If you know me at all, you know I like rhythm games. If you don't, well, now you do. It's a lot easier to get into than you'd think, and you can dive pretty deep. But a lot of the appeal, at least for me, is a quantitative difficulty system, or something that rates difficulty on a number scale. This is opposed to games that use an Easy/Medium/Hard scale, which I'll refer as to as the EMH scale.
There's a few games that do this. IIDX rates from 1-12, SDVX rates from 1-20, Groove Coaster rates from 1-20 or 1-15 depending on platform, DDR rates 1-20, jubeat rates 1-10.9 with ratings only higher than 9.0 getting the decimal point, and osu! and Etterna Online rate with no real cap and two whole decimal points on every song, with a different scaling for each. They do have an EMH scale, but it takes a back seat.
Fun fact: The DDR fangame Flash Flash Revolution goes from 1 to a massive 110!
This kind of difficulty scale is easy to understand: if I can't beat X, I should go lower. This helps with the problem that games that use EMH scales may have charts with harder "mediums" than other "medium" rated charts. I've found this to be apparent with Guitar Hero and Rock Band, but this is subverted in the actual games with the tier lists. (I play Clone Hero, which doesn't have those.) Beat Saber shares the same issue.
And then there's Taiko no Tatsujin. I can't find a genuine description of how it works, but from what I can tell it uses a blend between numerical and EMH. You select a difficulty from EMH, and then each song has a number, shown as a star count. The problem being is that, say, a 5 star Medium is way easier than a 5 star Hard. This indirect conversion fucks with me, and is probably the only reason why it's not my favorite.
Some games throw a difficulty scale out completely, like A Dance of Fire and Ice, but this is replaced with simple linear progression.
"Why should I care?" you ask. Go play Groove Coaster, it's good. Or one of the other free mobile rhythm games. Or something on the TFGD Rhythm Game list. I'm not picky.