CHAPTER VI 



INHARMONIC ANALYSIS. 



When inharmonic sinusoids are present in a vibration, as illustrated 

 b}^ the case of 3^Tin the preceding section, several successive waves may 

 be treated as a single wave of correspondingly long period (figure 88). In 

 this way the inharmonic of the single wave may be made a harmonic of 

 the multiple wave, if the latter is sufficiently long. Thus by repeating 

 the wave T once, the new double wave 7= 2T' is the fundamental of the 

 series of harmonics : 



V IV IV \V IV IV ]V IV IV IF iF AF 

 2T T \T \T IT IT \T \T IT \T ^.T ^T. 



The inharmonics |T, \T, \T, \T, ^T are all found as harmonics of 

 the double wave. A harmonic analysis of the double wave will yield 

 these inharmonics of the original wave directly as its own harmonics. 

 Such a modification of the method of the preceding section may be termed 

 an " inharmonic analysis." 



Fig. 88. -Six successive waves used as a single wave for an inharmonic analysis. 



This method needs little special explanation. What can be accom- 

 plished by using F = 67" with only 12 ordinates in measuring the original 

 wave is worth considering. We have the harmonic set 



F W IF \V \V W W \V W ly v.V l^ ^F iF iF ^F ^F iF 



er 3r 2T rr it t \t \t it it ^,t it ^,t ?r it it ^,t it 



hV^'^^^^y^^^^ ^sV^V ^F IV iF i,F IF IF ^F 

 ,|T ^J \Tl,TiT \T ^T^,T\T ^T I,T \T IT ^J ^T ^,T ^ IT 



in which a large number of inharmonics appear. Such an analysis requires 

 the use of schedules with 72 ordinates, but only 12 multiphcations are to 

 be made; these are then simply written over six times. If 24 ordinates 

 had been measured, an analysis with V=QT would require schedules 

 for 144 ordinates: if 36 had been done, then schedules for 216; if 72, 



' 99 



