The Muscial Scale and Its Tuning
William Braid White · The Journal of the Acoustical Society of America · 1931
The accepted system of tuning divides the octave into a succession of twelve tones, of which the frequency relations are such that if n be any tone n : n + 1 = 1 : 2112 from which also it follows that n : n + 12 = 1 : 2 This system, however, is purely artificial and was adopted in the eighteenth century in order to effect a practical compromise between the growing demand for freedom of tonal combination, and the limitations of a keyboard which had fastened itself upon practical musical performance. The paper discusses the nature of the musical scale and the anomalies which arise when an attempt is made to evoke intervals and chords in accurate relations of frequency with only twelve separate tones available in each octave. Some of the acoustical defects of equal temperament are pointed out especially in relation to music as heard. A thorough reconsideration of the subject is suggested for the general benefit of the reproducing arts and of the future of Music as a living form of expression.