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but in page 350, lays ("own an inapplicable and falfc rule for 

 calculating the place of the harmonic, or impHed fimul, as 

 he calls it ; -viz.. " when two different founds arc heard to- 

 gether, their combination always either really produces, or 

 effentially implies, a third found, -whtfe ■vibraiions are equal 

 to the d'tlference of the inbration, of the tiuo founds m the 

 fame tinTe." Tims C 240, heard together with G 360, 

 produces 120; which is can oftave below C, &c. Now 

 ft is obfervabk, that this empirical rule will give the iume 

 refults as ours above, only in fuch cafes where the lealt 

 terms of the ratio (in colnmn 3) differs by un'/;' ; which is 

 the cafe in tight of Tartinis examples out of tiic ten, but 

 not with the VI or the 6th : which, according to Holden's 

 rule, iland thus, 400 - 240 = 160, and i J§ = J. or the fifth 

 telowthe key, inflead of the Xlltn (as Dr. Robuon and 

 •tve have caku'ated it above); alio, 384- 240 = 144, ami 

 T44 _ i., or the otlave and fourth, or eleventh, beluw tlie 

 vpper note, infteadof the XXII. It is not a little furprif- 

 ing that Mr. H. (hould have overlooked tliefe glaring incon- 

 lillencies of his rule, with Tartini's experiments, on which 

 he profeffes to have founded it ; acknowledging, however, 

 <p. 351.) that he is imable to difcover any philulophical 

 principles on which thefe phenomena can be explained, and 

 tf courfe uracquainted with the writings of the two 

 authors, from wlience we have extracted as above. 



We 



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The grave harmonics found by the rules and table abo-rr* 

 are occaiioned by the coincidences of the vibrations of per- 

 feft confonances, or the teals of Mr. Sauveur, but fince ;he 

 beats of Dr. Robert Smith alfo, or thofe made by imperfect 

 concords, when they occur oftencr than 1 2 or 1 3 in a fecond, 

 occafion a grave harmonic note to be perceived, and no the- 

 orems for calculating fuch beats, except that of Dr. Smith 

 from the fractions of a comma of temperament, and Mr. 

 Eraerfon's from the lengths of llrings, having to our know- 

 ledge been publiflicd, we lliall here Inpply that dcfeft in our 

 article Beats, and give theorems for calcuhiting the beats 

 made by imperfect or tempered concords whofe vibrations 

 per fecond are given, -viz.. 



Let N and M be the number of complete vibrations made- 

 in one fecond, by the grave and acute notes refpeftively, of 



the tempered concord whofe pcrfedl' ratio is — (n being the- 



leaft term, in its lowed number), and let b be the number of 

 beats in one iecond of time. 



Then, if the temperament hejliarp, i ;= n M — m N, the 

 beats required. 



Or, if the temperament he fat, i = m N — n M,the beats 

 required. 



Take for example, the 3d in our table above, and we have 

 N = 240, M = 284-', n := 5, and m =: 6 : and by the fe- 



Ihould not perhaps liave thus adverted to Mr. Holden's effay, , cond theorem above 6 x 240 — 5 x 2844 — 17 J the beats iih 

 had it not been in other refpeds a mod refpeftable work, " ' '' ' . •" . . r ,.„,,,., 



and one tlirough which the'.e errors are likely to be widely 

 diffeminated among mnficians, and were not the fanciful 

 fyllem of harmony, which he builds folely upon them, cal- 

 culated to bewilder ftill further the mufical Undent, who may 

 happen to have but a flight knowledge of mathematics. 

 Among the novelties of Mr. Plolden's fyfteni, he pretends 

 to prove, by means of the implied founds, (calculated by his 

 rule,) that the minor third, ^, is a " fuperffrufted third," 

 and not the fundamental lefs third of the fcale, which he 

 fays is expreffed by the ratio \l, (though coiicei-ved probably, 

 as he fays, p. 371, ly the ratio j-^,) on which account we 



have introduced this comma-deficient minor third into our 



table, and when its harmonic is fliewn to be (3 e, five oilaves 



below the ipper note of the confonance, infteadof 284^ — 



■Zip = 44^, and 44I -^ 284-'; = -tV. \\'l"ch expreffes 



2 VIII 4- 6th, or a n inor twentieth below the upper note, 



as Mr. H.'s rule would have given it : whereas, had he ufed 



the true method of affigning the place of this harmonic or 



implied found, his boafted fundamental lefs third, (befides 



proving lefs agreeable to the ear on trial, p. 384, than-,) 



muft have bet n degraded from the rank of concords, as 



having an implied found more than thrte odfaves below the 



lowell of its notes, which is one of the effential properties of Mr. Farey'sneiv notation ; its common logarithm is .8819006, 



one fecond : which are, it will be obferved, juft double the 

 vibrations in column five of the table, and therefore the grave 

 harmonic thus occafioned, is four octaves below the upper 

 note of this comma deficient minor third. Tiie above theo- 

 rems for beats will be found of like eafy application, m al- 

 moil every inftance of mufical calculations. 



Grave Intervals is a term apphed by Mr. Max- 

 well and feveral other correft writers, to fuch confo- 

 nances as are flattened or lowered by a major Comma (ice- 

 that article) and it is ufual with them to dilling^iifh fuch in- 

 tervals by the grave accent thus, IP, IIP, IV, V, VI\- 

 5;c. V and on tlie contrary, to apply the acute accent to fuch 

 as are (harpened or raifed a major comma, as II', III', 4', 

 Stc. and to call fuch acute intervals or comma redundant inter- 

 vals, while thofe as much flattened are called Comma dtfi- 

 cient intervals, which fee. Mr. Holden, a modern writer^ 

 has, however, applied this term to intervals lowered by what 

 he calls a bearing, whofe ratio is |1 = 1 1.94709 S 4- m. 

 See Grave fourth. Sic. 



Grave fourth, according to Mr. Holden's fyflem 

 lately publifhed, is an interval lefs tlian a perfeft fourth, 

 by what he calls a bearing (which is f-J = 13.94709 S 

 4- m) having the ratio of J? = 240.05291 2 4 5*4 21m in 



concords, according to their new conceits. 



AnotKej refult of thefe falfe principles in the Effay is, 

 the admiflion of the integer 7 among harmonic ratios 

 (though to theexclufion of 5x7; f; 7 , Stc. 2 x 7, 2'x 7, 

 &c. page 341, and alfo of page 305, although 7, 11, 13, 

 19, &c. have real places in the fdfe notes of the trumpet, 

 horn, &c.), and the confequent introdnftion of what the 

 author calls a Ghave /c«/r//j (fi-e that article), in his de- 

 fcendiQc fcale, page 316. According to which alfo, the 

 acute or comma-redundant major fixtli (54)' helongs eflen- 

 tially to the fcale, in:le:id of the true concord 4 ! We truft 

 that we (hall have performed an acceptable piece of fervieci 



8792, its Euler's logarithm or decimal value of the odtave 

 is .3923 1 75, and it contains 21.89039 major commas. 



GuAVE/ro/icrytv/i/Vonf, is an interval in Mr. Holden's Syf- 

 tem of Mufic, whole ratio is 1° = 43.05291 i; 4-f4-4m; 

 its common logarithm is .9788107,1, and Euler's logarithm 

 .070389, and the number of major commas 3.92754 which 

 it contains. 



GRAVEDO, in Medieine, a Latin term, derived from 

 gravis, heavy, (ignifies that fpecies of catarrh, which is 

 ufually called a cold in the head ; and in which, together w-ifh 

 a Huffing of the noftrils, and blunting of the voice, there is 3 

 fenfe of fullnefs and weijjbt in the forehead. It is, accord- 



to the well-wiihers to the harmonic fcience, in pointing ouf^ ing lo Celfus, nearly fynonymous with the coryza of tlie 

 the fource of fuch incongruous abfurdities as the above ; and Greeks. See Catakkii. Celfus, de Med. lib iv. cap. 2. 

 hope, that in a fecond edition of this ufeful work nearly all GRAVEDONA, or Ghavidon.v, in Geography, a 

 which follows page 349 will be expunged, and configned to town of Italy, in the department of the Lario, on the lake 

 its merited oblivion. Como; 42 miles N. of Milan. 



I GRAVEL, 



