78 On Perfect Musical Intonation. 
chord. Many apparently commence combinations may be made 
ekg by attending to t epartment of passing notes. 
. There is a certain saahenaen of sounds, which has occu- 
pie = a separate department of most treatises. It is called the 
“chord of the diminished seventh,” and is supposed to possess 
some peculiar and extraordinary qualities. It would, of course, 
tion hitherto, with proper respect, to pass it over in silence. It is 
defined to be, and undoubtedly is, exactly like the chord of the 
seventh, with the exception that the lowest note (of the chord of 
the seventh) is in the “diminished seventh,” raised a chromatic 
semitone. It is supposed that there exists in this combination a 
* harmony” which is peculiar* Parana different from that 
— in the , so yd 2, 
—o—o--F o Z- 
is the common chord of 6-2 eres =e: Et 
It is intended t 
pass from this to the: minor chord of A. Now, although we 
might pass from the chord of G, directly to that of 'A, it is judged 
expedient to have the melody of the lowest part, instead of as- 
cending by a whole tone at once, ascend by two steps, viz., a 
chromatic and diatonic semitone. The G# introduced, does not 
belong to the harmony, but is merely a a note. The 
matter is very easily understood in this first example. The sec- 
ond example is precisely like the first, with the exception that 
the seventh has been added to the chord, and it would have been 
equally easy to understand, had not the subject been darkened me 
the “words without knowledge,” of the theorists who hav 
written on the “diminished seventh.” For if in the first oda 
ple, G# isa passing note, why should its effect be changed by 
the addition of the seventh to the chord? It is stated by the 
theorists that the root of the chord at a is G, but that at 6 (when 
G is changed to G#) the root changes to E. Now, as by the 
root of a chord is meant a note with which the remaining notes 
will be ina simple ratio, and will harmonize, we will inquire 
_ how this root, E, major r third below G#, will harmonize with 
the other several notes of the chord. The ratios of the vibra- 
a of these several notes will be as follows: 
rom these ratios we see that 
E will be discordant with F, Fete Oe cage 
(making the ratio 20: 42, 4 
10:21), and G# will be dusts with D and F (25:36, 
the se {n the firs 
exanple, the cae me 
* Wm. Gardiner, on hig Fania Nature,” gives the following as his idea 
of this mer “Tf four minor thirds(!) be combined, they form the chord of the 
extreme flat seventh, excites in us han ar and alarm, because it is a monn of 
ines @3 escape us in the ebu 
worst passions, and are heard in the nes murmurs of wild beasts. 
