements to 3-4ths III ; in c 

 tonic elements to 2 T + 2 t+3 S; = 1 1/+2~ + <2( 

 = 78 + 28 + 2^. Some others of its relations are, 

 8th = 2nd + 7th, = 4th + 5th, = VIII 1, = 9th 

 II, = llth IV, = 12th V, = 14th VII, 

 =VIII S, = 49C + 26 2 + 11 f, &c. By tuning 

 upwards from C, three perfect minor fourths, and down- 

 wards therefrom a perfect major third, this interval is 

 correctly produced on Mr Liston's organ, and is his 



EIGHTH Comma-deficient Major, (VIIT), or grave 

 octave (VIII C), or grave major eighth, has the ra- 

 tio T 8 ^j, = j , = 60l2 + 12f+52m; its common 



log. is .7043650,3623; =.9820781 X VIII; = 

 54.797632 X C ; = 3- 4ths _ 3rd ; = 2 T + 3 t + 2 S, 

 = 12/+28 + 2l2, =52C + 292 + I2f. It is C on 

 Mr Liston's organ, and is tuned above C thus, 4-4tlw 

 + III VIII; it is the lesser inconcinnous eighth of 

 some authors. 



EIGHTH Comma-deficient Minor, (8 1 ), or grave mi- 

 nor eighth, (8 C), the aptome-defective eighth 

 (VIII P), and deficient lesser flat eighth, &c. of 



different writers. Its ratio is |^-|-? = o"iT =5542 + 



1 1 f + 48 m : its common log. is .7274888,3507, = 

 .905266 X VIII, = 50.51151 xC, = 5-4ths 2-I1I 

 2-3ds, =T + 3t + 3S, =ll/+26+ 192=48 c + 

 262 + 11 f; it is C \) of Liston's scale, and may be 

 tuned above C, either by 7-4th 2 VIII, or 5-4th 

 2V. 



EIGHTH Comma-redundant Major, (VIII'), acute 

 eighth, or redundant eighth of some authors, has the 



2' x5 

 ratio ?, = * , = 623 2 + 12 f + 54 m : its com- 



9 



mon log. i* 

 56.797632 > 



.8642902, = 48.22538 X c, =3d + 3-4th 2 III, 

 =2T+t 4S, = 10/+26 + 19S, =46c+23s 

 + 10f, =7+: it may be tuned thus, 6th+2-4th 

 2 III, on Mr Liston's organ. 



EIGHTH Double-deficient, (VIII 2 c), is an inter- 

 s' 



val whose ratio is T VAV> = 7^ ?r> = 5 90 2 + 12 



2 y x 5 



f+51m; its common log. is .7097600,6812, =.9641566 

 XVIII, = 53.79764 xc, =5-4ths III 3-3ds, = 

 T-4t + 2S, = l'>/+27 +202, =51c + 5d92 + 

 12 f, = 3 T + 2t + 2 L ; on an organ with a suffi- 

 cient number of pipes, like Mr Liston's, it may be 

 tuned thus, 5-4ths V i!-3ds. 



EIGHTH Double Superfluous, ( VIII + 2c,) is an inter- 

 val whose ratio is f?, = ~ ,=63424-12f+55m; 



its common log. is .6881799,4057, =1.035843 x VIII, 

 =57.79764 xC,=5-3d + 3 III. 3-4th,=5T + 2S,= 12 

 /+31C4- 242, =55c+292 + 12f, =",T + -it + 2S ; on 

 Mr Liston's organ it may be tuned thus 3V th +2-3d 

 3-4th. 



EIGHTH Minor Comma Defective, (VIII ) or the 

 double tritone (2 IV,) is an interval whose ratio is 



, =602Z + 12f+52m ; its common log. 



Eigbth 



II 

 Einzellee. 



is .70387 9,2909,=.9837067 X VIII, =54.888 5-8 x c,= 

 2-3d + 4 III 2-4th, =4T + 'A, = lj ' / + 2C+22m, 

 = 52c+302+12f,=I + VII, =XI 5th,=XIV 8. 

 It is Mr Liston's acute redundant seventh, or note B'$, 

 and is tuned thus above c, +V + 2III 2V 1 1 1. 



EIGHTH Siipc'ftunus, (VIIl+d,) is an interval whose 

 2'x3 



f + 56m; its com- 



.6935749,7845; = 1.079219 X VIII, = 

 C, = VIII +C, = 3-3ds + 2 III 4th, 

 = 4 T + t + 2 S ; = 12 / + 30 + 23 Z, = 54 C 

 + 29 2 + 12 f, = 7th + T. It is C' on Mr Liston's 

 organ, and may be tuned above C thus, 2 V + 3d 

 4th : it is the greater inconcinnous eighth of some au- 

 thors. 



EIGHTH Defective of Holden, i* an interval not be- 

 longing to the diatonic system, because involving the 



2 1 

 prime integer 7 ; its ratio being ^, or 



3 ' 



598.0607662 + 11 f + 51 m: its common 

 .7058094,2887. 



EIGHTH Diminiithrd-majnr, (VIII 

 some writers the Greater Flat Eighth, the Comma-re- 

 dundant Minor Eighth, (8 + C), the Imperfect Diapa- 

 son, and by Liston the Acute Minor Eighth, (8'), &c. 



is an interval whose ratio is 44, = _, 1=5762 



ratio is Jf, = , , =648 







mon logarithm is .6812412,3738, =1.0.58894 xVIII, 

 = !M>8.77 XC, =2HI+4th, =3T + 3t + S, =13 / 

 +30 + 232, =56c+322 + 13f, =VU+T, =VtI + 

 II,=9th E, =IX S. On Mr Liston's organ it is 

 c'Sfc, and may be tuned thus, VI + 11 1. 



EIGHTH Superfluous of Bo^et^riedfr, (VIII + P,) 

 aptome-excessive eighth, or the superfluous diapason of 



io 



some writers. Its ratio is 



'X7- 

 log is 



~ 2* x 3' 



+ 11 f+ .50m: its common log. is .7166987,7130; 

 = .941 1061 X VIII, =52.51151 X c, = 2-3ds + 4th, 

 = 3 T + t + 3 S, = 11 / + : 28 + 21 m, = 30 c + 

 262 + 11 f; = 3d +6th, = 10th III, =13th VI, 

 = Vll4- On Mr Liston's organ C'p is this interval 

 above C, and may be tuned thus 6th f 3rd ; it is also 

 the greater seventh, and the semidiapason of Holden. 

 EIGHTH Diminished of Liston ( 8 J ), or diminished 



minor eighth, has a ratio |JJ, = 3 X ~, =5292 + 



z' 



10f+46m: its common log. is .7398225,7015, =s 



= - - ; its common log. 



is . (170451 1,7361,= 670 z + 13 f + 58m, = 1.094734 

 xVHI,=6l.08377xC=4-3ds, + 4 II 3-4th,=5T + 

 t + S,= 13/+32 + '252, =58c + 32 2 + 13f, =Vll + 

 T, = IX L. It is c'$ on Mr Liston's organ, and 

 may be tuned thereon thus, 4V 3- 1th. 



EIGHTH (supposed) of Mersennus. This author, 

 from an erroneous calculation, concluded the octave to 

 be equal to 584 major commas ; but which is :=(i,'!'>.y 

 called by 796 1 :i5 + 1 2 f + 55m, exceeding the major eighth by 

 more than a quarter of a tone major : its common loga- 

 rithm is .6h5730: ! ,02.0. (>) 



EIGHTEENTH MAJOR, in music (XVIII,) or the 

 tripled fourth major, (2 VI 11 + IV,) of Holden and 

 some other writers on the practice of music ; is a dis- 



I 

 cordant interval, whose ratio is T 8 r , =- --, = 15252 + 



3 X J 

 30 f + 132m, and its common log. is =.2498774,7322. 



EIGHTEENTH Minor, (18th,; the disdiapason-ch;ites- 

 saron, or tripled fourth minor, (2VIII+4 th ), of Holden, 



&c. is a concord whose ratio is T ' y , = , = 1478 2 + 29f+ 



128m, and its common log is .2780012,7206. ({) 

 EIMEO, or IMAO. See SOCIETY ISLANDS. 

 KINZELLEE. See CASPIAN SKA, VoL,V. p. .195, 



col. 2. 



1 



