214 



NATURE 



\7an. 13, 1876 



Similarly, with the sounds. Although the 103 vibra- 

 tion-sound and the 100 vibration-sound only coincide 

 with theoretical accuracy once in a second, yet there is, 

 three times per second, a coincidence so nearly accurate 

 (within T7T3Tir of a second) that the practical effect in 

 producing the beat is the same. 



The rule, therefore, is practically right ; but it should 

 be qualified scientifically with the following addition :— 

 When the two vibration-numbers are prime to each other 

 {i.e. when they are not both divisible by any whole num- 

 ber) the ride is not theoretically accurate, bnt if the times 

 of vibration are very small (as they always are in prac- 

 tice) the error has no practical effect, and the rule conse- 

 quently holds good. 



With the aid of this rule we can now tell the exact 

 number of unison beats that will correspond to any 

 amount by which the two notes are out of tune ; and, 

 vice versd, we can tell the exact quantity by which two 

 notes intended for unisons are out of tune by simply 

 counting the number of beats they give. For example, sup- 

 pose the A open string on the violin is played along with the 

 fourth finger note (first position) on the third string, and 

 that the latter is a little sharp, so as to give four beats per 

 second, we know that the upper note will have four vibra- 

 tions per second more than the other ; and as at this 

 point of the scale about twenty vibrations go to a semi- 

 tone, we can tell that the upper note is about one-fifth of 

 a semitone sharper than the lower one. To effect this, 

 the fourth finger must be moved about one-twelfth of an 

 inch nearer the nut than the former position, and this can 

 be measured if any player think it worth the trouble, as 

 a check to the calculation. 



We may next inquire what effect on the ear is produced 

 by changes in the rapidity of the beats. At first, when 

 they are slow, no very unpleasant sensation is perceived, 

 but as they become faster they give a sensation of rough- 

 ness which is disagreeable in a marked degree. With a 

 further increase of rapidity the effect becomes again less 

 unpleasant, until it arrives at the slight tremulousness 

 already mentioned in the voix celeste and vox hiimana 

 stops, and which, as it is purposely produced, may be sup- 

 posed to be rather agreeable than otherwise. 



If we carry the error farther, the beats become so fast 

 that the ear ceases to be able to appreciate them, and the 

 beating effect entirely disappears. 



Helmholtz, who has paid much attention to this sub- 

 ject, and who has founded on this property of beats some 

 important musical speculations, is of opinion that the dis- 

 agreeable effect increases gradually until the beats arrive at 

 about thirty per second, where the harshness is at a 

 maximum ; that then the unpleasantness lessens as they 

 grow faster, until, at about 100, or something more, per 

 second, the beating effect disappears. Hence he calls 

 from O to this point beatifig distance for any two notes 

 near each other. 



For example, if starting from the treble €,512 vibra- 

 tions per second, we sharpen the note to Di?, 546 vibra- 

 tions, and then sound this with the original C, we shall 

 get 546 - 512 = 34 beats per second, which gives a very 

 harsh effect. If we go on to D, 576 vibrations, we shall 

 get, for the interval C to D, 576 - 512 = 64 beats per 

 second, which is less harsh ; and if we go on to C with 

 Ei?, we shall have 614 - 512 = 102 beats, which is hardly 

 perceptible. For C to E, a major third, we have 640 — 

 512 = 128 beats, and no one can assert that this inter- 

 val, when in tune, has anything harsh or disagreeable 

 about it. 



A curious question has existed as to what becomes of 

 the beats when they thus vanish. Are they entirely an- 

 nihilated ? or do they in their more rapid shape produce 

 any other sensible effect of any kind .'' To explain the 

 answer that was, by early writers, given to this question, 

 one must mention a new phenomenon which occurs in 

 connection with double sounds, namely, what is called the 



"grave harmonic." When two notes are sounded together 

 they give rise to a third tone, of a fainter strength, and gene- 

 rally lower than both. Examples of this are usually taken 



from concords : thus, if the following two notes ^ — P— ^ 



are sounded on an organ, a violin, or any instrument of 

 sustained sounds, and are perfectly in tune, the ear will, 

 with attentive listening, hear a faint third sound resulting 

 therefrom, which will be an octave below the lowest note 



of the concord, thus 



the major third 



If, instead of the fifth, 



be sounded, in like manner 



the " grave harmonic " will be an octave lower than before, 

 namely, Oi^^^^zl This phenomenon was discovered 



by Tartini, the eminent violinist, and is often on this ac- 

 count called the " Tartini harmonic." 



Now it happens that the number of vibrations of 

 Tartini's harmonic, for any two given note?, is exactly the 

 same as the number of the unison beats for the same 

 notes, as hereinbefore described : and hence the idea arose 

 that when the beats became so rapid as to lose their 

 beating character, they gave rise to the grave harmonic j 

 the explanation naturally presenting icself, that a beat j 

 recurring regularly with the proper rapidity would pro- 

 duce on the ear the effect of a musical sound. Dr. Young 

 was the first to publish this explanation : he says (*' Ex- 

 periments and Inquiries respecting Sound and Li^^ht," 

 sec. xi.), " The greater the difference in the pitch of the 

 two sounds, the more rapid the beats, till at last they com- 

 municate the idea of a continued scund, and this is the 

 fundamental harmonic described by Tartini.'' 



Young's theory has been generally accepted until within 

 the few last years, and in consequence the kind of beat 

 we have been describing has been called " Tartini's beat." 

 Helmholtz has lately thrown doubt on the correctness of 

 Young's explanation, but the analogy of the numbers 

 may warrant us in retaining the name, as distinguishing 

 this beat from others which we will now proceed to 

 describe. 



[To be continued.) 



UNITED STATES NATIONAL ACADEMY OF 

 SCIENCES. 



HTHE half-yearly mee'ing of the National Academy of 

 •^ Sciences was held a: Philadelphia, Nov. 2, 3, and 4, 1875. 



Prof. Joseph Henry hzs for several years been conducting the 

 researches of the U. S. Lighthouse Board in respect to Fog 

 Signals and the Transnission of Sound. While these experi- 

 ments are not yet completed, the results up to the present time 

 give the following inc'ications : — The echo of sound passing over 

 the ocean is more prjbably due to reflection from the surface of 

 the waves than fron the air ; sound coming against the wind 

 can certainly be heird at an elevation from a greater distance 

 than at the sea le^el ; with the velocity of the wind at about five 

 miles an hour, somd was heard five times further with the wind 

 than against it ; lound is heard furthest with a moderate wind ; 

 with a strong wild it is not heard so far as in still air. 



Prof. Joseph J-e Conte, of California, contributed the results of 

 his observations on mountain ranges of the Pacific coast. The 

 author's theorf is that the mountain chains in question were 

 formed whol^ by a yielding of the crust of the earth, along given 

 lines, to horizontal pressure ; not, however, resulting in a convex 

 arch filled ind sustained by liquid beneath, but by a mashing to- 

 gether of :he whole crust, producing close folds and a swelling 

 upwards ;)f the squeezed mass. Prof. Le Conte went on foot 

 through a cut made by the Central Pacific railroad from near S 

 Francisco Bay eastward, a distance of 30 miles through the Coa^ 



