The music of different periods in the world's history has rested upon the various scales recognized during those periods as fundamental, which scales have been more or less complete as they have approached or receded from the absolutely fundamental scale as given by nature. The scales now in use are not identical with the natural scale, but are, in different degrees, _derived_ from it. The natural scale is, in its commencement, harmonic, and is found by the consideration of the natural progression of sound consequent upon the division and subdivision of a single string. It ought to be familiar to every student of acoustics. The sound produced by the striking or twanging of a single string (on a monochord) is called the tonic, and also, from its position as the lowest note, the bass. If we divide this string in half, we will obtain a series of vibrations producing a sound the _same in character_, but, so to speak, _doubly high in pitch_. This sound is named the octave, because it is the eighth note in our common diatonic 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.