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. 
The two first of these triads are considered in musical theory 
as the fundamental triads from which all others are deduced. 
They may each he regarded as composed of two Thirds, one major 
and the other minor, superimposed in different orders. The chord 
G E G, in which the maj or Third is below, and the minor above, is 
a major triad. It is distinguished from all other major triads by 
having its tones in the closest position, that is, forming the smallest 
intervals with each other. It is hence considered as the funda¬ 
mental chord or basis of all other major chords. The triad G Efy G, 
which has the minor Third below, and the major above, is the 
fundamental chord of all minor triads. 
The next two chords, G F A and G F A\}, are termed, from their 
composition, chords of the Fourth and Sixth, \G to F being a 
Fourth, and G to A a major, but G to A\) a minor Sixth]. If we 
take Gy instead of G for the fundamental or bass tone, these chords 
of the Fourth and Sixth become Gy G E and Gy G E\). Hence we 
may conceive them as having been formed from the fundamental 
major and minor triads G E G and G Eh tr, by transposing the 
Fifth G an Octave lower, when it becomes G y. 
The two last chords, G E\> A\) and G E A, are termed chords of 
the Third and Sixth, or simply chords of the Sixth, [G to E being 
a major, but G to E\> a minor third ; and G to A a major, but G 
to A\) a minor Sixth]. If we take E as the bass note of the first, 
and E\) as that of the second, they become E G c, E\) G c, respec¬ 
tively. Hence they may be considered as the transpositions or 
inversions of a fundamental maj or and a fundamental minor chord, 
G E G, G Et> G, in which the bass note G is transposed an Octave 
higher and becomes c. 
Collecting these inversions, the six consonant triads will assume 
Appendix XVII. there will be found a description of an harmonium with just in¬ 
tonation. But for merely experimental purposes, a means of tuning an ordinary five- 
octave harmonium, and an English concertina (either of which can be obtained for a 
few pounds), so as to give all the theoretical forms of the major and minor chords in 
just intonation, will be added in App. XIX. Sect. Gr. 1,2. All who wish to have an 
aural acquaintance with such chords (without which much of the text will be scarcely 
more than words) are strongly recommended to avail themselves of one or the other 
of these simple instruments. No instruments are better suited for distinguishing 
harshly between just and tempered intonation. Pianofortes and monochords are 
practically useless for such purposes. On the experimental harmonium these chords, 
can be played as in the text. On the justly intoned concertina the contrast of major 
and minor cannot be attained, unless the chords are replaced by 1) ë g't b',. 2) ë g' bf; 
3) ë a' c"t, 4) ë a' c"; 5) ë g' ë', 6) ë g'I ë% .—Translator.]


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