204 Introductory Paper 



irregular distances, the musical sounds produced, are at irre- 

 gular intervals from each other. But the native instrument, 

 having its vents bored at regular distances, will emit notes 

 at regular intervals of acuteness. The reason why the 

 sounds of the latter are so unpleasant to our ears, will 

 appear, when we consider the theory of the musical scale. 



7. Taking the natural scale of C major, we find, that it 

 consists of seven unqualified notes, designated by the seven 

 first letters of the alphabet, in the following order, C, D, E, 

 F, G, A, and B. The intervals or musical distances be- 

 tween these notes are not equal, since those expressed as 

 iT 5 ¥' \' X~' an( ^ % 3 are k nown as tones ; while those ex- 



E JB 



pressed as ^ and — - are half tones. On examining the 

 German-flute, the vents will be found to bear a correspond- 

 ing relation to each other. Besides this peculiarity, it has 

 been found, that the scale of seven notes, possesses another 

 inequality. Dividing the scale into two tetrachords, expressed 

 as c.D. E. R and g. a. b. c, — it is asserted, that there is not a 

 strict mathematical equality between the two divisions. 

 Though aJl assume this equality for practical purposes, there 

 seems to be reason to suppose, that in this want of symmetry 

 is hidden, a key to the difficulty of tuning compound instru- 

 ments like the Oro-an and the Piano-forte. And I further 

 beg to remark, that the necessity for what are called " the 

 golden rules" of harmony, has probably arisen from the 

 difference, thus established by nature. There is no doubt, 

 that the scale of intervals, as above described, is pleasing to 

 an European ear. When it is considered, also, that in the 

 course of improvement, the European instrument must have 

 resulted by gradual perfection from its rudest and simplest 

 form, — we should consider it, as the result of endeavours 

 tested by the criterion of a good ear, and assimilated to the 

 standard of existing ideas. The native musician, however, 



