Bauhaus-Universität Weimar

Titel:
Essay on Perfect Intonation; with Remarks, Showing the Practicability of Attaining it in the Organ; Together with a Brief Description of the Enharmonic Organ, of Messrs. Alley and Poole
Person:
Poole, Henry Ward
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit39335/24/
24 
Essay on Perfect Intonation. 
35. The Equal Temperament has this great advantage over 
all others—its twelve keys can all be used, as they are all tempered 
alike. The ear, too, is better satisfied when all the chords are 
equally out of tune, than when it listens to constant transition 
from a better to a worse chord. It can also be demonstrated that 
in equal temperament, the sum of the temperament of all the 
chords—if the instrument be used in the twelve keys—-will be 
less than in any olher. Any other than the equal system, is sim¬ 
ply an attempt to improve part of the thirds, by sacrificing, not 
only the fifths, but the remaining thirds. 
36. The following table will exhibit the temperament of the 
principal chords and intervals in the two systems. 
EQ.ÜAL TEMPEi 
HAM ENT. 
MEAN-TONE SYSTEM. I 
( Fifths, 
1 
1 2 
of 
comma Flat. 
l 
¥ 
of comma 
Flat. 
{ Fourths, 
] 
T2 
tt 
tt 
Sharp. 
i 
4 
tt tt 
Sharp. 
j Major Thirds, 
2 
y 
it 
tt 
Sharp 
Perfect. 
1 Minor Sixths, 
It 
it 
tt 
Flat. 
Perfect. 
( Minor Thirds, 
3 
3T 
tt 
tt 
Fiat. 
1 
¥ 
of comma 
Flat. 
\ Major Sixths, 
3 
¥ 
tt 
tt 
Sharp. 
1 
¥ 
tt tt 
Sharp.| 
Perfect Sevenths, 
■A 
tt 
tt 
Sharp. 
J¥ 
tt tt 
Sharp. 
Major tones and Ninths, 
1 
o 
ct 
tt 
Fiat. 
JL 
tt tt 
Flat, j 
Minor Tones, 
5 
F 
tt 
tt 
Sharp. 
1 
2 
tt tt 
Sharp. 
Diatonic Semitones, 
7 
1 2 
tt 
tt 
Flat. 
i 
tt tt 
Sharp. 
Chromatic Semitones, 
5 
1 2 
tt 
tt 
Sharp. 
1* 
tt tt 
Flat. 
Grave chro. Semitones, 
1 5 
1 12 
tt 
tt 
Sharp. 
tt tt 
Flat, j 
37. In the mean-tone system, the chords are tempered as above, 
only within the limits referred to in (33.); beyond these limits 
each is still further false by the addition of the diesis. As no pro¬ 
vision is made in either system of temperament for the chords of 
“ perfect sevenths,” it will be seen from the table that they will 
be extremely harsh, being false by about a comma and a half. 
These two systems embrace every advantage that can be found 
in any, and every intelligent tuner knows that no mixed system 
embraces advantages beyond either of the original temperaments. 
It is the quack and pretender only, who professes to unite in one 
system the advantages of both ; in other words, to favor the fifths, 
as they are in the equal, and the thirds, as they are in the mean- 
tone system. It is certain that no new system of tempering 
twelve sounds, so that they will perform correctly the office of 
several times that number, has been discovered during the last 
century, and we think we have shown that such a system never 
will be discovered, while the laws of nature and the mathematics 
continue the same. 
38. In whatever manner the temperament is set, the best chords 
are given imperfect, and this imperfection is so obvious that the 
common ear, entirely unskilled in music, can most readily distin¬ 
guish between chords that are tempered, and those that are tuned
        

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