Musical Ear Research Articles

The Subjective Lowering of Pitch

As a question arising out of Mr. Harding's letter (p. 103), it would be interesting to know what is the effect produced by sounding a note loud enough to produce the subjective distortion, while at the same time the note to which it appears to be flattened is sounded more quietly. I suppose discord would be inevitable, but possibly a musical ear would be able to judge whether subjective distortion was prevented in the loud, or produced in the softer, note.

On Measuring the Vibratory Periods of Tuning-Forks

THE tuning-fork when its number of double vibrations, to and from in a second, or briefly its frequency, has been ascertained, is a most convenient instrument for measuring minute divisions of time. As such it is now extensively used for physical, physiological, and military purposes (velocity of bullets and cannon balls). The antecedent difficulty of ascertaining the frequency, is however very great. The old processes, sufficient for roughly ascertaining musical pitch, and depending upon wires of known weight, length, and tension, or the action of the siren, are totally insufficient for modern purposes. It was the contradictory nature of the results furnished by the monochord in the division of the Octave into twelve equal parts that led Scheibler to his system of a series of tuning-forks differing from one another by known numbers of vibrations, leading to countable beats, and extending over an Octave. Nothing can he more convenient to use than such a series of forks for all musical purposes. They enable the frequency not only of any small as well as large tuning-fork, but also of any sustained tone to be ascertained within one-tenth of a vibration, that is, one vibration in ten seconds. The writer has for some years been in the constant habit of using such a set of forks with the most satisfactory results. His own forks were measured by Scheibler's (exhibited in the Historic Loan Collection of Musical Instruments at the Albert Hall this year), but extend over a greater range, from about 224 to about 588 vib., that is, rather more than an Octave and a major Third. The great advantage of such a tonometer is extreme portability, immediate application to any sustained tone (even that of a pianoforte string), and the independence of the result from any (almost always imperfect) estimation of unison by a musical ear. There are of couise antecedent difficulties in ascertaining the pitch of each particular fork, but these are overcome by patient observation, the extension of the series beyond an Octave furnishing in itself the required check.

Equal Temperament of the Scale

IN your number of November 8, 1877, p. 34, Mr. Chappell, F. S. A., has intimated that mathematicians who propose to divide the octave into twelve equal semitones instead of “equally tempered semitones,” are deficient in musical ear. I have not noticed that any mathematician has replied to him.