MUSIC AND SCIENCE. 
183 
Bach could have used a modern concert-grand piano, with its 
powerful long-continuing sounds, it is pretty certain he would 
never have advocated in preference to tiie other temperaments 
of his day the one called “equal;’’ and it took more than a 
century to bring the organists generally to accept that tun- 
ing. In our times occasionally practical instruments are 
made that provide for “Just” tuning in several keys; they are 
called “Enharmonic Instruments” and are usually made with 
reeds, which stand in tune much better than strings. It 
would contribute incalculably to musical education if a 
thousand such instruments were in use in this country. 
The facts that have been given, and others for which there 
is not time, show that many principles have been used in 
actual practice to fix the notes of a musical scale ; that most of 
these give results in close agreement for a very few intervals, 
but for the other intervals the results conflict ; that there is no 
preeminently natural scale; that our scale or scales, as de- 
fined by theorists or rendered by the best violinists, or fixed 
by good tuners, reveal elements as diverse as the elements of 
our language or our population. Our scale does not corre- 
spond exactly to any theory founded on the laws of any 
vibrating bodies or of the ear ; it is a compromise as every one 
knows, no interval, unless it be the Octave, having exactly the 
ratio of whole numbers; and even the higher Octaves of the 
piano are tuned sharp by every tuner I ever talked with. To 
further complicate matters the usual instruments cannot be 
kept in exact tune long, so the scales actually heard are quite 
uncertain. 
There have been numerous schemes on paper for new 
scales; the newest one is in a recent British patent; here the 
Twelfth, C to g, is taken as the unit, and divided into 24 
equal steps, each equal to nearly eight-tenths of a piano-semi- 
tone; so 15 of them make nearly a true Octave. Obviously 
the proposal is as arbitrary as one to introduce a new lan- 
guage, like Volapuk, which has no literature of its own. 
Returning again to non-European and primitive scales: 
Perhaps there is no blunder more common than to speak of 
Oriental scales as using very small intervals; if the scale 
