912 



SCIENCE 



[N. S. Vol. XLI. No. 1068 



of the scale — thus breaking the octave into 

 twelve instead of seven intervals, and second, 

 the pitches of the various tones are so altered 

 as to make the interval between any two suc- 

 cessive tones the same. This scale is known as 

 the scale of " equal temperament " or briefly, 

 the tempered scale. 



The " interval " between two tones, as the 

 term is here used, is the ratio of the pitch of 

 the higher tone to that of the lower. It follows 

 that on the tempered scale this ratio is the 

 same for any two adjacent tones. The numer- 

 ical value of this interval is 1.05946, since the 

 sum of twelve such intervals is 2, the numer- 

 ical value of the octave interval. 



These considerations coupled with the fun- 

 damental law of string vibrations, to the effect 



which 0c/00=0C/0d=0d/0D = etc., the 

 value of this ratio being 1.05946 by construc- 

 tion. 



If this diagram is drawn on the top of a 

 sonometer, or a table-top across which a string 

 is stretched, and bridges are placed under the 

 string opposite and c, it forms a complete 

 finger board for running the major, minor and 

 chromatic scales. 



The device lends itself to the demonstration 

 of the following relations : 



(1) Comparison of the major and minor 

 scales. (2) Comparison of the major and 

 minor chords. (3) To show that on the tem- 

 pered scale any note may be taken as key note, 

 and all scales are equally good. For this pur- 

 pose choose any point as starting point, call- 



that, for a string of given weight and tension, 

 the frequency of a vibrating segment is in- 

 versely proportional to its length, suggest a 

 simple method of finding those string lengths 

 which will give the successive tones of the 

 tempered scale. 



Draw two intersecting straight lines includ- 

 ing any convenient angle (see accompanying 

 diagram). From the point of intersection lay 

 ofi on one line any convenient length Oc = L, 

 on the other a length 00 = L^ 1.05946. Join 

 the points Cc by a straight line. 



Locate the corresponding points B and d 

 and join by a dotted straight line. Now draw 

 the series Cd, dD, Be, etc., and the dotted 

 series, parallel to Bet and cG. By this means 

 the points c#, d, d$, e, etc., are determined at 

 which a string of length L (==0c) must be 

 stopped to give the successive tones of the 

 tempered (chromatic) scale. This will be evi- 

 dent from the construction of the figure in 



ing it point 1. Number the points from point 

 1 upward. Sound in succession the tones 

 given by the string when stopped at points 1, 

 3, 5, 6, 8, 10, 12 and 13. (4) Comparison of 

 just and tempered scales. Lay off from on 

 Oc lengths equal to 8/9, 4/5, 3/4, 2/3, 

 3/5 and 8/15 of L. The points so determined 

 are those at which the string should be stopped 

 to give the tones of the just scale. A glance 

 at the board will now show to what extent 

 each interval of the tempered scale is falsified. 

 L. B. Spinney 

 Iowa State College 



three strawberry fungi which cause fruit 



ROTS 



In my investigation of strawberry troubles 

 in Louisiana last year,^ and later in a study of 

 market berries in this state, I frequently found 

 upon spotted berries the fungi described be- 



1 Science, N. S., 39: 949, 1914. 



