620 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



sound. Air is the common medium of sound-force, in which waves of 

 density move outward in all directions from the point of impact or of 

 original agitation. Air waves moving irregularly, produce the sensation 

 called noise, hut when regular or isochronal, they generate a musical 

 sound. 



The loudness of sound depends on the density of the wave, which may 

 increase or diminish without changing the rate of vibration, the same as 

 the oscillations of a pendulum may vary in extent, but not in number in a 

 given time. 



TJie qualily of sound, which the French call timbre, probably depends on 

 the order in which the particles of air in each wave are arranged. Waves 

 of water change their form, as they near the shore, without changing their 

 velocity; we may, therefore, compare the same note of a trumpet, when 

 round and full, or when harsh and shrill, to smooth or crested ocean waves. 



The pitch of sound depends on the velocity of air waves. The lowest or 

 gravest sound has the smallest number of waves, and the highest or most 

 acute sound has the greatest number, in a given time. Any change in 

 pitch is thereft)re the result of a change in the rate of vibration of a series 

 of waves. The lowest sound which can be perceived by the most sensitive 

 human ear is caused by air waves moving at a little less than the rate of 

 sixteen per second, while the highest sound is the result of a rate of more 

 than sixteen thousand waves per second. 



Music is a combination of sounds varying in pitch, timbre, intensity, 

 duration and in distances of time between them. Melody is a succession 

 of single sounds, and harmony a succession of chords, that is, several dif- 

 ferent sounds at the same time, which harmonize with each other. As the 

 highest expression is derived from Contrasts, discords and even noise are 

 introduced to give greater effect to pure harmony. 



A musical scale consists of a series of sounds at fixed intervals, in which 

 the first sound and the eighth sound above it, so nearly resemble each 

 other, that they are distinguished by the same letter. The cause of this 

 resemblance arises from the fact that the eighth note is produced by a 

 series of waves, just double the number of tliose producing the first note. 

 If the scale be further extended upward, the fifteenth sound will be the 

 result of four times as many waves as the first, and is consequently dis- 

 tinguished b}'- the same letter. The distinct series therefore consists of 

 seven sounds, and any extension. of the scale, above all below, will be the 

 whole or part of a similar series. Great difficulty has arisen in compre- 

 hending musical changes by what the speaker regarded as an error in 

 counting. The notes distinguished by the same letter should also be dis- 

 tinguished by the same number. The tonic or key note should not be 

 'called the first, eighth or fifteenth, but always the first of three similar 

 series of notes. 



The greatest complication is involved in changing the pitch of the tonic 

 or fundamental sound, because the seven sounds of a series are not at equal 

 intervals, that is, the number of waves producing the so called octave 

 above, divided by seven, will not give the rate of increase in waves 

 required for each note in regular succession. The seven sounds of the 



