"Preferred numbers" in engineering and product design; standardized near-logarithm increments to make both interchanging parts and mental arithmetic as easy as possible. (I've liked 1-2-5 for some time, myself.)
The "19-equal temperament" scale in music, a proposal to divide the octave (doubling of frequency) into 19 near-logarithmic parts. Argued in composer Joel Mandelbaum's PhD thesis that it's the only viable system with a number of divisions on this order of magnitude. Coincidentally matches the Hebrew calendar system and its pattern of leap years.
