12-TET, the usual musical tuning, kinda sucks. Or is bland. Or whatever. (Seriously, listen to some music by Sevish. It will change your perception of what music can be. But not before weirding you out first.)
But what if we tried to make a musical tuning even less consonant?
One obvious place we could start out is by making the basic interval something not consonant. In the case of 12-TET (or 12-EDO), the basic interval is an octave, with a frequency ratio of 2:1. We can choose something irrational, like $\pi$ or $e$. But ideally we want something that is maximally far away from a rational approximation. Diophantine approximation is the field concerned with approximating real numbers by rational numbers. It turns out that the golden ratio $\varphi$ is such a maximally-irrational number, from a result by Adolf Hurwitz.
So, let's make a scale with the basic ratio of the golden ratio. This corresponds to an interval of $1200 \times \log_2(\varphi) = 833.09$ cents.
Similar scales have been done before, like Bohlen's 833 cent scale. But this re-introduces the octave by stacking $\varphi$'s and folding them on the octave. We want to decouple from the octave and other consonant intervals.
As such, I went for something simple and known-to-be-non-consonant: equal division of the interval. In our case, equal division of the golden ratio. I found that 6 divisions resulted in a good balance between enough notes to be composable and not being close to a nice ratio (except for interval 5 being 7 cents from the 3/2 perfect fifth, oops!). 8 divisions of the golden ratio also works quite well, although it ends up being too close to 12-EDO for my liking. Here is the 8-EDGR tuning in barebones Scala format:
104.13627
208.27255
312.40882
416.54510
520.68137
624.81765
728.95392
833.09020
And 6-EDGR:
138.848366
277.696733
416.545100
555.393467
694.241834
833.090201