844 



SCIENCE 



[N. S. Vol. XXVII. No. 700 



ages, with several parts, but without regard 

 to any independent musical significance of 

 the harmonies, extending from the tenth to 

 the seventeenth century." 



3. "Harmonic or modern music char- 

 acterized by the independent significance 

 attributed to the harmonies as such. ' ' 



Polyphonic music was the first to call for 

 the production of simultaneous sounds and 

 therefore for the hearing or the experi- 

 ence of musical harmony. Homophonic 

 music, that which alone existed up to the 

 tenth or eleventh century, consisted in the 

 progression of single-part melody. Struck 

 by this fact, Helmholtz recognized the 

 necessity of seeking another explanation 

 for the invention and the use of a scale of 

 fixed notes in the music of this period. To 

 borrow his own words, "scales existed long 

 before there was any knowledge or ex- 

 perience of harmony." Again, elsewhere 

 he says in emphasizing the point: " The 

 individual parts of melody reach the ear 

 in succession. We can not perceive them 

 all at once ; we can not observe backwards 

 and forwards at pleasure." Between 

 sounds produced and heard in discrete suc- 

 cession, there can be neither harmony nor 

 discord, there can not be beats, or rough- 

 ness or interruption of continuous vibra- 

 tions. Regarding the sounds of a melody 

 as not merely written in strict and non- 

 overlapping succession, but also as pro- 

 duced and heard in discrete succession, 

 Hehnholtz sought another basis for the 

 choice' of the notes to constitute a scale for 

 homophonic music. His explanation of 

 this invention can be best presented by a 

 few quotations: 



Melody has to express a motion, in such a 

 manner that the hearer may easily, clearly and 

 certainly appreciate the character of that motion 

 by immediate perception. This is only possible 

 when the steps of this motion, their rapidity and 

 their amount, are also exactly measurable by 

 immediate sensible perception. Melodic motion is 

 change of pitch in time. To measure it perfectly, 



the length of time elapsed, and the distance be- 

 tween the pitches, must be measurable. This is 

 possible for immediate audition only on condition 

 that the alterations in both time and pitch should 

 proceed by regular and determinate degrees. 



Again Helmholtz says: 



For a clear and sure measurement of the change 

 of pitch, no means was left but progression by 

 determinate degrees. This series of degrees is 

 laid down in the musical scale. When the wind 

 howls and its pitch rises or falls in insensible 

 gradations without any break, we have nothing 

 to measure the variations of pitch, nothing by 

 which we can compare the later with the earlier 

 sounds, and comprehend the extent of the change. 

 The whole phenomenon produces a confused, un- 

 pleasant impression. The musical scale is as it 

 were the divided rod, by which we measure pro- 

 gression in pitch, as rhythm measures progression 

 in time. Hence the theoreticians of ancient as 

 well as modem times. 



Later he says: 



Let us begin with the octave, in which the rela- 

 tionship to the fundamental tone is most remark- 

 able. Let any melody be executed on any instru- 

 ment which has a good musical quality of tone, 

 such as a human voice; the hearer must have 

 heard not only the primes of the compound tones, 

 but also their upper octaves, and, less strongly, 

 the remaining upper partials. When, then, a 

 higher voice afterwards executes the same melody 

 an octave higher, we hear again a part of what 

 we heard before, namely, the evenly numbered 

 partial tones of the former compound tones, and 

 at the same time we hear nothing that we had 

 not previously heard. 



What is true of the octave is true in a less 

 degree for the twelfth. If a melody is repeated 

 in the twelfth we again hear only what we had 

 already heard, but the repeated part of what we 

 heard is much weaker, because only the third, 

 sixth, ninth, etc., partial tone is repeated, whereas 

 for repetition in the octave, instead of the third 

 partial, the much stronger eighth and tenth occur, 

 etc. 



For the repetition in the fifth, only a part of 

 the new sound is identical with a part of what 

 had been heard, but it is, nevertheless, the most 

 perfect repetition which can be executed at a 

 smaller interval than an octave. 



Without carrying these quotations 

 farther, they will suffice to illustrate the 

 basis which Helmholtz would ascribe to 



