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acoustics amplification amplitude analysis arise aural harmonics base note basic basilar membrane bowing cavities Chapter characteristic clarinet clearly combination tones completely components conical pipe consider constant convolution corresponding curve damping diapason diatonic scale discussed displacement effect electrical electronic electronic organs Equal Temperament equation example exponential exponential decay Figure force formant Fourier transformation frequency-space fundamental hence holes important initiation intervals involved large number length loudness mathematical mechanism method modes of vibration motion musical instruments musical sounds noise oboe occur octave organ oscillations oscillograph pattern peak function period phase physical piano pitch plate played plucked possible pressure pulse pure tone Pythagorean radians radiated ratio reciprocal space reed relative represent resonance result rods scale sequence shown in Fig sine wave sinusoidal slits solution sound produced spectrum starting transient steady string tion tuning variations various velocity vibration violin wave form zero