VOL. XVII.] PHILOSOPHICAL TRANSACTIONS. 



All writers on the mathematical part of music agree. 



46q 



ra half 

 That by a third part 

 shortning •^ a fourth 

 a string j a fifth 



I a sixth 



the sound 

 is raised 



'an eighth 

 a fifth 

 a fourth 

 a sharp third 

 a flat third. 



From this foundation all the other notes are derived. The flat and sharp 

 sixth are to be the flat and sharp third to the fourth, and the seventh the like 

 to the fifth, the second to be a fifth to the fourth below, &c. By this rule 

 let us examine what notes a monochord fretted in its aliquot parts will produce. 



Suppose the monochord, fig. 17> to consist of 720 parts, and its tone double 

 C fa-ut, the first note in the table, then half of it will be 36o, and a third part 

 240, &c. Now fretting, or stopping with the thumb, at 36o, must produce 

 C fa-ut; because 36o being half 720, the sound will rise an eighth from double 

 C fa-ut. Again 36o being C fa-ut, 240 must make G sol-re-ut, the third note 

 in the table ; because 240 being just a third part less than 36o, the sound will 

 rise a fifth from that note. After the same manner, proceeding step by step, 

 it will be evident that, 



fCsol fa-ut the 4th' 



E la- mi 

 G sol-re-ut 

 C sol-fa 

 D la-sol 

 E la-mi 

 G sol-re-ut 

 B fa-bi-mi 

 C sol-fa 



5th 



6th 



8th 



Qth 



10th 



12th 



15th 



16th 



note in the 

 table. 



which 

 is less 

 than 



102-f the 7th"Jnoteinr flatter 

 65tL llthf the ta-l sharpei 

 55-,V 13thtbleisaj flatter 

 51f 



■B fa-bi-mi flat 

 I F fa-ut 

 I A la-mi-re 

 A fa-bi-mi flat. 



By the same reason. 

 fa 6th^ 



by just -j^^J^^ produces 



(half ) 

 And consequently, 



B fa-bi-mi flat . 



a-ut 



-mi re 



14th3 little I flatter 3 (.A fa-bi-mi flat. 



Which answers the second inquiry. 



Now to apply this to the trumpet, where the notes are produced only by the 



different force of the breath ; it is reasonable to imagine that the strongest blast 



raises the sound by breaking the air within the tube into the shortest vibrations, 



"but that no musical sound will arise unless they are suited to some aliquot part. 



• ■) rBfa-bi- 

 r f ^. IF fa-ut 



• r^'^MA la-mi 



• 3 (Afa-bi- 



