Bauhaus-Universität Weimar

Titel:
On sound and atmospheric vibrations, with the mathematical elements of music
Person:
Airy, George Biddell
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit38525/259/
INSTRUMENTAL MUSIC. 
243 
Now if we begin (as the most advantageous place) 
from one of the notes marked F, as F = 160, we have 
the following succession of perfect Fifths (the propor¬ 
tion of vibrations being always 2 : 3) : 
From 160 to 240, F to C ; 
From 240 to 360, C to Gr. 
From 360 to 540, G to D ; 
From 540 to 810, D to a note beyond a, 
vibrations = of those 
80 
Thus we find that, even beginning at the most advan¬ 
tageous place, we cannot have more than three consecu¬ 
tive perfect Fifths ; and, generally speaking, we cannot 
have so many. If we could put up with an error 
81 
represented by the factor — (either in the last interval, 
oU 
or distributed through the threaisptervals) we might 
proceed further. It will be seerie nat we must either 
o 
diminish the Fifth interval a little below - (“flatten the 
Fifths ”) or increase the Octave interval above 2 
(‘‘sharpen the Octave”); no compositor for the piano 
dares to recommend the latter course. TVe are inclined 
to think that it is best also to leave the Fifths un¬ 
altered. 
In the use of the violin, however, the temptation 
to retain the perfect Fifths is very strong. In the 
process of tuning, every interval of the fundamental 
16—2
        

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