A Scale for Specifying Frequency Levels in Octaves and Semitones
Parry Hiram Moon · The Journal of the Acoustical Society of America · 1953
A new system of specifying frequency level is proposed. It utilizes the logarithm (base 2) of the relative frequency, expressed in duodecimal notation. In this way the designation of musical intervals and musical scales is related directly to frequency, yet the numbers repeat in each octave and the semitones of the equitempered chromatic scale are expressed exactly as 0.100, 0.200, 0.300, ⋯. The new notation is applied to the macrodesignation of semitones and octaves, and to the microdesignation of true intervals and of Pythagorean and Ptolemaic scales. A slide rule is developed to allow easy visualization of the relations among musical intervals.