No bass: the instrument is there, but not the tone, a guitar cutting through the mind like an iced scalpel and a psychopathically confident singer walking on pink clouds made of 'golden brown'--obviously.
Of course I get the artsy idea as a whole and times enjoy it. It has to be so, it's not a hifi-test-record for 'critical listening'. It's Birthday Party!
I did an analysis of this song and it confirms that this song has plenty of bass, even stereo bass. The bass guitar is a bit boomy and "roomy" as can be heard, but it is also likely close to the unprocessed sound of how that instrument sounded in the recorded space. Very raw.
The overall sound of the song is severely mid-scooped. That mid-scooped sound can have been exaggerated in the mixing process of the song but it can also be the settings of the amps and the sound the band was going for, as that tone/sound was "a thing" many other similar bands were going for at the time.
Just like the bass guitar, the guitars do also have a roomy and distant sound to them. I don't find the sound of the guitars to be "cutting through the mind like an iced scalpel" as you describe it, it can probably appear so thanks to that mid-scooped sound like all the other instruments in the mix have.
Again, that mid-scooped tone was most probably pretty representative of how the instrument's amplifiers were set up and sounded in the recording space. And again, the mid-scooped sound may have been a bit exaggerated in the mixing stage as that sound was trendy in that era of time among that genre of bands.
In the mastering analyzing program I used, it can be seen that very little processing has been done to the overall master, and no limiter has been applied to make the song less dynamic than the final mix. The song has plenty of headroom to digital zero/clipping point, and it also has a nice and healthy Crest factor. Minimal adjustments may have been done with EQ to the final master but not so much to make the overall mix mid-scooped.
But with all the above said, I can completely understand that the sound of this record may not be everyone's cup of tea, but I think the sound of this record was all intentional to get the tone/sound they aimed for. But no, it's not a "HiFi test record".
