Ke 
s 
4 
Se eee Rr ete oe ne eg, Se ee 
HT, W. Poole on the Musical Ratios. 291 
Next, the fifth, 2 : 3, is “very pleasing, but the consonance is 
hardly so perfect as in the last instance; there is a barely per- 
ceptible roughness here. Next to the octave, this is the most 
pleasing combination.” The “roughness of the fourth, 3 : ; 
is a little more pronounced.” The harmony of the major third 
: 5, is declared “less perfect,” and that of the minor third, 
5 : 6, “usually [?] less perfect still.” And he declares the law 
that “the combination of two notes is the more pleasing to the 
ear, the smaller the two numbers which express their vibrations.” 
No ratio higher than 5 : 6 is mentioned, except 13 : 14, which 
is declared “altogether discordant.” As a reason, it might be 
stated that the prime 13 is far beyond the limit of musical 
ratios. The ratios 6: 7,5: 7,7: 9, and all reference to the 
chords derived from seven, are omitted by Professor Tyndall in 
this course of lectures, But he says that musicians have chosen 
the simple intervals “empirically, and in consequence of the 
pleasure they gave, long before any thing was known regarding 
eir numerical simplicity,” 
If musicians have chosen the most simple intervals as most 
pleasing, it is not true that they have considered fifths as in- 
ferior to octaves, or the latter as less pleasing than unisons, 
properly combined, are entirely perfect and equally pleasing, 
one with the other. Beyond these limits, all are incomprehen- 
ed fifths as “ perfect concords,” thirds, as 
er and worst of all, the beautiful concord of the seventh, 
73 
1m; viz., “beats.” And, following Helmholtz, he says that 
ve— 
Here our rates of vibration, are 
512—256; difference—256. 
It is plain that in this case we can have no beats, the difference be- 
ing too high to admit of the : ae | 
et us now take the fifth, Here the ratios of vibration, are 
? 
