HISTORY OF MUSICAL SCALES. 433 



flageolet 2 inches long- and liiivino- only thive holes. By partialh' or 

 wholly closing- the end of the tube with his hand he made use of the 

 resonator principle to lower the pitch of his notes; so he obtained a 

 compass of more than two octaves. The instrument is similar to 

 Prfetorius's .schtrelgeP except that it is shorter, and the accuracy of 

 the notes performed would depend almost wholly on the performer. 

 Later a traveling troupe appeared in European cities with seven 

 instruments called ocarinas. These are familiar to us, being on sale 

 everywhere. They are properly resonators, but the holes are more 

 numerous than in the instruments already considered and vary widely 

 in size. The scale, which the instruments furnish with more or less 

 precision, is not dependent on any simple principle, but is adjusted by 

 the maker by varying the sizes of the holes so as to conform to a scale 

 fixed on other instruments. 



V. THE INFLUENCE OF THE HAND. 



All the instruments of the three groups now discussed are ' ' fingered;" 

 that is, the acoustical dimensions of the vibrating string or mass of 

 air are varied as the player manipulates the fingers of one or both 

 hands. These instruments therefore involve a feature not associated 

 with drums and other instruments of percussion, or with primitive 

 harps. Instead of using the hand as a whole, the more delicate 

 fingers are utilized separately; so the simple instrument becomes in a 

 peculiar sense a part of the pWer's means of self-expression and is 

 specially responsive to his own moods, as many legends of the power 

 of music testify. But leaving to the musical writers such compari- 

 sons between instruments, it is important to the physicist to recognize 

 that the dimensions of the human hand have fixed absoluteh'^ some 

 dimensions of these instruments. 



The first thing to strike one, considering the hand from this point of 

 view, IS the fact that only with difiiculty can the five digits be brought 

 into line, so the thumb is not used on primitive instruments for finger- 

 ing, so far as observed. In the more highly developed flutes there 

 may be a hole for it on the back side, while on our own flutes, clari- 

 nets, etc, it governs one or more kevs. Similarly, the little finger 

 does not readily fall in line with the three longer ones, and, besides, is 

 much weaker. The remaining three fingers on a hand of medium size 

 can be brought into a space of about 1 cm., or spi'ead to span perhaps 

 12 cm, (.5 inches). To fix one's ideas before comparing these limits with 

 measures on some actual instruments, it will be convenient to recall 

 that on piano key])oards the distance between key-centers an octave 

 apart is 165 mm, {^Sh inches), the same as on a spinet of 1002; but on 

 the physiologically designed Janko keyboard, with the octave distance 



* Syntagma Miisicum, p. 39, pi, ix. 



