3 864] 



Mr. A. J. Ellis on Musical Chords. 



395 



tones, the intensity of the primary in each case being the same. The 

 results will be sufficient to explain the nature of chords on a quartett of 

 bowed instruments, but may be much modified by varying the relative 

 intensities of the combining tones. 



On examining a single compound tone, we may separate its partial tones 

 into two groups : the first disjunct, which will never beat with each other ; 

 the second pulsative, which will beat with the neighbouring disjunct tones. 

 Thus 



Disjunct. . 1, 2, 3, 4, 5, 6, - 8, 10, -,12, -, -, 16, 

 Pulsative . -, -, -, -, -7,-9, -,11, -, 13, 14, 15, -, 



Disjunct.. -, -, -,20, -, -, -, 24, -, -, -, -,30. 

 Pulsative. 17, 18, 19, -, 21, 22, 23, -, 25, 26, 27, 28, 29, -. 



When any compound tone therefore developes any of the harmonics 

 above the 6th, there may, and probably will, be beats, producing various 

 degrees of harshness or shrillness, jarring or tinkling. These, however, 

 are all natural qualities of tone, that is, they are produced at once by the 

 natural mode of vibration of the substances employed. But if we were to 

 take a series of simple tones having their pitches in the above ratios, and to 

 vary their intensities at pleasure, we should produce a variety of artificial 

 qualities of tone, some of which might be coincident with natural qualities, 

 but most of which would be new. This method of producing artificial 

 qualities of tone is difficult to apply, but has been used with success by 

 Professor Helmholtz to imitate vowel- sounds, &c. 



If, however, instead of using so many simple tones, we combine a few , 

 compound tones, the pitches of which are such that their primaries might 

 be harmonics of some other compound tone, then the two sets of partial 

 tones will necessarily combine into a single set, which may, or rather must 

 be considered by the ear as the partial tones of some new compound tone, 

 having very different intensities from those possessed by the partial tones of 

 either of the combining compound tones. That is, an artificial quality of 

 tone will have been created by the production of these joint harmonics. 

 Such an artificial quality of tone constitutes what is called a musical chord. 

 The two or more compound tones from which it is built up are its consti- 

 tuents. The primary joint harmonic is the real root or fundamental bass 

 of the chord, which often differs materially from the supposititious root 

 assigned by musicians. 



If the primaries of the constituents are disjunct, and all their partial 

 tones are disjunct, then the joint harmonics will be also disjunct, unless 

 some pulsative differential tones have been introduced. If, however, the 

 constituents have pulsative partial tones, the chord will also have them. 

 Such chords, which are generally without beats, and are only exceptionally 

 accompanied by beats, are termed concords, and they are unisonant or dis- 

 sonant according as the beats are absent or present. Their character 

 therefore consists in having the pitches of their constituents as 1, 3, 5, or as 



