380 PHILOSOPHICAL TRANSACTIONS. [aNNO I677. 



of a theatre there should be vases or hollow pots of several sizes, to answer all 

 the notes of music placed on the stage in such manner that the voice of those 

 who sang on the stage might be augmented by their ringing ; Vitruvius men- 

 tioning divers ancient theatres, where there were some of brass, some of earth. 



After this, he descends to the consideration of the nature of keys in music, 

 and of a single tune. Next he treats of schisms and the scale of music. 



Having dispatched that work, he proceeds to music that consists of several 

 parts in concert, which is made up of harmony, formality, and conformity. 

 Of which, harmony is the grateful sound produced by the joining of several 

 tones in chord to each other; formality requires that the succeeding notes be 

 agreeable to the former; and conformity, that each part have the like tendency 

 to the succeeding notes. Lastly, he speaks of time, or the measures of music; 

 the due observance of which is grateful, for the same reason given for the for- 

 mality of a single tune, because the subsequent strokes are measured by the 

 memory of the former, and if they comprehend them, or are comprehended by 

 them, it is alike pleasant; the mind cannot choose but compare one with the 

 other, and observe when the strokes are coincident with the memory of the 

 former. 



On the Trembling of Consonant Strings, a new Musical Discovery. By Dr. 



Wallis. N° 134, p. 839. 



Sir. — I have thought fit to notice a discovery that has been made here, about 

 three years since, or more, which I suppose may not be unacceptable to those 

 of the Royal Society, who are musical and mathematical. It is this, whereas 

 it has been long since observed, that if a viol or lute string be touched with the 

 bow or hand, another string on the same or another instrument not far from 

 it, if an unison to it or an octave, or the like, will at the same time tremble of 

 its own accord. The cause of it having been formerly discussed by divers, I do 

 not now inquire into. But add this to the former observation, that not the 

 whole of that other string trembles, but the several parts severally, according 

 as they are unisons to the whole, or the parts of that string which is so struck. 

 For instance, supposing AC (fig. 7? ph xi) to be an upper octave to «y, and 

 therefore an unison to each half of it, stopped at (3; now if, while ay is open, 

 AC be struck: the two halves of this other, that is, a|3 and ^y, will both 

 tremble, but not the middle point at p. Which will easily be observed, if a 

 little bit of paper be lightly wrapped about the string «y, and removed succes- 

 sively from one end of the string to the other. In like manner if AD (fig. 8) 

 1t)e an upper twelfth to x$, and consequently an unison to its three parts equally 



