Bridges 2012 Short Paper
A Non-Pythagorean Musical Scale Based on Logarithms
(Proceedings pages 549–552)
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.