On Perfect Musical Intonation. 17 
tone, for the reason that every vibration of one of its notes, coin- 
cides with every second vibration of the other, while in the 
major tone it is necessary that that one note perform eight, and 
the other we vibrations before there is any coincidence. And 
from this, will appear the increased difficulty in tuning, as the 
chords become more complicated. 
18. From the introduction of the perfect seventh is obtained 
appear. 
At a, Bb is the fourth of the 
scale of FE‘, while at 8, it is the 
perfect seventh to C; and the © Oia 
last Bb is lower than the first Gzpe - 
by about a comma and a quar- | 
ter. Consequently in singing 
the melody with the accompa- ee iM te 
niment as written, the voice will give the second BD lower than 
the first by that interval. It will be found on experiment, that a 
good natural singer, if asked to sing the melody with this accom- 
paniment, will naturally, and no doubt unconsciously, make the 
distinction referred to. 
As it has been stated that musical ratios, in order to 
be harmonious, must not exceed a certain limit of simplicity, 
the question naturally arises, shall no other notes be heard to- 
gether in music but those which have, each to every other, 
these simple ratios? Abundant examples can be selected from 
the best composers, in which notes are heard together, which 
make more complicated ratios, and which cannot be rega 
harmonious. To illustrate this we take the following 
example. With the chord of the 
dominant seventh as accompa- 
niment, are heard at the same 
time the notes D, C#, D and D#. 
The melody in the first and third 
hotes is in harmony with the 
accompaniment. But though C# and DF appear, while the 
chord is sounding, they can make no harmony with it. Neither 
are they discordant. ‘The ear regards the progression of these 
notes as parts of the melody, and only requires that the melodié 
intervals (diatonic and chromatic semitones ) be given truly, with- 
out regarding the ratios which the accidentals make with the 
accompanying chord. In other words, these are PASSING NOTEs, 
which have nothing to do with the harmony, and are to be 
thrown out when we would find the notes which compose the 
