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. 
The great gaps in the scales between e and / in the first, and 
between G and c in the second are filled up by tones related in the 
second degree. Since the tones related to the Octave can only be 
repetitions of those directly related to the tonic, the next tones to 
be considered are those related to the upper Fifth g, and lower 
Fifth F, and these are d (the Fifth above the upper Fifth g) and B\} 
(the Fifth below the lower Fifth F). We thus obtain the scales 
1 ) Ascending c — d — w/ — g — a — w- d 
iv a a a 2 
2) Descending G—E\> — F—G—wjB\> — c 
1 f I I V6 2 
But in place of the tones more distantly related to the tonic 
in the first degree, both systems of tones related in the second 
degree might be used, and this would give a scale resulting from 
a simple progression by Fifths, as 
3) c — — — g — — 
12 A3. 13 2 
Then there are also some more irregular forms of this scale of 
five tones, in which the major Third e replaces the Fourth /, 
which is more nearly related to the tonic c. This transformation 
is probably due to the modern preference for the major mode, and 
it has made its appearance in very many Scotch melodies. The 
scale is then 
4) c —■ d — e — ^ g — a —■ w d 
1 v A 3 a 2 
X 8 4 2 3 ^ 
The examples of a similar exchange of the Fifth g for the 
minor Sixth a\) are doubtful. This would give the scale 
5) G — ^ E\) — F — w- A\} — B\) — g 
1 A A A 1.6 2 
1 5 3 5 9 " 
The scale c — w e\}—/—g—a — w c 
1 _AAA 2 
X 5 3 4 3 -1 
in which all the notes are related in the first degree, but for which 
the nearest notes to the tonic, either way, are a Tone and a Semi¬ 
tone distant from it, has not yet been discovered in actual use. 
The above five forms of the scale of five tones can all be so


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