468 ENERGY MAY BE PROPAGATED BY VIBRATIONS of four tones in the ratios of 24 : 30 : 36 : 48 produces major chords. A scale constructed on these ratios will have the following frequency ratios: C Scale Ratios . . .
THE SCIENTIFIC BASIS OF MUSIC 469 When we compare the frequencies of E on the C and D scales above, it is seen that on the C scale E is 320, while it is 324 on the D scale. To make possible the major scale in each key would require so many notes that musical instruments would be too complex for the average person to play. In order to avoid the difficulty of having two different frequencies to represent one note, the international or equal-tempered scale was devised. In this scale middle C represents a frequency of 258.7, and the frequencies for each of the thirteen tones in each octave are equally spaced. The equaltempered scale produces a pitch for each key that is not ideal for best harmony, but the difference between the ideal pitch and the actual pitch can scarcely be recognized by the human ear. How Musical Instruments Produce Sounds. As already pointed out, all musical instruments consist of two parts: the generator and the amplifier. The generator supplies the energy and fixes the frequency, while the amplifier enlarges the sound by forced vibration or resonance. There are two main types of instruments: the stringed instruments and the wind instruments. Stringed Instruments. The generator in stringed instruments consists of strings or wires which are bowed (as in the violin), plucked (as in the harp or violin), or struck with a hammer (as in the piano) in order to produce the vibrations. The amplifier in such instruments may consist of a hollow wooden body (as in the violin) or a sounding board (as in the piano). The different frequencies are produced in stringed instruments by the use of strings of different length, diameter, and tension. The heavier strings are wrapped with wire in order to provide inertia without impairing their flexibility. The piano and the harp contain many strings of fixed length, diameter, and tension, whereas other stringed instruments contain only a few strings whose effective length can be