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...Slide mathematical harmonies music is periodic variation in air pressure p a sin f t where decibels or pascals time seconds period sound has two characteristics volume amplitude pitch frequency hertz hz sec loud note quiet low high piano violin tuba piccolo soprano alto tenor bass ranges of various instruments audible frequencies range from to linear scale pa n m logarithmic db ppa pdb log vibrating string tension length thickness we can change three ways tighten the use thicker line density fingers on frets specifically halving will double diagram middle octaves this sequence e geometric previous term multiplied by constant case example form vibrates many modes called harmonics harmonic fundamental second third fourth c fifth sixth approx g seventh eighth an arithmetic added...