Terminology for Logarithmic Frequency Units

Fletcher has proposed the use of a logarithmic frequency scale such that the frequency level equals the number of octaves, tones, or semitones that a given frequency lies above a reference frequency of 16.35 cycles/sec., a frequency which is in the neighborhood of that producing the lowest pitch audible to the average ear. The merits of such a scale are here briefly discussed, and arguments are presented in favor of this choice of reference frequency. Using frequency level as a count of octaves or semitones from the reference C₀, a rational system of subscript notation follows logically for the designation of musical tones without the aid of staff notation. In addition to certain conveniences such as uniformity of characters and simplicity of subscripts (the eight C's of the piano, for example, are represented by C₁ to C₈) this method shows by a glance at the subscript the frequency level of a given tone counted in octaves from the reference $C0 = 16.352 cycles/sec$⁠. From middle C₄, frequency 261.63 cycles/sec., the interval is four octaves to the reference frequency, so that below C₄ there are roughly four octaves of audible sound. Various subdivisions of the octave are considered in the light of their ease of calculation and significance, and the semitone, including its hundredth part, the cent, is shown to be particularly suitable. Consequently, for general use in which a unit smaller than the octave is necessary it is recommended that frequency level counted in semitones from the reference frequency be employed.