Mplayer makes small popping/static sound when speed_set is used

Over the past two years I've developed a command-line front-end to MPlayer
called Aletheia that features front-and-center pitch controls using music
intervals (e.g. 1/12 of an interval for a semitone, but works with any
EDO), and it utilizes speed_set to adjust. Everything works great; however,
there is a slight clicking/popping/static sound on a speed_set change. It's
not a big problem and I feel like it might be out of my control; perhaps
even a symptom inherent to the audio frequency itself. I was wondering if
anyone had any ideas on if this could be reduced or eliminated if it is
something that can be fixed? It seems that even small increments produce
the sound and I can't imagine it's my code as I'm just sending commands to
a pipe to mplayer. I thought that perhaps mplayer itself could scale small
increments to reduce the static, or perhaps another solution would be
better. Aletheia is just a bash script, so the optimization would likely
have to come from your end.

https://github.com/apeitheo/aletheia

Thank you in advance for any help or insight into this matter.