2013/12/18 by Robert Schneider, Robert P. Schneider, Schneider, Robert P.
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO) #Music Technology and Sound Studies #Music and Audio Processing #Neuroscience and Music Perception #Number Theory (math.NT) #math.HO #math.NT #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1312.5020
Proceedings of Bridges: Mathematics, Music, Art, Architecture, Culture Conference (June, 2012)
arxiv created 2013/12/18 · openalex publication_date 2013/12/18 · arxiv updated 2013/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.