VIBRATION OF STRINGS 359 



iy placing the bar of wood previously mentioned under- 

 .eath it, and pressing upon the string with the finger 

 lose to the edge of the bar. The free portion nowbehaves 

 ike a shorter string, and if the edge of the wooden bar 

 : 3 placed at the division 60, the vibrating portion of the 

 tring will be half as long as previously, and its note will 

 ,Q an octave above the fundamental note of the string, 

 f 80 cm are allowed to vibrate (frds of the whole 

 length), the note will be the fifth ; at 90 cm (fths of the 

 tfhole length) it will be the fourth ; and if the vibrating 

 ^ortion has successively the lengths of 120, 106f , 96, 

 |0, 80, 72, 64, and 60 cm , the complete series of notes of 

 ! he gamut will be produced. 



Thus one-half of the original length produces the 

 ctave, that is, double the number of vibrations which pro- 

 uced the original note ; frds of the length makes f nds 

 f the original number of vibrations ; fths of the length 

 takes frds of the number, &c. ; or, generally, if the tension 

 c a vibrating string remains constant, the number of vibra- 

 \9ns in the same time varies inversely as the length of the 

 I'liKj. It is a consequence of this law that in instru- 

 =.ents with few strings, as in the violin, guitar, &c., a 

 i^eat variety of notes can be produced by pressing the 

 | rings with the fingers upon the ' finger board ' of the 

 Istrument, thus shortening them at will, and allowing 

 uying lengths to vibrate. 



[f the student has no musical ear and no good recollection for the 

 fx;h of notes, it is best to tune both strings of the monochord until 

 i unpractised ear cannot recognise any difference in pitch between 

 ^m. Both are then plucked with thumb and second finger at 

 13 same time, and if they are really in unison the sound must have 

 > miform intensity throughout ; but if this is not the case, the sound 

 'U become alternately louder and fainter. These alternations are 

 tmed leats (about which more will bs found further on) anl they 



