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The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. The author uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of examples of past and prevalent tone systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems,Well Tempered Systems, and Ptolemy Systems. Appendices provide extended lists of tone systems and a catalogue of historical organs with subsemitones.