Bauhaus-Universität Weimar

On the sensations of tone as a physiological basis for the study of music. Translated with the author's sanction from the third German edition, with additional notes and an additional appendix by Alexander J. Ellis
Helmholtz, Hermann von
Chap. XII. 
and form a major Third, because in any other position they would 
produce an unsuitable combinational tone. The fundamental tone 
and the Fifth must never form an Eleventh, because in that case 
the resulting combinational tone would make them into a major 
triad. These conditions can be fulfilled by only three positions'*of 
the minor chord, as follows :— 
The most Perfect Positions of the Minor Triad. 
12 3 
r; u 1 
I V 
L * 
r 1 — 
1 (Ei t? w 
V p 12-- 
The remaining positions which do not sound so well are :— 
The less Perfect Positions of the Minor Triad. 
4 5 6 7 8 9 10 11 12 
The positions 4 to 10 each produce two unsuitable combina¬ 
tional tones, one of which necessarily results from the fundamental 
tone and its third ; the other results in 4 from the Eleventh O G, 
and in the rest from the transposed major Third E\) G. The two 
last positions, 11 and 12, are the worst of all, because they give rise 
to three unsuitable combinational tones.1 
The influence of the combinational tones may be recognised by 
comparing the different positions. ’Thus the position 3, with a 
1 [On the experimental harmonium of Appendix XIX. these chords maybe played 
as written ; but on the just concertina there named they should be taken from the 
minor triad e g b, which will allow of their being immediately contrasted with the 
examples on p. 334, note. They will then be as follows, the first numbers shewing


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