There are several options.
Many of them require Soundtouch, which is a plugin from the Gstreamer set "bad".
Run
sudo apt install gstreamer1.0-plugins-bad
I wouldn't know which of the options listed below do not satisfy your requirement "just as I do with the volume", and why (e.g., playitslowly).
Sound stretch
Soundstretch seems to do the trick.
SoundStretch is a simple command-line application that can
change tempo, pitch and playback rates of WAV sound files. This
program is intended primarily to demonstrate howthe "SoundTouch"
library can be used to process sound in your own program, but it can
as well be used for processing sound files.
Usage:
soundstretch infile.wav outfile.wav [options]
Options:
...
-pitch=n Change the sound pitch by n semitones (n = -60.0 .. + 60.0 semitones)
...
Play it slowly
playitslowly
(official documentation) is a GUI, which also provides for a change in pitch. See also here.

ffmpeg
Apparently, ffmpeg
can also be used to change pitch.
Audacity
Same as with ffmpeg.
PitchBox
See official info.
Others
There may be other options associated with different pieces of LADSPA software.
Related:
- How can I apply a LADSPA plugin to a PulseAudio stream?