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. XVII. 
cl — / — ci, and may lienee be called the false minor triad, is, 
as Hauptmann has correctly shewn, dissonant, and on justly- 
intoned instruments it is very decidedly dissonant. It sounds 
almost as rough as the chord b — d —/. If in G major, without 
confounding d with d, we form the cadence 1 or 2 
1 2 
the chords a' — cl" —f" and f' — of — d" —f" are quite as dis¬ 
sonant in their effects as the following b' — d" — f" and g' — b' — 
cl" —f". But on account of the incorrect intonation of our 
musical instruments we cannot produce the same effect without 
combining an inverted chord of the Seventh with the subdomi¬ 
nant in the cadence, as / — a — c' — cl'. Hauptmann doubts 
whether in practice the false minor chord of the key of G major 
can be distinguished from the minor chord of D. I find that this 
is most distinctly and undoubtedly effected on my justly-intoned 
harmonium, but allow that we cannot expect the correct intonation 
from singers. They will involuntarily pass into the minor chord, 
unless the progression of the parts which execute D, strongly 
emphasise its connection with the dominant G.1 
1 [The chord on the Second of the major scale is in fact the crux of the translation 
of tempered into just intonation, as I have already intimated (p. 504, end of note). It 
is very easy to play ex. 1 and 2, and a third example as 
a’ \d" f" f a' %d" f> f a \d" 
b' d" f" and a' b' d" f and a' V d'' 
c" c" c" C c" c" e" f V d" 
e' c" c" 
and the effect is not bad. In the first the %d" might be held on to the second chord, as 
b' \d" f, without materially increasing the harshness of the dissonance, but in the 
second this would give g' b' \d" f", where the low Fifth is very harsh. • In the second 
case, then, there is least harshness in playing d" in both chords. And in both cases 
there is most smoothness in playing them as just written. The effect is one on which 
I have repeatedly experimented, but I find that the small interval %d" d" in the 
highest or lowest part, produces a strange effect, which in singing, and perhaps on the 
violin, seems to be overcome by a glide, if the other voices are strong enough to pull 
this voice out of its course, even though the words and parts are written so as to 
imply that this note is sustained. When the d" is in the principal partin the melody, 
as in the third example, I find it best on the whole not to play as written, %d" d", but 
to sustain d". In some cases an attempt to avoid the dissonance, which is really 
harsh, would lead to such melodic phrases as d\dd, which would be simply impossible


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