i OP 
F IF 821 
toisinda iting teorereast Bits ural ssh 
TE. $2 m, and its common 
ti Major Firma (V), has the ratio i, 
— 52 = 3475 +74 30m, its log. = =.8293037,7283, 
=. 567042 x VIII, = $1.639526 x c; =V—c, = 5— 3, 
£4t, =VI—II, =7—3, =T+2t+S, =2 T+t+L, 
af Hi6e4193;, =2-4ths—Srd ; by which last 
may &e. This Sheetal has 
. Comma-deficient Minor Fiera (5), has the ratio 5 
= Fp =3002 4614.26, its log. =.852,4275,7167, 
= .490228 x VIII, = 27.35340 xe; =5—c, =V—P, 
=VILI—3T, =2t+28, —=2T+ 2L, =2$rds—2c, = 
T4t+s ty sotpely Oc, eebc4 lar 46f = 
Ofte 102; equal also to 4 4ths—2 Vths, by 
w it may be ‘correctly tuned. This interval has 
Trihemitone of some, 23°, 2 (2 re +S+5); 
the Grave Minor FiAK of Liston, fe ¥f 
Comma-redundant Major Firtu (V"), has the ratio= 
= 22 = 9692 47 £-+32 m, its log. =.8185137,0905, 
cease Xx VILL, =33.639526 xc; =V+c, =5+P, 
Teeaties; met jonas wit’ may be 
w 
ned. * ab g fifth of Maceall tad Lis Lis- 
ton, oa Poti fifth « of » &e. 
Comma-redundant Minor Furrn (5°), has the ratio =>, 
=o> 322 54 6f+28m, its log. =.8416375,9790, 
= 526068 x VIII, =29.35340 xc; are, =Vv—4d, 
=10th—VI, ene an 8, Try 12z; it is 
the double minor third third, by whi means it 
. gresterdimininbed fith of Chladni, the imper , &e. 
Comma-redundant 
~<a (or superfluous) Firta 
Gs Rented a = 5 Ree Seem 
ae ant eran akin Gh a ol = 36.92566 x 
VIEL =I+ ,=U+IV, 1x5, 
=21ll +c, =3T+4=5+t+>5, 
=8. 19€+4152; 
ae =i M2 hs, 
ual also to 
idieese tries See: Commadeficient Major 
é 
Defeient Firen of wher writers, has the ratio TOE 
VOL. IX, PART L. 
FIF 
= 3005 4 6f-+426 m. See Comma deficient Minor Fifth. 
Firts. 
» Diaschi. ective Major Firru (V,); its ratio is 
177,447 3" 
262,144 = pre =3462+7f+30m, its common log. 
is .8297938,7996, =.565417 x VIII, =31.548683 xc; 
=V—4, —545—J,—5— —€, 542c—S,=442L, 
=5L42P, =4t—2, =T42t435, =5 T+f+r, 
BIL FIST + U3 =, =380c417 =+-7 f.. This interval 
bearing, or wolf fifth, when 11 
_ in succession, in 7 octaves, or =7 VIIL 
—11V; and 7 4ths—4 V: by either of which it may 
be tuned. 
soniaicied Fare, the greater of Chladni. . Its ra« 
tio is 36° = 322 +6f+4 28. See Comma-redundant 
Minor. Firru. 
Diminished Fivru, the least. Its ratiois “72, =276s, 
+5424 m. See Extreme Flat Minor Firru. 
PP nay 5 gt the lesser of Chladni. Its ratio is 
i =3115+46f4+27m. See Minor Firru. 
67” Khel Major Firrn (), has the 
2187 _ an 
PP ny tT = .549121 x VIII, = 30.63952 xe; = 
+2t+L, =%9e 4 
V—2e,=>54 iti =3t+S, =T 
Ep ean. te slpoageal tn. dein? 
hich means this interval may be tu« 
gti eee Sharp Firre, (XV") ; its 
ratio is $090 ==, =H16248f 436m; its log. is 
-7953899,1021, = .679696 x VIII, = 37.92561x ¢; 
=V4P, =54S+P, =54T+2, =4T, =2 114 
2c, =4P+4L, 36c4205+8F, athe oy chat 
also equal to 8V—4 VIII, vo either of 
which it may be tuned. This interval is also called the 
Double Ditone, the Quadruple Major Tone, and the 
Fifth of Bemetzrieder ; eis also the Schie. 
ma-excessive Minor Sixth, or 6-4-5, (6*). 
Tepe aeons Minty Perks, has a ratio of 5, 
=> =383 3+4+8f+ 33m; its log. is .8115750,0587, 
of =-625935x VII, =34.92566 xc; =5429, =—V+f, 
=V+5—c, =T+St, =33c418E48f, —8 f+ 
17€ 4 132; equal also to III 4 2 —2 rds, by 
which it may ‘be taned. 
Equal-beating Firtus, are ne. as, when tuned in 
succession, beat a eons ; of which there are a 
oe variety. See the article 
Bevar Be now Bn ape where the values of several of them 
given, anda theorem, by which such fifths 
aay bee in any given case. 
Extreme Diminished Firrn has the ratio }1i, = 
275 re Ft Gs See Extreme Flat (minor) Firrn, 
major) Firru of Liston, (pV), has 
ine rato ft = ane 27m. See Minor Firtu. 
Extreme Flat (minor) Firra. of Liston, () 5); has 
the ratio 27%, = 5, =975245f4-24m; its log. 
is pRSn TORI O6TS: = .4492528 x VIII, = 25.06728 
xe; =5—JS, =—V. , =V—25—0, =T+3S, 
Suth+é, eras =5 f+ 14 €+ 105; it 
