September 15, 1911] 



SCIENCE 



329 



play the same note it would be different. 

 But so long as we keep to the same instru- 

 ment, whenever the same note recurred we 

 should find, generally speaking, the same 

 shape of wave : and we could resolve it into 

 its constituents, one being the main wave 

 and others harmonies of different intensi- 

 ties. The analysis of such a record would 

 thus be a comparatively simple matter, on 

 which we need scarcely dwell further. 

 Very different is the case of the orchestral 

 record. There are numerous instruments, 

 playing notes of different pitch, intensity 

 and character, each of which, if playing 

 alone, would produce its own peculiar rec- 

 ord. But when they play together the 

 records are all combined into one. The 

 needle can only make one record, but it is 

 a true sum of all the individuals ; for when 

 the instrument is set to reproduce the play- 

 ing of the orchestra, a trained ear can per- 

 ceive the playing of the separate instru- 

 ments — when the strings are playing alone, 

 and when the wind joins them: when the 

 horn comes in and whether there are two 

 players or only one : nay, even that one of 

 the second violins is playing somewhat flat ! 

 This could not happen unless the indi- 

 vidual performances were essentially and 

 truly existent in the combined record; and 

 yet this consists of only one single wavy 

 line. The waves are, however, now of great 

 complexity, and it seems at first sight hope- 

 less to analyze them. The mathematician 

 knows, however, that such analysis is pos- 

 sible, and is quite simple in conception, 

 though it may be laborious in execution. 

 Selecting a note of any given pitch, a 

 simple calculation devised by Fourier will 

 reveal when and how loudly that particular 

 note was being played. This being so, it 

 is only necessary to repeat the process for 

 notes of different pitch. But though this 

 can be stated so simply, the carrying out in 

 practise may involve immense labor, by 



reason of the number of separate notes to 

 be investigated. It is not merely that these 

 will extend from low growls by the double 

 bass to high squeaks by the fiddles, but that 

 their variety within these wide limits will 

 be so great. The series is really infinite. 

 We might indeed prescribe a certain scale 

 of finite intervals for the main notes, as in 

 a piano: but the harmonics of the main 

 tones would refuse to obey this artificial 

 arrangement and would form intermediate 

 pitches which must be properly investi- 

 gated if our analysis is to be complete. 

 Moreover the orchestral instruments will 

 not keep to any such prescribed intervals, 

 but will insist on departing from them 

 more or less, according to the skill of the 

 performer. There is a story told of an ac- 

 companist who vainly tried to adjust the 

 key of his accompaniment to the erratic 

 voice of a singer. At length in exaspera- 

 tion he addressed him as follows: "Sir, I 

 have tried you on the white notes, and I 

 have tried you on the black notes, and I 

 have tried you on white and black mixed: 

 you are singing on the cracks ! ' ' Some in- 

 struments will almost certainly "sing on 

 the cracks" so that we shall not easily es- 

 cape from the examination of a very large 

 number of possibilities indeed — we may 

 well call them all the possibilities within 

 the limits of audibility. The illustration 

 is already sufficiently developed for provi- 

 sional use. My suggestion is that science 

 has only dealt so far with the easy records 

 and that the genuine hard work is to come. 

 If we can imagine a number of deaf per- 

 sons turned loose among a miscellaneous 

 collection of gramophone records, with in- 

 structions to make what they could of 

 them, we can readily imagine that they 

 would pick out those of single instruments 

 first. We must make the researchers deaf 

 so that they may not use the beautiful 

 mechanism of the human ear which has as 



