respecting Sound and Light. 143 



tiofl, or, according to Euler's expression, the equation of 

 the curve conceived to correspond with this motion, and thus 

 produce the various characters of the vowels and semi-vowels. 

 The principal sounding board seems to be the bony palate : 

 the nose, except in nasal letters, affords but little resonance ; for 

 the nasal passage may be closed, by applying the finger to the 

 soft palate, without much altering the sound of vowels not 

 nasal. A good ear may distinctly observe, especially in a loud 

 bass voice, besides the fundamental note, at least four harmonic 

 sounds, in the order of the natural numbers; and, the more 

 reedy the tone of the voice, the more easily they are heard. 

 Faint as they are, their origin is by no means easy to be ex- 

 plained. This observation is precisely confirmed, in a late dis- 

 sertation of M. Knecht, published in the musical newspaper of 

 Leipsic. Perhaps, by a close attention to the harmonics entering 

 into the constitution of various sounds, more may be done in 

 their analysis than could otherwise be expected. 



XVI. Of the Temperament of musical Intervals. 



It would have been extremely convenient for practical musi- 

 cians, and would have saved many warm controversies among 

 theoretical ones, if three times the ratio of 4 to 5, or four times 

 that of 5 to 6, had been equal to the ratio of 1 to 2. As it hap- 

 pens to be otherwise, it has been much disputed in what inter- 

 vals the imperfection should be placed. The Aristoxenians 

 and Pythagoreans were in some sense the beginners of the 

 controversy. Sauveur has given very comprehensive tables of 

 a great number of systems of temperament ; and his own now 

 ranks among the many that are rejected. Dr. Smith has written 

 a large and obscure volume, which, for every purpose but for 



