  A new musical scale devised by the author, based on natural logarithms, is
described. Most of the logarithmic pitches bear no correspondence to the twelve
tones of the ancient tuning system attributed to Pythagoras, based on ratios of
whole numbers, nor to the chromatic tones of scales in equal temperament used
widely in the modern era. Logarithms obey a special arithmetic compared to
whole and rational numbers, which can be heard in beat frequencies between
tones of the scale, suggesting extended harmonic possibilities by incorporating
the beat frequencies into compositions. The author uses the broad term
"non-Pythagorean" to describe the logarithmic musical scale, as the ratios of
pitches are usually irrational numbers.
