QUALITY OF AUDITORY PERCEPTIONS. QOI 



The minor chord is just as agreeable to the normal ear as the major, 

 from which it differs in the fact that its third is a half-tone lower. It may be 

 readily shown by the siren that the minor third is produced by a number of vibra- 

 tions that have the relation of 6 : 5 to the fundamental tone; that is if 5 vibra- 

 tions occur in a given time in the fundamental tone, then 6 occur in the minor 

 third; and its vibration number is, therefore, f. 



From these relations of the major and minor chords, the relations of other 

 agreeable tones in the scale may readily be calculated, and it must be remembered 

 that the octave of a tone always yields the fullest and most complete harmony. 

 It is evident that if the major third, the minor third, and the iifth harmonize 

 with the fundamental tone, or keynote, they must also harmonize with its octave. 

 Hence, from the major third, with the vibration-ratio f, there is obtained the 

 minor sixth = |; from the minor third, with f, the major sixth = (fa =) |; 

 from the fifth, with f , the fourth = f . This process is known as the inversion 

 of the intervals. These tone-relations are, collectively, the consonant intervals 

 of the scale. 



The dissonant intervals of the scale may be estimated from these consonant 

 relations as follows: There are known the fundamental tone C, with the vibra- 

 tion-number i, the third E = f , the fifth G = f, the octave C 1 = 2. From 

 the fifth, or dominant, G there is constructed a major chord ; this is G, B , D l . The 

 vibration-ratio of these three tones is evidently the same as in the major chord 

 C, E, G. Hence, the number of vibrations of G : B, is as that of C : E. Substitut- 

 ing the values in this equation, we have f : B = i : f ; so that B = - 1 /-. Further, 

 D 1 : B = G : E; therefore, D : -\* = f : f, or D 1 = V, r E) an octave lower 

 = f. If a major chord is constructed upon F (subdominant), that is F, A, C 1 , 

 the relation of A : C 1 = E : G; or A : 2 = f : f, and A = f . Finally, F : A 

 = C : E; or F : f = i : f , and F = f. Consequently, all the tones of the scale 

 have the following vibration-ratios: I. C = i; II. D = f; III. E = f ; IV. 

 F = f ; V. G = |; VI. A = $; VII. B = V; VIII. C 1 = 2. 



Since 1885 it has been agreed to call a tone of 435 vibrations per second 

 a. The previous agreement was 440 vibrations for a. From this the absolute 

 number of vibrations for the tones of the scale is estimated, using the foregoing 

 vibration-ratios: C = 33 vibrations; D =37. 125; =41.25; F=44; 

 G = 49-5J A = 55; B = 61.875. The number of vibrations of the tones of the 

 octave above are found by multiplying these figures by 2. 



The lowest notes used in music are: double-bass E, with 41.25 vibrations; 

 piano C with 33; grand piano A 1 with 27.5, and organ C 1 with 16.5. The highest 

 notes in music are the piano c v , with 4224 vibrations, and d v on the piccolo-flute, 

 with 4752 vibrations in the second. 



The limits of audible sounds lie between 16 and 23 vibrations per 

 second, on the one hand, and 20,480 e vn (at the most a vn ) on the 

 other; they embrace about ioj octaves. These boundaries, however, 

 depend a good deal upon the intensity of the tone. Fewer vibrations than 

 1 6 in the second (organ-tones) are not heard as tones, but as separate, 

 rumbling impulses. Beyond the highest tones, produced by stroking 

 small tuning-forks, or by metallic rods, harmonica-tongues, or small 

 whistles, the ear likewise no longer appreciates the vibrations as tones, 

 but these cause instead a piercing, painful impression upon the ear. 

 The highest tones, which the ear is no longer capable of appreciating, 

 still affect the sensitive flame. 



The power of hearing high notes decreases with advancing age about an 

 octave. In rare cases tones of 35,000 vibrations can be perceived. During 

 contraction of the tensor tympani, tones of from 3000 to 5000 vibrations higher 

 may be heard, but rarely more. According to Lucae there are among normal 

 individuals, and especially among those hard of hearing, some whose ears are 

 better adapted for hearing deep tones, others for hearing high tones. He calls 

 them deep-hearing or high-hearing persons respectively. Both conditions are 

 disadvantageous for the normal perception of speech. The deep-hearing individ- 

 uals hear the high consonants imperfectly, for example ch in "Kirche"; while 

 the high-hearing individuals hear the deep consonants indistinctly, for example 

 ch in "Auch." Diminished tension of the sound-conducting apparatus decreases 



