76 On Perfect Musical Intonation. 
viz.: 1:2:3:4:5:6:7:8:9:10. All of these chords are per- 
fectly harmonious, and in all respects appreciable by the ear. 
The last contains within itself every musical chord and _har- 
mony, that can be obtained from ratios whose terms do not ex- 
ceed ten. Examples of these chords, as written, we here exhibit. 
ggleghgeyelga at 
= Se 
Resolution. 
nS 
The vibrations in the various ratios of the full chord of the 
tenth may be represented to the eye by the ADE diagram. 
E.10 ‘ ’ ’ 1 0 
} Mixon Tone, 
D. 9 2 ‘ ‘ ‘ ’ ' 9 
t Masor Tone. 
Cc. 8 ‘ ’ A ' 8 ) Extenpep 
§ Seconp(?) 
Bb. 7 ‘ “ 2 : : 7 ! DIMINISHED 
Trev (2) 
G. 6 ’ ‘ 6 Be 
THIRD. 
Es : 5 es 
as | ; THIRD. 
Foourts 
G8 8 
t Firra 
O..2 ) 
t Octave. 
me 2 ; ies 
Assuming any length of time,.for a single vibration of the lowest 
note, it is evident that the other several notes of the chord will 
in the same time perform Fivarbon equal in number to the num- 
bers expressing their ratios respectively ; and that at the expira- 
tion of this time, the vibrations of every note will coincide with 
each other. There are also points within this assumed time in 
which two, three, four or more of these notes will coincide in their 
vibrations. These coincidences are represented in the diagram by 
dotted lines. By means of the diagram, the vibrations of any other 
chord, as the common chord, the chord of the seventh, ninth, &¢., 
may be examined, as they are all contained in the full chord of 
the tenth. The difference i in the effect of the different chords is 
seen in the less frequent coincidences in the more complicat 
chords. tee seeare ie much more simple than the major 
ee 
; 
§ : 
f 
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