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Smooth wavelength tuning over 10 nm has been realized in a dispersion-tuned harmonically mode-locked fiber ring laser. Supermode noise is suppressed by 13 dB by adding a semiconductor optical amplifier (SOA) into the cavity and the suppression improves as the SOA gain increases. 5.3-ps pulses are obtained at a repetition rate of 10 GHz. A simple numerical model demonstrates the effects of the intracavity dispersion and the SOA on the pulse characteristics.