520 



Mr. A. J. Ellis. 



[June 17, 



June 17, 1880. 



THE PRESIDENT in the Chair. 



The Presents received were laid on the table, and thanks ordered for 

 them. 



Prof. Charles Niven and Dr. William A. Tilden were admitted into 

 the Society. 



The Right Hon. Alexander James Beresford Hope, whose certificate 

 had been suspended as required by the Statutes, was balloted for and 

 elected a Fellow of the Society. 



The following Papers were read : — 



I. " Notes of Observations on Musical Beats." By Alexander 

 J. Ellis, B.A., F.R.S., F.S.A. Received May 28, 1880. 



During the last three years I have been greatly occupied with 

 observing and counting musical beats, for the purpose of discovering 

 the cause and amount of error in Appunn's reed tonometer, and of 

 measuring the number of vibrations made in a second by tuning-forks 

 and organs, as materials for my " History of Musical Pitch." * The 

 following are brief notes of some of the observations then made : — 



When two musical notes nearly but not accurately form a con- 

 sonance, or are in unison, they beat. Under ordinary circumstances 

 the number of beats in a second of a disturbed unison is equal to the 

 difference of the number of double vibrations in a second made by 

 each note. It is not so always, as will be shown later on. If x and y 

 be the "pitch " or number of vibrations in a second, made by two 

 musical tones, of which y is the sharper; then, if my—nx=0, the 

 tones form what I have termed a considence, that is, the nth. partial of 

 x falls on the same rank or seat as the m th partial of y. Considences 

 are not always consonances, because other partials of the notes may 

 beat roughly, as when m : n = S : 9 or 9 : 10 or 15 : 16, which are well 

 known dissonances, but give appreciable considences. But if the pitch 

 of either x or y be slightly altered, so that my — nx= + b, the two 

 consident partials become what I have termed dissident, or placed on 

 different ranks or seats, and b beats in a second are heard, being called 

 "sharp" when positive, that is when my>n%, and "flat" when 

 negative, that is when my < nx. This includes the unison for which 



* A paper read before the Society of Arts on March 3, 1880, and printed in their 

 Journal for March 5, with an appendix on April 2, 1830. 



