G R A 



»ote than any of its contlituents, feeing the time of a c\'c]e 

 exceeds the greateft vibration tliat enters into tlie compofi- 

 tion of it. The ftrength of a grave harmonic is alfo weak, 

 tvhen compared with tlie notes compoling it, becaiife thefe 

 fecondary founds, being nothing more than certain unavoid- 

 able efforts of the imagination, they aflume the charaiSler of 

 a feeble found, which is jull ilrong enough to be heard in 

 the company of one or more louder tones ; for the power 

 of the imagination is always inferior to external imprefiions, 

 eKcept in Iks of iiifanity, when the organs of fenfe appear 

 po be blunted by phyfjcal caufes. The grave harmonics 

 flways Lcp the dired'ion of the cars, let the pofition of the 

 head be changed a; often as you pleafe, refembling m this 

 circumiiance a (hrill piping note, called the rir.ging of the 

 eai-s ; which every one afcribcs to a (light affection of the 

 auditory duct, becaufe it differs from external founds, in 

 having no fixed direction. The grave harmonics agree with 

 the ringing of the ears in this remarkable particular ; which 

 is a ftrong proof that their immediate caufe is feated in the 

 perfon of the hearer ; and it is evident from the nature of 

 things, that this caufe originates in the mind." Nicholfon's 

 Journa', 8vo. vol. iv. p. 2. 



We have been thus particular in quoting from two very 

 able writers on the fubjeft of the grave harmonics, or Tar- 

 tinian founds, in order to fliew the foundation of the rules 

 which we fnall here give, for deternoining the grave harmo-, 

 nic of any given perfect confonance, •viz.. 



G R A 



I ft. Find the number of Tibrations made in one fecond of 

 time by each of the given founds : wliich, fuppofing C^/- 

 fa-ut, or c of the German tablature, or that on which the 

 tenor chff is placed, to make two hundred and forty com. 

 plete vibrations, is obtained, by multiplying thii number br 

 the larger tenn of the ratio of the given foundt to C, anil 

 dividing the produft by the fmallertcrm of that ratio, if the 

 given founds lie above C, or the revcrfe if below it. 



2d. Having thus obtained the vibration^ of the gtTen 

 confonance, divide the larger number of them, by the larger 

 term of the given confonance, and the fmaller number i>y 

 the fmaller term, cacli of which, if the op'-ration be rigfrtly 

 perfonr.cd, will give the fame refult, and fhew the number of 

 coincidences of the pulfes of tlic two given founds in one f*". 

 cond, and alfo the vibrations in that fame period, of the grave 

 harmonic fought. 



3d. Compare th.-- number of vibrations lafl found with each 

 of the vibrations of the given confonance, and reduce their 

 ratios to the lowell terms, which will then exprefs the inter- 

 vals or dillances of the grave harmonic, below each of the 

 given founds. 



Bv way of examples of thefe rules, we fubjoin the follow- 

 ing table, fhewing the grave harmonic, and feveral other ufe- 

 ful particulars, of the principal confonanccs in the o£tav^ 

 above C-fol-fa-ut. 



The experiments of M. Tartini, the difcoverer of thefe 

 founds, extended to ten of the confonances m our table above, 

 „«. the V, 4th, III, 6th, 3d, VI, II, ir, (fecond mmor,) 

 2d, ("-rearer femitone,) and mmor femitone (5?), but m 

 all of which he feems to have miftaken an oaavc, w aflign- 



\n" the place of the harmonic in the fcale, and has mention* 

 cd'each of them as being higher by an ofta\e than in our 

 table. Mr. John Holden, the author of " An EHVy towards 

 a rational Syftem of Mufic,"' printed at Edinburgh in 1807, 

 p 5f2j fcems to have been aware of tliis latter circumllance, 

 ^'^ xQz but 



