166 LECTURES TO SCIENCE TEACHERS. 



the octave is divided into twelve semitones, and the result 

 of this is that the fifths are a schisma flat. This is not a 

 great flattening, but the interval of the fifth is very sensi- 

 tive. It very soon beats, as it is termed ; that is to say, 

 the interference of sounds caused by the flattening of the 

 schisma produces about one beat a second. On the other 

 hand, the equal temperament disfigures the third very much 

 indeed. It makes it seven schismas too sharp. The sixth 

 also, which is a very peculiar and beautiful interval, and 

 which has been called the sorrowful sixth (if I am not 

 mistaken, the bagpipes derive their peculiar wailing effect 

 from the use of the sixth which occurs in the archaic scale of 

 that instrument) that sixth is disfigured very much. The 

 number is 22185 in just, and 22577 in equal temperament, 

 or eight schismas too sharp. The seventh again, in the old 

 temperament is rather flattened, as you see. The numbers 

 are 27165 in the first column, and 27300 in the other; 

 whilst it is terribly wrong in equal temperament, namely, 

 27594. There is another discrepancy in the tempered scale 

 affecting the second. If I had time I could show you that 

 this is a variable note, and requires to be used in two ways. 

 In the old temperament it is about half way between the 

 two, but in the equal temperament it is ninety- eight divisions 

 too sharp for the acute form, and in the flat form it is nine 

 schismas too sharp. This shows that the equal temperament 

 is about as bad a system as we can employ. It has only one 

 advantage, and that is that it is simple, and everybody can 

 learn it easily. There is another accusation to be brought 

 against it, though perhaps you may look upon this view of 

 the question as rather Hibernian, namely, that we never get 

 it ; the tuning of the fifth a schisma flat, which gives one 

 beat a second, is a delicate process, and I firmly believe that 

 very few pianoforte tuners are really able to accomplish it. 

 Mr. De Morgan used to say that he never could manage it, 

 although he separately tuned a number of strings himself to 

 beat one beat a second ; for when he compared them together 

 they never were in tune. Now if he could not do it on a 

 single note with his great mathematical ability and mechanical 

 skill, I doubt if the ordinary class of tuners can. However, 

 although I object to equal temperament on these grounds, 

 which you will see are obvious facts of nature, not at all 

 matters of opinion, I must allow that it does afford great 



