Logarithmic calibration of the range of audible frequencies serves both physical and musical acoustics. Logarithmic assessment of frequency intervals leaves open the choice for a log base, for divisive multipliers, and for some reference frequency serving tabulations of “acoustical logarithms.” Euler's binary‐log measure describes intervals in terms of fractions of an octave; the characteristic counts the octavesrethe frequency standard and the mantissas are invariant with the tonal species. Different forms of binary systems, their transforms (especially duodecimal), and other log systems (common, natural, commatic, etc.) are discussed. The angular transform of 2x, representable as an exponential spiral (helix), portrays the periodic properties of frequencies as perceived by the musical ear in the octave system. Huygens used common logs and antilogs to compute cycles of 12 and 31; Mercator proved the merits of the cycle of 53 by natural logs; Sauveur invented the first acoustical log step scale. Lambert, DeProny, and Drobisch elaborated binary measures, while Ellis, Hornbostel, Young, and Husmann constructed tabulations.