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
offers no real difficulty. Using capitals for white, and small letters for 
black studs, its 14 notes are tuned thus :— 
C fcS, fD d, E fdfî, F ft, G tgît, A fa, B bb. 
The directions to the tuner are : Tune the following eight major chords 
without beats, putting low D on the usual D stud, D on the usual US stud, 
Dît on the usual Eb stud, and high A on the usual Ab stud : Bb, low D, F ; 
F, A, C; C, E, G; G, B, D ; D, Fit, high A ; A, CS , E ; E, Gît, B ; 
B, Dît, Fît. The concertina is ordinarily tuned in the mean tone tem¬ 
perament, with the studs as 
C ctt, D dît, E eb, F ft, G g#, A ab, B bb, 
and sometimes in equal temperament, in which case dît, eb, and gît, ab 
are tuned as unisons, and the double studs merely facilitate fingering. I 
keep two concertinas thus tuned, and one tuned on the Pythagorean 
system, for constant comparison with just intonation. 
2. Just Experimental Harmonium. 
Intonation.—For ordinary lecture and illustrative purposes, this is the 
cheapest and best instrument, and it is almost indispensable for those who 
wish to study the musical effects mentioned in Part 
III., above. It contains the portion of a heptadecad 
shewn in the margin, and hence contains the duo- 
dene of C -with the exception of FÖ, the whole 
decad of C, and the major scales of fEb and fAb. 
The two last shew vertical modulation. Again, 
fEb major or fAb major to C decad shew's right 
lateral, and inversely, C decad to fEb major or fAb major shews left 
lateral modulation. The F and f F shew the influence of a comma, and 
the difference between the just triad, Db -f F —f Ab, and the Pythagorean 
triad, Db fF j fAb. Also in the key of fEb major the difference 
can be shewn between the true minor chord, F — fAb -f C, and the false 
minor chord, fF | fAb + C. This instrument also contains the German 
Sixth Db -p F — fAb x +2 B, which is a close imitation of the chord 
of the natural Seventh ; the Italian Sixth, Db + F x2 +B, and the 
French Sixth, Db + F ... G + B. The five tones, Db, fAb, fEb, fBb, F, 
allow of playing all Scotch airs in Five-Fifths scales on the black digitals 
(p. 400, note 1). Using capitals and small letters for the black and white 
keys, they are arranged thus :— 
C db D feb E F ff G fab A fbb B. 
The f F is placed on the Fff digital, and the other fingering is normal. 
The following directions were found sufficient for the tuner of a com¬ 
mon four-octave harmonium, which he tuned in my presence in two hours, 
fBb D 
fEb G B 
fAb C E 
Db F A


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