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32                                                HOPI SONGS
to be constant, we can determine whether the rate of vibration of the other varies, by noting whether the pulsations made by the two when sounded together are subject to change. For since the one source vibrates at a con­stant rate, a change in the rapidity of the beating of the two will mean that the other is vibrating slower or faster than before. In this indirect way varia­tions in pitch may be detected which would entirely escape notice by the ear. Moreover, if the vibration rate of the source producing the constant tone be known, we are enabled to determine also the interval which the variation in pitch of the other represents, for this interval is expressed by the ratio of the vibration rates of the note before and after the change; and these are found by adding to (or subtracting from) the number of vibrations per second exe­cuted by the constant source the number of beats formed with it by the varying source before and after the variation.
The constant source of tone which I used in applying this test to the phono­graph was a tuning-fork by Koenig of Paris making 250 vibrations per second, that is, giving the pitch called by the French Ut3. The phonographic inscrip­tions which were compared with it were taken from the middle c' of a Mason & Hamlin harmonium, a pitch higher than Ut3 by a fraction of a semitone. This note was in each case held uninterruptedly until the inscription covered the cylinder.
There are two possible sources of variation from a constant pitch in such a reproduction as this. While the phonograph may not give back accurately the sequence of pitch it received, there may also have been a variation in the origi­nal note. The pitch of a note produced as in the harmonium, by the action of a current of air on a reed, is found to vary somewhat with the strength of the current employed. In order to estimate what importance should be attributed to this factor of original variation, when all possible care was taken to keep the inscribed note constant in intensity, I compared the beats made with the Ut3 fork by the nearest semitone on the harmonium at its faintest and at its loudest. The note b, when just audible, made with the fork, which was slightly higher in pitch, eleven beats in ten seconds ; when given with all possible in­tensity, twenty-two beats in ten seconds. The greatest possible change which could be produced in the vibration rate of the reed by differences of intensity of blowing was therefore but little over one vibration per second, corresponding at this pitch to an interval of about one twenty-ninth of a tone. The original variation being so small when the conditions were made as unfavorable as possible, I concluded that when all possible care was taken to make them favorable it might be neglected; and that any irregularities which should
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