M U 
anil philofophy, that they have long defcended from thefe 
heights, and taken their proper and feparate ftations upon 
earth; fo that we no longer admit of mufic that cannot 
be heard, or of philofophy that cannot be underjlood. 
Anilides Quintilian us afiures us, that mufic compre¬ 
hends arithmetic, geometry, phyfi.es, and metaphyfics, 
and teaches every tiring, from ftilfaiifg the Icale, to the 
nature and cbilftruftibn of the foul of man and the foul 
of the univerfe. To confirm this, he quotes,.as a divine 
faying, a moil curious account of the end and bulinefs of 
mufic, from one Panacmns, which informs us, that the pro¬ 
vince of mufic is not only to arrange mufical founds, and 
to regulate the voice, but to unite and harmonize every 
thing in nature. This writer, in folving the queftion, 
Whence it is that the foul is fo eafily. affefted by inftru- 
mental mufic ? acquaints us, in the Pythagorean w'ay, how 
the foul, frilking about, and playing all kinds of tricks 
in the purer regions, of lpace, approaches by degrees to 
our grots atmofphere; gets a tafte for matter and lolidity, 
and at length acquires a warm and comfortable body to 
cover her nakednefs. Here the picks up nerves and arte¬ 
ries ; there membranes; here fpirit or breath ; and all in 
a moil extraordinary manner; efpecially the arteries and 
nerves : for what Ihould they be made of, but the circles 
and lines of the fpheres, in which the foul gets entangled 
in her paflage, like a fly in a fpider’s web! Thus", conti¬ 
nues he, the body becomes fimilar in its texture to in- 
flruments of the wind and ftringed kind. The nerves and 
arteries are firings, and at the fame time they are pipes 
filled with wind. “ What wonder, then,” fays Ariftides 
QUintilianus, “ if the foul, being thus intimately con- 
nefted with a body fimilar in conftruftion to thofe in- 
ilruments, (hould fympathize with their motions.” 
Pythagoras is faid, by the writers of his life, to have 
regarded mufic as fomething celeftial and divine, and to 
have had fuch an opinion of its power over the human 
affections, that, according to the Egyptian fyftem, he or¬ 
dered his difciples to be waked every morning, and lulled 
to deep every night, by fweet founds. He likewife conli- 
dered it as greatly conducive to health, and made ufe of 
it in diforders of the body, as well as in thofe of the 
mind. His biographers and fecretaries even pretend to 
tell us what kind of mufic he applied upon thefe occa- 
fions. Grave and folemn, we may be certain; and vocal, 
fay they, was preferred to inftrumental; and the lyre to 
the flute, not only for its decency and gravity, but be- 
caufe inftruftion could be conveyed to the mind, by 
means of articulation in flinging, at the fame time as the 
ear was delighted with fweet founds. This was faid to 
have been the opinion of Minerva. In very high antiquity, 
mankind gave human wifdom to their gods, and after¬ 
wards took it from them to beftow it on mortals. In peru- 
fing the lift of illuftrious men who have fprung from the 
fchool of Pythagoras, it appears that the love and culti¬ 
vation of mufic was fo much a part of their difeipline, 
that almoft every one of them left a treatife behind him 
upon the fubjeCf. 
Euclid, as a writer on mufic, has ever been held in the 
higheft eftimation by all men of fcience who have treated 
of harmonics, or the philofophy of found. As Pythagoras 
was allowed by the Greeks to have been the firft who 
found out mufical ratios, by the divifion of a monochord, 
or Angle firing, a difeovery which tradition only had 
preferved, Euclid was the firft who wrote upon the fub- 
ject, and reduced thefe diviiions to mathematical demon- 
flration. His Introduction to Harmonics, (Eicraywyvj 
‘Aphonic,],) which in fome MSS. was attributed to Cleonidas, 
is in the Vatican copy given to Pappus. Meibomius, how¬ 
ever, accounts for this, by fuppofing thofe copies to have 
been only two different MS. editions of Euclid’s work, 
which had been revifed, correfted, and reftored from the 
corruptions incident to frequefi t tranfeription, by Cleonidas 
and Pappus, whole names were, on that account, prefixed. 
It firft appeared in print with a Latin verfion, in 1498, at 
Venice, under the title of “ Cleonidse Harmonicum lntro- 
Vol. XVI. No. 111a. 
SIC. ' \ 21)3 
duftorium but who Cleonidas was, neither the editor, 
George Valla, nor any one elfe, pretends to know. It was 
John Pena, a mathematician in the fervice of the king of 
France, who firft publifhed this work at Paris, tinder the 
name of Euclid, in 1557. After this, it went through feveral 
editions with his other works. His Seftion of the Candn, 
Ka.ra.ToiJ.fi Kavofo; follows his Introduction; it went 
through the fame hands and fame editions, and is men¬ 
tioned by Porphyry, in his Commentary on Ptolemy, as 
the work of Euclid. This traft chiefly contains fhort and 
clear definitions of the feveral parts of Greek mufic, in. 
which it is ealy to fee that mere melody was concerned ; 
as he begins by telling us, that the fcience of harmonics 
confiders the nature and ufe of melody, and confifts of 
feven parts : founds, intervals, genera, fyftems, keys, 
mutations, and melopceia; all which have been feverally 
confidered in the diflertation. 
Of all the writings upon ancient mufic, that are come 
down to us, this feems to be the moll con-eft and com- 
preffed: the reft are generally loofe and diffufedj tlie 
authors either twilling and diftorting every thing to a 
favourite fyftem, or filling their books with metaphyfical 
jargon, with Pythagoric dreams, and Platonic fancies, 
wholly foreign to mufic. But Euclid in this little treatife 
is like himfelf, clofe and clear; yet‘fo mathematically 
fhort and dry, that he bellows not a fyllable more upon 
the fubjeft fiian is abfolutely neceffary. His objeft feems 
to have been the comprefting into a fcientific and ele¬ 
mentary abridgment, the more diflufe and lpeculative 
treatifes of Arilloxenus. He was the d’Alembert of 
that author, explaining his principles, and at the fame 
time feeing and demonllrating his errors. The mufical 
writings of Rameau were diffufe, obfeure, and indi- 
gefted ; but d’Alembert, extrafting the efience of his 
cohfufed ideas, methodized his fyftem of a fundamental 
bafs, and compreffed, into the compafs of a pamphlet, the 
fubftance of many volumes. 
According to Dr. Wallis, (Phil. Tranf. No. 242.) 
Euclid was the firft who demonftrated that an oftave is 
fomewhat lefs than Jix whole tones: and this he does in 
the 14th theorem of his Seftion of the Canon. In the 
15th theorem, he demonflrates that a fourth is lefs than 
two tones and a half, and a fifth lefs than three and a 
half: but, though this proves the neceflity of a tempera¬ 
ment upon fixed inftruments, where one found anfwers 
feveral purpofes, yet he gives no rules for one, which 
feems to furnifh a proof that fuch inftruments were at 
leaft not generally known or ufed by the ancients. What 
Arilloxenus called a half-tone, Euclid demonftrated to be a 
fmaller interval, in the proportion of 256 to 243. This 
he denominated a limma, or remnant; becaule, giving to 
the fourth, the extremes of which were cailed foni-ftabiles, 
and were regarded as fixed and unalterable, the exaft 
proportion of 4 to 3, and taking from it two major 
tones fxf, the limma was all that remained to complete 
diateflaron. This divifion of the diatonic genus being 
thus, for the firft time, eftablifhed upon mathematical 
demonftration, continued in favour, fays Dr. Wallis, for 
many ages. But thefe ancient fyftems have been juftly 
laid afide lince the invention of a temperament, as being 
unfit for the execution of mufical compofitions in feveral 
parts. See Smith’s Harmonics, p. 33. 
The firft lyre, with three firings, is faid to have been 
invented in Egypt by Hermes, under Oiiris, between the 
years 1800 and 1500 before Chrift. The fecond arid 
third llring were, perhaps, the oftave and fifth of the 
firft, or more probably its fifth and fourth, as it would 
be eafy to fing the oftave with the accompaniment of the 
primitive note only. The melody might be either always 
in unifoii with one of the firings, refeinbiing a very Am¬ 
ple modern bafs part; or the intervals might occafionally 
be filled up by the voice, without accompaniment. We 
have, in modern mufic, a fpecimen of a plealing air, by 
Roufleau, formed on three notes alone, the key-note, 
with its fecond and third ; but there can be little doubt 
4 F that 
