, and A =401,344539 ane per 
Earl Stanhope, in the controversy above alluded to, 
has mentioned another of equal-beating 
sounded at the oo 
two tem concords ; his two bi-eq 
Sa testense, Sten Geaeee pb A and c; so adjust- 
ed, that there shall be no beatings between the two beat- 
; that is, that the beatings of Ep A and b Ac shall 
SESE cote oot (as in our first example,) or one 
be exactly some concordant tals as 2, 4, 8, &c. 
ae ag ag 
2’ Bit alt 
ven ~* ee cae Magazine, vol. xxxiii. 
P EQUAL Harmony, has, by one class of musical 
ga tntd Emerson, Mr Cavallo, Mr Chambers, &c. 
to the equalization of the harmony of the 
or systems of eight notes, above every finger- 
the organ or piano-forte, considered as a key- are 
note ; which system is, however, more commonly, and 
ought always to be denominated, the equal temper- 
ament, or Isoronic system, and by another and more 
correct class of writers, as Dr Robert Smith, Dr Robi- 
son, &c. the term equal , has been restricted to 
to attemper the scale so, that all the con- 
cept the unisons and octaves, which are kept 
sap uy may be equally and the most harmonious, within 
a given compass of notes. 
_— Bs his ard Harmonics feteies un- 
deserving censures that have w 
has endeavoured to lay the foundation for’ such 
a system as has ne of the her on his im- 
+ : ° 
3 ors, of the other, in a gi- 
es 
Hd 
tem Seeger er ): 
ve 
product ofthe ems of (each of) the perfect ratios of 
corresponding ect 
of arithmetical gO ahmonieal mean 
nances, parcels, 
Vths, Viths, and I[Ids, and their compliments to, and 
with VilIths, Dr Smith's investigations 
lead to the conclusions, that 
A ee va een 
is Cocunt V, and II 
b (or 
lows, 
» in one octave, must have 
, tempered, (or +,) or 
—,) in parts of major comma, or nearly as fol- 
360° = 360’ 360’ 
or those tempered concords, are V—3,088325, VI+4 
1.74290z, and [1] —}.34542z. 
EQUAL. 
Kn tre cote, ee Pe aera MEE) 
ie pg 
32 
or V—3.095962, vI 7 + 1.719983, end I—1.8766 
In three octaves, these temperaments Iara. 
nearly - 
ae a re 
Ts “is 78? 
or V—3.0577422,V1 + 1.834643, and IT —1.2230992, 
and, 
In four octaves, ee 
pnt eRe RT 
a “4 4’ 
orV—3. ner Ae, Vig Sas cane 
i 
ue 
F 
base respectively ; 
tions, at om the same differs 
a system W ae eager eae and 
the latter X. Farey has shewn in 
yol. xxxvi. p. 51, that the temperaments in 
by ultimate ratios, are 
—2 +1 1 
7? maiko ad 
or V—3.1451042,VI + 1.5725523 anit—t ST25522. 
The Doctor likewise shews, a syssem, (prexi- 
ously proposed by M. Henfling,) wherein 
tone is to the major limma as 8 : kn vee ae: 
vided into 50 equal parts, approaches 
favourite system oa haroon, ating i tempera 
ments (p. 157) at sina 
+25 16 i 
—41 oer) “i 
14s’ “148° 
i 
a 
PEPEEEE 
7 
148’ 
which are equivalent toV—3. 0494752, VI41 1. oe 
and I1I—1,1900383. of 
BE Nog various systems 
vin, orth crane chm geese eit 
ae eee Wit cake cestar oceans 
readily, ater areca ata 
p. $70 of our third volume. () 
EQUAL Temperament, is applied to a of 
ee wherein each concord par, pri te Baa 
alike tempered, and wherein there are twelve semi- 
cme, precisely ; and thence it is called the Iso- 
tonic System; each ‘of which semitones are = 51 = 
Fe Aiam, ny and thet ratio the Hr Ble which 
incommensurate. 
Fa- 
eligi: that a commensurate , seven of 
Thoda tall Gade are peas Se ech 4 f+ ae and 
five of them of the value 51 gran 
of whose fifths are of the value neste sti a 
one of the value 357 24+f+430m, differing 
