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. XIV. 
All Greek tonal modes may be formed from the tones in the series 
of Fifths-— 
F — G — G — D — A — E — B.1 
Directly we proceed to the natural intonation of Thirds, the series 
of Fifths is interrupted by an imperfect Fifth, as in 
F — G — G — D — A — E — B 
where the Fifth D — A is imperfect. And when finally the sharp 
leading note is introduced, as by the use of G$ for G in A minor, 
the series is entirely interrupted. 
In the gradual development of the diatonic system, therefore, 
the various links of the chain which bound the tones together 
were sacrificed successively to the desire of connecting all the 
tones in a scale with one central tone, the tonic. And in exact 
proportion to the degree with which this was carried out, the 
conception of tonality consciously developed itself in the minds of 
The further development of the European tonal system is due 
to the cultivation of harmony, which will occupy us in the next 
But before leaving our present subject, some doubtful points 
have stiil to be considered. In the preceding chapter I have shewn 
that the melodic relationship of tones can be made to depend upon 
their upper partials, precisely in the same way as their consonance 
was shewn to be determined in Chapter X. Now this method of 
explanation may in a certain sense be considered to agree with the 
favourite assertion that 4 melody is resolved harmony,’ on which 
musicians do not hesitate to form musical systems without staying 
to enquire how harmonies could have been resolved into melodies 
at times and places where harmonies had either never been heard, or 
were, after hearing, repudiated. According to our explanation, at 
least, the same physical peculiarities in the composition of musical 
tones, which determined consonances for tones struck simultane¬ 
ously, would also determine melodic relations for tones struck in 
succession. The former then would not be the reason for the latter, 
as the above phrase suggests, but both would have a common 
cause in the natural formation of musical tones. 
1 [In the notation of App. XIX., 
F — C — G — 1) — fA - - fE — f J5,—Translator.]


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