The angular measure of musical intervals, traceable to Ptolemy (1 oct=180°; 2 oct=360°), was first determined correctly by Drobisch (1855) as 360° × log2 r, where r is the frequency ratio. Using this concept, Drobisch sketched an ascending tonal spiral (i.e., a helix) without giving its equation. Donkin (1874) provided an equation for a spiral on a plane surface, Baravallee and Tipple (1946) presented an equi-angular spiral on a plane surface to demonstrate Mercator's equal temperament of 53. Elaborating upon Euler's (1739) binary-log measure of musical intervals (log2 r) for rotational angles, we propose a helix with the equation f201.63=261.63×2ω/2π=261.63×e0.09315(ω/2π) to represent, reference middle C, the growth of frequency in the octave system as a function of the rotational angle ω/2π in radians. Applications of this equation to the invariances of the relative pitch sense (e.g., MAJOR THIRD+MINOR THIRD=PERFECT FIFTH) are discussed. Furthermore, the model is made descriptive for orientation by the absolute-pitch sense, also for diplacutic, paracutic, and Doppler shifts, and expanded to the imaginary domain. To the diameter, one can assign intensity re 0.0002 dyn/cm2. A family of nonintersecting helices can incorporate the function of equal loudness and portray the field of audition in the three dimensions of the tonal species (“chroma”), frequency and intensity with respect to normal and abnormal hearing. The equation for the helix of the fifths is f201.63=261.63×(3/2)(ω/2π); and in cyclically tempered systems 3/2 is “flattened” by the respective “schismata.” Use of a digital computer to determine the spiral points is reported.”