DEN-SMOEE] TETON SIOUX MUSIC 41 



the compound tone of their root as well as the major chords; their 

 third, indeed, does not form any part of this compound tone."^ In 

 this connection it is observed that the tonality of a song does not 

 determine its general character as much in Indian music as in that 

 of the white race. The melodic feeling in many Chippewa and Sioux 

 songs seems to be for the interval between successive tones, while 

 the melodies of the white race are based upon "keys," which are 

 groups of tones having a systematic and definite relation to a key- 

 note. Subsequent analyses will show that the prevailing interval 

 of progression in a song may be minor, though the interval between 

 the keynote and its third is major, thus giving a predominance of 

 minor intervals in a song of major tonality.^ 



Tahle 2A. — Before considering this phase of analysis let us recall 

 certain fundamental principles of the musical system developed by 

 the white race. In that system the tonic chord, or triad on the key- 

 note, may be said to be the framework of the group of tones called 

 a key. This chord is based on the laws of acoustics and comprises, 

 if the chord be major, the first four overtones of the keynote or fun- 

 damental tone. It is understood, of course, that the tone produced 

 by a stretched strmg or other body capable of strong sympathetic 

 vibration is a compound, not a simple sound. In addition to the 

 tone produced by the vibrations of the entire body there are higher 

 tones which are less distinct, but which can be perceived. These 

 are called overtones, or upper partial tones. 



Helmholtz says: 



We must . . . not hold it to be an illusion of the ear, or to be mere imagination, 

 when in the musical tone of a single note emanating from a musical instrument, we 

 distinguish many partial tones. . . If we admitted this, we should have also to 

 look upon the colours of the spectrum which are separated from white light, as a 

 mere illusion of the eye. The real outward existence of partial tones in nature can 

 be established at any moment by a sympathetically ^'ibrating membrane which 

 casts up the sand strewn upon it.^ 



The series of these upper partial tones is precisely the same for all compound mu- 

 sical tones which correspond to a uniformly periodical motion of the air. It is as 

 follows: 



The first upper partial tone ... is the upper Octave of the prime tone, and makes 

 double the number of vibrations in the same time. 



The second upper partial tone ... is the Fifth of this Octave . . . making three 

 times as many vibrations in the same time as the prime. 



The third partial ... is the second higher Octave .' . . making four times as 

 many \dbrations as the prime in the same time. 



The fourth upper partial tone is the major Third of this second higher Octave . . . 

 with five times as many vibrations as the prime in the same time. 



. . . And thus they go on, becoming continually fainter, to tones making 7, 8, 9, 

 &c., times as many vibrations in the same time, as the prime tone.* 



1 Holmholtz, T)3e Sensations of Tone (translated by A. J. Ellis), pt. 3, p. 300, London, 18S5. 



2 See analyses of sangs Nos. 175, 177, 187. 



3 Helmholtz, op. cit., pt. 1, p. 48. 

 «Ibid., p. 22. 



