8l2 PERCEPTION OF PITCH. 



series of holes in turn, we distinguish successively the four tones of the accord (major chord 

 with its octave) ; when all the four series are blown upon simultaneously, we hear in complete 

 purity the major chord itself. The relative number of the holes in the four series indicates in 

 the simplest manner the relative pitch of the tones of the major chord. While one revolution 

 of the disc is necessary to produce the fundamental ground-tone (key-note or tonic) with 40 

 condensations and rarefactions of the air in order to produce the octave, we must have 

 double the number of condensations and rarefactions during one revolution in the same time. 

 Thus, the relation of the number of vibrations of the Ground-tone or Tonic to the Octave next 

 above it, is 1 : 2. In the second series we have 50 holes, which causes the pitch of the third ; 

 hence, the relation of the Ground-tone to the Third in this case is 40 : 50, or 1 : lJ-$, i.e., for 

 every vibration of the Ground-tone there are vibrations in the Third. In the third series are 

 60 holes, which, when blown upon, yield the fifth ; hence, the ratio of the Ground-tone to the 

 Fifth in our disc is 40 : 60, or 1 : lj-f. In the same way we can estimate the pitch of the 

 Fourth tone, and we find that the number of vibrations of the First, Third, Fifth, and Octavo 

 are to each other as 1 : | : : 2. 



Th<- minor chord is quite as characteristic to a normal ear as the major. It is distinguished 

 essentially from the latter by its Third being half a tone lower. We can easily imitate it by 

 the siren, as the Minor Third consists of a number of vibrations which stand to the Ground- 

 tone as 6 : 5, i.e., if 5 vibrations occur in a given time in the Ground-tone, then 6 occur in the 

 Minor Third ; its vibration number, therefore, is . 



From these relations of the Major and Minor common chords, we may calculate the relative 

 tones in the scale, and we must remember that the Octave of a tone always yields the fullest 

 and most complete harmony. It is evident that as the Major Third, and Minor Third, and the 

 Fifth harmonise with the fundamental Ground-tone or key-note, they must also harmonise with 

 the Octave of the key-note. We obtain from the Major Third with the number of vibrations 

 I, the Minor Sixth f, from the Minor Third with f, the Major Sixth (&-) I; from tne Fi fth 

 with $, the Fourth . These' relations are known as the "Inversions of the intervals." These 

 n-lations of the tones are, collectively, the consonant intervals of the scale. The dissonant 

 stages, or discords, of the scale can be obtained as follows : Suppose that we have the Ground- 

 tone or key-note C, with the number of vibrations =1, the Third E = |, the Fifth G = f, and the 

 Octave 2, we then derive from the Fifth or Dominant G a Major chord this is G, B, D 1 . 

 The relative number of vibrations of these 3 tones is the same as in the Major chord of C|, C, E, 

 G. Hence, the number of vibrations of G : B is as C : E. When we substitute the values we 

 obtain $ : B-l : { i.e., B= V- But D : B = G : E ; so that D : V * : h **., D'-V, or 

 an octave lower, we have D = |. Deduce from F (subdominant) a Major chord, F, A, C 1 . The 

 relation of A : C -E : G, or A : 2-| : $, i.e., A-f. Lastly, F : A = C : E, or F : = 1 : f, 

 i.e., F |. So that all the tones of the scale have the following number of vibrations : I., 

 C-l; II.,D=8; III., E=* ; IV., F = $; V., G=$; VI.; A = f ; VII., B=V; VIII., C'-=2. 

 Conventional Estimate of Pitch. Conventionally, the pitch or concert-pitch of the note, a, 

 is taken at 440 vibrations in the second (Scheibler, 1834), although in France it is taken at 435 

 vibrations per second. From this we can estimate the absolute number of vibrations for the 

 tones of the scale: C = 33, D-37'125, E-41'25, F-44, G = 49'5, A = 55, B = 61'875 vibra- 

 tions. The number of vibrations of the next highest octave is found at once by multiplying 

 these numbers by 2. 



Musical Notes. The lowest notes used in music are the double-bass, E, with 41*25 vibra- 

 tions, pianoforte C with 33, grand piano A 1 with 27 '5 and organ C 1 with 16*5. The highest 

 Inotes in music are the pianoforte c T with 4224, and d v on the piccolo-flute, with 

 4752 vibrations per second. 

 Limits of Auditory Perception. According to Preyer, the limit of the 

 perception of the lowest audible tone lies between 16 and 23 vibrations 

 per second, and e Tlil with 40,960 vibrations as the highest audible tone ; 

 so that this embraces about 11 J octaves. 

 [Audibility of Shrill Notes. This varies very greatly in different persons ( Wol- 

 laston). ^ There is a remarkable falling off of the power as age advances (Galton). 

 For testing this Galton uses a small whistle made of a brass tube, with a diameter 

 of less than ^th of an inch (fig. 596). A plug is fitted at the lower end to lengthen 

 or shorten the tube, whereby the pitch of the note is altered. Amongst animals 

 Galton finds none superior to cats in the power of hearing shrill sounds, and he 

 Fig. 596. attributes this "to differentiation by natural selection amongst these animals until 

 Galton's the y have , the P wer of hearing all the high notes made by mice and other little 

 Whistle C1, ' atim ' s they have to catch."] 



' Variations in Auditory Perception. It is rare to find that tones produced by 

 more than 35,000 vibrations per second are heard. When the tensor tympani is contracted, the 

 1< r .ption may be increased for tones 3000 to 5000 vibrations higher, but rarely more. Patho- 

 logically, the perception for high notes may be abnormally acute (1) When the tension of the 



