to what Extent, and how most readily attainable P" 4 1 



the faculty of comparing, through the medium of the ear, the 

 relative magnitude or number, or perhaps the peculiar arrange- 

 ment of those particles, equally as the proportions of a picture 

 through the medium of the eye, appears too reasonable to dis- 

 pute. This is all we can offer upon the subject. 



To obviate the allegation of partialit_v, I shall meet the advo- 

 cates of vibration upon their own ground : but, acting much more 

 fairly than they have done, I shall not content myself with the 

 selection of some half-a-dozen of the mo&X. favourable numbers: 

 on the contrary, I shall follow up their own ])lan of calculation 

 throughout the scale, and present to vou in regular order the result. 

 Dr. Rees, in his recent Encyclopaedia, article Concord, has 

 given us the modern table, from the octave to the minor 6th in- 

 clusive, rating the qctave as 60; viz. 



Octave = \ string, value 60 coincidences. 

 5th = ^- . . 30 



4th = I . . 20 



Major 6th =4 . . 20 



Major 3d =4- .. 15 



Minor 3d = |- . . 12 



Minor 6th = -^ .. 12 



Her« the calculation ceases ; and for the best of reasons — be- 

 cause it is fallacious. Let us take then every interval upon the 

 scale ; and reduce it to a common standard, by dividing the nu- 

 merator into that number which represents the octave — such 

 being the uniform process *. 



', "" r Octave = I strinfr, value 1000 coindences. 

 posmg the J i c 



Then shall follow in 



regular grad£ 



4th = f . . . . 333 



Major 6th = 4 . . . . 333 



Major 3d = 4- . . . . 250 



Minor 3d (as on our 1 ^ ona ah u 



, ,• » 1 I \ V~ ii •• •• 200 -.All har- 



pubhc tables) . . J " J . , 



Sharp (or Major) 4th = f , . . . 200 (. '""'?'^^' 



Minor 6th. = i .. .. 200 f f'l"'^' 



Seventh = a . . . . 200 -J '^"^^ " 



Second = f . . . . 125 



Sharp (or Major) 7th = J- . . . . 125 



Semitone = t|- . . . . 66 

 Minor 3d (as really found ■^ 



on well-tempered V = ^-;l . , . . 58 ! ! 



pianos) J 



" As the denominators iire supposed to hate some tnflinjf influence upon 

 the value, the preference is j^ivcn by the Doctor to the lowest. 



I fear, 



, . > ;>th = -> . . . . 500 

 iationj 



