c scale. If we divide the string into three parts, the result
will be a sound called the large fifth; a division into four parts gives
the next higher octave of the bass; into five, gives the sound known as
the large third, commonly called major third; into six, the octave, or
next higher repetition, of the large fifth; into seven, the small
seventh; into eight, the third repetition of the octave of the bass. The
progression thus far is hence: Bass--1st octave of bass--large fifth--2d
octave of bass--large third--1st octave of large fifth--small
seventh--3d octave of bass. Employing the alphabetical names of the
notes (always ascending): C--C--G--C--E--G--B flat--C.

This progression may truly be called _natural_, as it is that into which
the string naturally divides itself when stricken. An attentive ear can
readily distinguish the succession of sounds as far as the small
seventh. The longer bass strings of any piano of full tone and resonant
sounding board will suffice for the experiment. These are also the
natural notes as found, with differences in compass, in the simple horn
and trumpet, and the phenomenon is visibly shown in the well-known
experiment of grains of sand placed on a brass or glass plate, and made
to assume various forms and degrees of division under the influence of
certain musical sounds.

This is not the place to elaborate the subject, or to show the
progression of the natural scale as produced by further subdivisions of
the string. Suffice it to say that the remaining notes of the common
diatonic scale are _selected_ (with some slight modifications) from
sounds thus produced. This scale cannot then be considered, in all its
parts, as the fundamental, natural one. Nature permits to man a great
variety of thought and action, provided always he does not too far
infringe her organic laws. She may allow opposing forces to result in
small perturbations, but fundamental principles and their legitimate
consequences must remain intact.

No one can ponder upon the above-mentioned harmonic foundation of the
musical scale without conceiving a new idea of the beauty and
significance of that glorious art and science which may be proved to be
based upon laws decreed by the Almighty himself. The one consideration
that, in all probability, no single musical sound comes to us alone, but
each one is accompanied by its choir of ascending harmonic sequences, is
sufficient to afford matter for many a wholesome and de