Finh. 
FIF 
is also equal to 644—2IIT, or 1I—S HI, by either of 
which it may be tuned. This interval has also been 
called by some the Diminished, and the Extreme Di- 
sninished Fifth, and it is the Minimum Fifth of Hen- 
fi 
ing. 
Extrewe sharp (major) Firtu of Liston (% V): 
the ratio is es =9915 48 4-34'm; its log. is 
.8061799,7398, = .6438566 x VIII, = 35.92564 x ¢; 
=V 45, =54844d, =5425S +6, =6—E, =VI—2, 
=ViIl—3, =X—6, = VIII» 4th, =2T +2t, =2T+ 
t+S4J, =4S42842d9, —34e4+20548f, —8 f+ 
18S€+4142; it is also equal 2VIII—26th =2VI— 
2 4th, = 2V—2 Srds, and =2 III, from any of which, 
but the last in particular, it may be readily tuned. 
This interval has also been called, the Tretratonon by 
Dr Calleot, the Superfluous (major) Fifth, by Tartini, 
Marsh, Chladni, &c. the Sharp Fifth, the Redundant 
(ma ) Fifth of Liston; also, the Double major Third, 
Sixth of Holder, the Diesis Defective minor 
Sixth of Euler, and of the Trumpet scale (.,).. Mr F. 
Webb has lately said, that the ratio of this interval, nearly 
corresponds with that of the diameter of a semicircle to 
its are, taken as = 399348463 = 48 f4-34m: where- 
as the true diesis and are, give 389.55534 54-8 f 
$4 m. 
False Fiera of Chambers and Bemetzrieder ; its ra~ 
tio is 45, =31154-6f427m, See the Minor Firra. 
False Minor Firru, of the common trumpet scale 
(i); its ratio is 15, =320.460258: 46 f +28m, =5th 
+-9.0460258 = 4m: and its com. log. =.8428921,4664. 
Fiat Fiera, of Overend, &c. (pV), has a ratio £3, 
oy f 427m. See Minor Firru. 
Flat Firru of Hussey and Webb, has the ratio 5%, 
=314,947096 = 46f+27m, and its common log. is 
.84509080,4001 : it is also their lesser fifth, and the pois 
fourth of Holder. : 
Greater Firtu of Holder, has the ratio 1$°, =369 
2+7f£+4+32m, See Comma-redundant Major Firrn. 
Imperfect Fivru of Marsh, has the ratio thy oe 
=46f 428m. See Comma-redundant Minor Firtu. 
Isotonic Fiera, or Equal-Temperament Fifth, has the 
ratio 1 *4/2, =357.0072072 = 4-7 f 430m, =357 = 
+7f+4303im, its log. is .8248991,6920, =,,VIII, 
=V—>— 3m, =5 + *,m; and the length of ering 
answering thereto, is .6674199, See Isoronic,. an 
Farey’s Equa, TEMPERAMENT. 
Less, a Lome parse a Hone 5 its Ba ie > = 
47 = +-7f +350m. mma-deficient Major Firrn. 
. Lesser Firru of Hussey and Webb. See their Flat 
IFTH. 
Major Firrn, (V) is a concord, that is very commois 
ly denominated the Perfect Fifth, or simply the Fifth ; 
it has the ratio of ¢, =358 = 4-7 f +-31m; its common 
log. is .8239087,4094, =.5849626 x VIII, =32.639526 
Xc, 359.2913613K =; =54 3,=—1+5, =24 IV, 
=H+44; =6—2, = VII—III, = 9—5, = IX—V 
=11—7, =XI—VII, =12—8: —44-T, =4L+ 3P, 
=oT tl, =2T +t4+S, =4849545, =4$4254 9 
+ 2€,= T +2t4+ L420, =8ic+172 47f, =7/ 
+ 17€+413: it is also =34 I], =VII—4, =10 
—6=X—VI, by which its tune may be checked, and 
adjusted to the greatest nicety. 
interval was anciently called the Pentachord ; 
the D te of Holder, &c. ; the Hypate prima of Hen- 
fling ; the quint of Earl Stanhope ; and on account of 
its great importance in the scale, the upper of its notes, 
322 
FIF ? 
above the key-note, is very talled the Domi- 
se This interval is heard in a very marked manner 
on the trumpet, ora freely sc string, owing to 
its numerous repli $s $ x» xt &c, that are usual- 
ly heard in the octaves : it can be tuned, by the 
more accuracy than the octave or unison, and being, 
(except its compliment the minor fourth, ) the con- 
cordant or t le interval, that being 12 times 
ed, (and returning by octaves as often as is 1 ry,) 
uces as many different notes, that are not gr 
Frc iad each deatans Mad each other, and the last © 
of such notes nearly coinciding with, the octave of 
the first ; on which account, it is the interval almost 
exclusively used in the tuning of instruments. See 
Succession of Fierus, and TEMPERAMENT. ~ 
Major Firtuof Hussey, has the ratio 7 =399.348463 
=+8f+434m, and its common log. =.8037053,5486. 
Mean-tone Firtu, has the ratio 1 + 4/5, = 355. 
2558968E 4-7 f4+ 30m, =35542 +7 f 4302 f; its log. 
is tee ere = V— ie, =} pe 3 this tem- 
pered , four times repeated, peculiar } 
ey of producing an exact replicate of the Major 
ird, and gives the only system that seems adapted 
to the tuning of the common coger M. Loeschman 
likewise uses it, with excellent , in tuning his pa- 
tent enharmonic piano-fortes and organs, with 24 sounds 
in each octave. } 
Minimum Firrs of Henfling; its ratio is $2, = 
2753+45f+4+24m. See Extreme Flat (minor) Firts. 
2 sy 
Minor Firtu (5) has the ratio 44, = = = 311 
6£+427 m; its log is .8470325,3979, =.5081467 x 
VIII, =28.35340x¢; =V—S, =4th4S, =23—c, 
pat My: =V—I, =6—I1, =7—ILI, =8—4,. = VI 
—IV, =9—V, =11—VII, =III4+2S, =T ry + 
28, =484534¥9, =2843584942€, =2704 
6f, eat Be eters A it is =2 4th—III, 
ch it may be tuned. This interval was ancient- 
ly called the Hemidiapente, or Semidiapente ; it is the 
ritonius of Euler, the False Fifth of Chambers and 
Bemetzrieder, the Lesser Diminished Fifth of Chladni, 
the Flat (major) Fifth, and the Extreme Flat (major) 
Fifth of Liston, (pV). ji-L= Se Sp peels 
Minor-Comma excessive Major Firru (V,'); its ra- 
; 3 5 : , on r = 
tio is $234, = ae = 368 © 4 7f+4- 32m, its log. is 
.8190038,1619, =.6012559 x VIII, =33.54839 xe, = 
V+e€, =5+4S, =2+5, =6—I, =8—I1], =9—IV, 
=12—VII, =T +t 438, =32c-46247f, =7/4418 
€4.135 ; it is also =3 4th—2 III, by which it may 
tuned. It is the diminished (minor) sixth of Liston. 
14E4 
by 
Redundant flat Firru (pV’) of some writers, has the: 
fia (oV’) . 
ratio 34, =322z6f428m. See Commu t Mis 
oO Leads (Major) F f Liston (V) ; its rati 
’ nt (Major) Firru of Liston '; its ratio 
is 3 =394z nf al See Extreme sharp (Major) 
IFTH. > 
Redundant Firrn of Holder, has the ratio 33, = 
371.947096> + 7f+ 32m. See Bearing Firtu, 
Schisma defective Major Firru (V.) has the ‘ratio 
ney Bi A 
$993 5) —= a, =3575-47f-4-Slm 5 its Jog, is 8249988, 
4807, =.583334 x VIII, =32.54869 xc; =V—Z, = 
541, =VI--29, =I] +3—2, =2%-4 38, =3le4 165 
+78, =7/ +17€ 4-125, =5 4ths—2V—III, by which 
means this eq r ent Fifth of Farey’s | 
may be tuned. Its length of string is .6674194, and 
a eh ee en 
