846 



SCIENCE 



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



compound tones with different funda- 

 mentals is one of the conditions of har- 

 mony, and the scale devised by considera- 

 tions of the mutual harmony of the notes 

 sounded simultaneously would, in every 

 respect, be the same as that of a scale 

 based on repeated upper partials. In the 

 one case the identity of upper partials is 

 an act of memory; in the other it is de- 

 termined by the harmony of sustained 

 tones. All the arguments by Helmholtz 

 based on historical considerations and on 

 racial and national differences are equally 

 applicable to the hypothesis of sustained 

 tones. In fact, they take on an additional 

 significance, for we may now view all these 

 differences not merely in the light of dif- 

 ferences in racial development and temper- 

 ament, but in the light of physical environ- 

 ment. Housed or unhoused, dwelling in 

 reed huts or in tents, in houses of wood or 

 of stone, in houses and temples high vaulted 

 or low roofed, of heavy furnishing or light, 

 in these conditions we may look for the 

 factors which determine the development 

 of a musical scale in any race, which de- 

 termine the rapidity of the growth of the 

 scale, its richness and its considerable iLse 

 in single-part melody. 



The duration of audibility of a sound 

 depends on its initial intensity and on its 

 pitch, to a small degree on the shape of the 

 confined space, and to a very large degree 

 on the volume of the space and on the 

 material of which the walls are composed. 

 The duration of audibility is only a loga- 

 rithmic function of the initial intensity, 

 and as the latter is practically always a 

 large multiple of the minimum audible in- 

 tensity, this feature of the problem may be 

 neglected when considering it broadly. 

 For this discussion we may also leave out 

 of consideration the effect of shape as 

 being both minor and too intricately 

 variable. The pitch here considered will 

 be the middle of the musical scale; for the 



extremes of the scale the figures would be 

 very different. The problem then may be 

 reduced to two factors, volume and ma- 

 terial. It is easy to dispose of the prob- 

 lem reduced to these two elements. 



The duration of audibility of a sound is 

 directly proportional to the volume of a 

 room and inversely proportional to the 

 total absorbing power of the walls and the 

 contained material. The volume of the 

 room, the shape remaining the same, is pro- 

 portional to the tube, while the area of the 

 walls is proportional to the square of the 

 linear dimensions. The duration of audi- 

 bility, proportional to the ratio of these 

 two, is proportional itself to the first power 

 of the linear dimension. Other things be- 

 ing equal, the duration of audiblity, the 

 overlapping of successive sounds, and 

 therefore the experience of harmony in 

 single-part music, are proportional to the 

 linear dimensions of the room, be it dwell- 

 ing-house or temple. 



Turning to the question of material, the 

 following figures are suggestive : Any open- 

 ing into the outside space, provided that 

 outside space is itself unconfined, may be 

 regarded as being totally absorbing. The 

 absorbing power of one-half-inch hard pine- 

 wood sheathing is 6.1 per cent., of plaster 

 on wood lath 3.4 per cent., of single-thick- 

 ness glass 2.7 per cent, of brick in Port- 

 land cement 2.5 per cent., of the same brick 

 painted with oil paint 1.4 per cent. Of 

 the others wood sheathing is nearly double 

 any of the rest. On the other hand, a man 

 in the ordinary clothing of to-day is equal 

 in his absorbing power to nearly 48 per 

 cent, of that of a square meter of unob- 

 structed opening, a woman is 54 per cent., 

 and a square meter of audience at ordinary 

 seating distance is nearly 96 per cent. Of 

 significance also in this connection is the 

 fact that Oriental rugs have an absorbing 

 power of nearly 29 per cent, and house 

 plants of 11 per cent. 



