FAREY’S NOTATION. ats 
ble us to find the expression for any interval whose ra Farey’s 
= tm 
less 5 22 tio is given. We can, on the present occasion, only N' 
161 3 14 find room, for the first 25 numbers of Mr Farey’s Tae pa ft 
hos 2° 9 ble of this kind, viz. py 
93 2 8 ' — ; 
a7 1 5 New Notation | 
11 0 1 Nos. | 
46 1 4 = f m 
58 1 5 
44 0 4 2} 612.00000 | 12 | . 53 
210 3} 970. 19 | 84 
— 4) 1224, 24 | 106 
010 5 1421. 28 123 
» Ba A » | gazseooorr |. 34° | 199 
remaining in- 7 34 1 
; 1718.05290: 84 149 
lien poy 8 | 1836, 36 | 159 
310 9} 1940. - 38 168 
roo 10| 2088. 40 | 176 
5 10 11 | 2117.10204 | 42 | 188 
12 pa 45 an 
; 3073 | 44°] 1 
After several lundred intervals, 13 | }.2264.58107 | 45 | 196 
ap te 6 been collected 14 46 | 202 
; -other sources, 15| 2391. 47 | 207 
eteaiingsnbon 16} 2448. 48 212 
was observed, that all but a 17 2501.53067 49 216 
a regular series, in which each of the three 2501,53181 49 217 
formed a ‘tnoreasing | 18 | 2552. | 50 | 221" 
“that, 1, 2, 3,4, &e. first appeared with Z, 23, 80, 12 19 | 2599.72902} 61. | 225 
174, 231, “tener or a 20 | 2646. $2 229 
respectively ; and m, 1, 268806077 | 53 | 232 
Sialed with, & 19; 34,44, 21 |} 2688.20257' | 52 | 233 
123, 149, 159, 170, 185, | §2729.25171 |. 53°} 236 
258, 268, 274, 289, 300, 310, 22 | J e729.24884 | 33 | 287 
378, 298, 404, 414, 425, 440, 497 23 | 276846027 | 54 | 240 
508, 518, 529, 544, 554, 565, 576, ; 622, 24] 2806. 55 | 243 
633, 648, 658, 669, &c. respectively. i »251 2842, | 66 | 246 
Jr ni pe — eas 
sometimes 5, commencing = m; 4 = f 
intervals of the beginnings of the ee From this Table the. primes 7,11, 13, 17, 19, &c. 
commencing with 8 © 4 m’s, by and their multiples, are not excluded, because intervals 
tal aden ray ren ‘conatrac involving these do sometimes to be calculated : 
of the above 71 the reason why two values are to 7,.and to some 
‘wiaisiaast cenit OiietSon want of soon. others of the primes differing. by m.or f, is, in order 
‘All such i in Mr Farey’s general Table, asdo that a regular interval may be made betweenevery ad« 
not conform to the above, with to the number of Saget BUDE edad Ae, A simple subtraction 
t's and ofm’s that they contain with their 2’s, have been Will give the value, whenever the terms of the ratio are 
denominated irregular intervals, such as d, F, r, x, $e, in the first column ; and when this is not the 
Feed eek By mene: of wih ought to have either or case, the ee ROE SE SP AN a De waips - 
, but consist 's only, to constitute them corresponding notations of eachadded % 
aa Pp and and fto then the sums are to be subtracted ; thus if the value 
“have anand only two m’s, &c. and these changes may ote evans tails were wanted, we have its ratio 
fiom byhdeake 2 deciunls, in the schiera celewn, 35 
equivalent to the f’s or m’s, that may be added or taken 970 19) 8% 612 12 58 
away ; reckoning each f as .14966096 =, and each m as 970 19 8 and 1421 28 123 
007862412 ; thus, for example, d in a regular Ta- 
ble, will be .5588795 2,9 = 10.149661 = 4 m, f= 1940 : 38-168: 8033 40 176, the dif. 
31-8582014 © + f m, &c. ? ference of which sums, is, 932 4 2f 4 8m, the value 
is found involved or multiplied in the numerator, or _Since; in the use of this notation, a carrying or bor. 
least term of any musical it is equivalent to de. rowing to strat radia tories to another, never takes 
ting an octave 4 from it; and if, in thedenomina- place, in whole numbers at least, as with columns of 
tor, tothe addition of VIII; so 3 denotes the es 20 ee ee 
that a Table of theintervals [cocdescimecns aspneear eliotn some cases. 
2) to d fy See, expressed in the new notation, wilbenas | The middle column having 12 £’s to the octave, it is 
