Bohlen-Pierce scale

"J.R. Pierce, lately of Stanford University, has recently proposed a new musical scale based on dividing the frequency ratio 3:1 (instead of the 2:1 octave) into 13 (instead of 12) equal parts. This scale matches such simples integer ratios as 5:3 and 7:5 (and 9:7) with an uncanny accurancy, resulting from the number-theoretic fluke that certain 13th powers of both 5 and 7 are very close to integer powers of 3. To wit: 5¹³ = 3.0077¹⁹, and 7¹³ = 3.0037²³. Since the integers appearing in the exponents (13, 19, 23) are also coprime (in fact, all three are prime), it is easy to construct complete musical scales exclusively from the small-integer ratios 5:3 and 7:5. The basic chords of the new scale, 3:5:7 and 5:7:9, are superbly approximated by the equal tempered scale 3^k/13 and were found by M.V. Mathews, A. Reeves, and L. Roberts to provide a strong harmonic foundation for music for music written in the new scale."

(Number Theory in Science and Communications, M.R. Schroeder)