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General Structure of Expanded Tunings
The Question of Chroma and
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1U 5cale 1U HZ beat of measure calculate Catalog of Tunings CB 1U Chapter chord chroma axes complex tone composers composition computerized musical instrument consonance and dissonance constant Diff discrete frequencies electroacoustic music equal steps equal temperament expanded chroma perception exponential base family A-n family of tunings five tunings fixed intonation harmonic series HZ 1U HZ CB HZ Ui HZ Ul induce expanded chroma Initial Catalog keyboard labeled ln order major second melody morenoctave musical scales musicians octave octave-based tunings perceived perception of expanded performance piece pitch class possible powers of three present problem intervals psychological quasi-octaves relationship scale degree Scale Ueg semi-expanded tunings serial music seven basic characteristics similarity sixteen cts steps per scale subsets tablature Table 1 continues theory timbral timbres tonal centers true expanded tunings tuning A-12 tuning tables tuning units twelve-tone and serial Western musical tradition