402 POPULAR LECTURES AND ADDRESSES. 



and to support these slips of wood on a board with 

 nails to guide them so that they may be placed in 

 groups of two, three, or four, one over the other, and 

 any of them moved in the direction of its length to 

 illustrate the different phase-relations of a harmony. 

 Suppose now, one note of a perfect binary har- 

 mony to be very slightly sharpened or flattened : 

 so slightly that during a large number of the 

 periods of the perfect harmony, the phase-relation 

 in the imperfect harmony experiences but little 

 change. Let the two notes of the imperfect har- 

 mony be sustained long enough with perfect uni- 

 formity as to pitch and intensity : the effect will 

 be that of perfect harmony, modified by a slow 

 change of its phase-relation through a cycle ; which 

 in the case of an even binary harmony is from 

 coincident maximums gradually to coincident 

 minimums, and thence gradually round again to 

 coincident minimums ; and in the case of an odd 

 binary harmony is from oppositions to coinci- 

 dences, and round to oppositions again ; and so on 

 in cycles. In favourable circumstances, and with 

 careful attention, a variation of the quality of the 



