# Traditional Hopi Songs - online book

## Native American Songs With Sheet Music, Notation & Commentary

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 THE PHONOGRAPHIC METHOD                           31 The span in pitch of an interval is smaller as its ratio approaches unity, becoming zero at this ratio, in the interval of unison. The amount of a distor­tionwill therefore be zero when the product of the ratios This will occur when one of these ratios is the reciprocal of the other, that is, when the variation in the rate of the cylinder from n to v is in the same pro­portion in the reproduction as in the inscription. When this ratio of varia­tion is unity, we speak of the rate as constant. A constant speed in both inscription and reproduction is therefore a special form of the conditions for an undistorted copy of an inscribed music. Moreover, according as the pro­duct of the above ratios approaches unity, that is, as one comes nearer to being the reciprocal of the other, the distortionwill be smaller. A special form of these conditions is given in the close approach of both ratios to unity. In other words, the distortion of a texture will be inconsiderable when in both its inscription and its reproduction the rate of the phonograph has varied very little from perfect constancy. Further, the motor of the phonograph being specially designed to give the cylinder as nearly constant a velocity as possible, this proposition may be simply converted, and we may affirm that if a texture of tone is little distorted in phonographic reproduction it is be­cause the rate of the instrument has been very closely constant during both inscription and reproduction. The following observations of where and v are different segments in the reproduction of a constant note ac­cordingly afford data for estimating the degree of approach of the phono­graph cylinder to constancy of rotation during the performance of each of its functions. The physical cause of tone is the regularly periodic vibration of the body producing it, this vibration being more or less rapid according as the tone is higher or lower in pitch. It is found that if two tones sufficiently near together in pitch be produced simultaneously, the resultant sound is no longer constant in intensity, but regularly waxes and wanes. The number of these pulsations, or beats, as they are called, in any given time proves to be equal to the difference between the numbers of vibrations executed in this time by the two sources of tone employed. If the united sound makes in ten.seconds forty pulsations, the one tone is produced by four more vibrations per second than the other. Let us suppose a sounding body giving a tone which cannot be certainly affirmed on the testimony of the ear to change its pitch. If we are in posses­sion of a source of tone of nearly this pitch, whose rate of vibration is known