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
although it contains two tones foreign to the original mode, as 
otherwise we could not prevent the prevalence of the impression 
that a is the tonic and a — c — e the tonic chord. It follows, 
therefore, that the mode of the minor Sixth must he still less 
consistent in its harmonisation and still more loosely con¬ 
nected than the minor mode, although it admits of very con¬ 
sistent melodic treatment. It contains three essential minor 
chords, namely the tonic e — g — b, the subdominant a—a — e, 
and the chord which contains the two tones slightly related to the 
tonic d—/—a. It is exactly the reverse of the major mode, 
for whereas that mode proceeds towards the dominant, this mode 
proceeds towards the subdominant. 
Major : / — a — c — e — g — b — d 
Mode of I I ‘ I 
minor Sixth : b\> — d\> —f — — c — ë\> — g 1 
For harmonisation the difference of the two cases is, first, that 
the related tones introduced into the scale by the subdominant/, 
jiamely b\> and are not partials to the compound tone of the 
subdominant, whereas tones b and d, which are introduced by the 
dominant, are some of the partials of the tonic ; and, secondly, 
that the tonic chord always lies on the dominant side of the tonic 
tone. Hence in the harmonic connection, the tones and d[> 
cannot be so closely united with either the tonic tone or the tonic 
chord, as is the case with the supplementary tones introduced by 
the dominant. This gives the mode of the minor Sixth, when 
harmonised, a kind of exaggerated minor character. Its tones 
and chords are certainly connected, but much less clearly and 
intelligibly than those of the minor system. The chords which 
can be brought together in this key, without obscuring reference 
to e as the tonic, are d minor and / major on the one hand and b 
major on the other, chords which in the major system could not 
1 [In the notation of Appendix XIX., 
f + a — c + e — g + b — d 
bb — db + / — fab + c — feb + g. 
Observe here that fJb, which should form the last term according to the former 
scheme, is omitted. See No. o, p. 461. In the major mode there is formed one chord 
a Fifth above, and another a Fiftli below the tonic. Whereas in the mode of the 
minor Sixth, no chord is formed on the Fifth above. A more complete analogy is 
obtained by comparing G pâmama (of Appendix XIX., Table III., C, No. 1) with F 
mimipi {ibid. No. 54) thus— 
c + e - g + b - d + fn -fa 
bb — db + / - fab + c - fcb + g. Translator.]


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