It goes down to what I mentioned when responding to October Scream -- it's all down to pattern construction.
For example 4k map has a density of let's say 10 notes/s and 7k has a density of 17.5 notes/s due to having more keys. Even though the number is different for each but is the same considering we have different amount of keys. Let's also pretend these maps are without crazy patterns, just simple triplets, doubles and alternation.
The unfortunate matter is that you simply can't judge based off of the note density itself, because patterns are going to be inherently harder on 4K than 7K for different reasons. Despite only using index/middle or middle/ring, there are some patterns that are going to lend themselves to more difficulty. Assuming that there's no crazy patterns, and that doubles are used regularly/alternated, you can expect more patterns on 4K to be anchor-heavy (an anchor is a situation where the same arrow implicitly/explicitly repeats multiple times) because there's less room to play with layering in charts. Being that there are less pattern combinations overall on 4K, Agka brings up an arguable point:
Agka wrote:
Under a different number of keys, an equal density would lead to the intensity being major more likely on the lower amount of keys.
Before going on though, I do want to make a note that overall note density shouldn't be increased simply because there are more keys: this simply implies that you are increasing the layering by n(k) when the number of keys isn't going to dictate the map's layering: the mapper is going to dictate the map's layering. Think in a more unbiased scenario, where the number of keys is not going to dictate the layering -- let's say we have an area of the song where there is a single synth in a melody and nothing more, and it's running at 1/4 snap at 150 BPM (to make your 10 notes/s example). In an instance where we have the same structure, it's going to depend strictly on patterning. Something that frequently leans towards one hand on 6K/7K/8K is obviously going to be more difficult than just about any 4K stream because you have a massive amount of patterning permutations. Likewise, a fluent stream on 6K/7K/8K is likely going to feel easier than a fluent stream on 4K to an experienced player because the overall feel is more natural.
Assessing at 17.5 N/S is a huge way to illustrate that chart compositions on 4K/7K are extremely different. To get an idea of how fast this is: 17.5 N/S is equal to 262.5 BPM 1/4 snapped stream, which is incredibly fast. Agka's point holds true again: the intensity would feel considerably higher on 4K because there are less patterns to choose from, whereas a 6/7/8K situation would a bit smoother. Cramming 17.5 n/s requires you to hit 1050 notes in 1 minute. This is achievable under easier circumstances in higher key values: taking a look at another musical example, we'll assume that a section has a bass drum hitting every beat in a measure, snare drum hitting beats 2 and 4 every measure, clap hitting beats 2 and 4 every measure, a closed hi-hat running on the up-beat of every beat, falling in between your bass drum, snare drum, and clap in even intervals, and a melody running straight 1/4 stream (a basic/generic song structure). Most 7K/8K map would be able to handle layering this directly, accounting for every sound appropriately, but the layering would be heavy. However, the 4K map would have to compensate to make the chart reasonably playable, possibly being forced to ignore the fact that a snare/clap exists at certain points to more suitably account for the melody.
Xcrypt said it best:
Xcrypt wrote:
if you have the same density per lane, then the higher keymode would most likely be quite a bit more difficult, due to needing more muscle memory and reading skill to deal with all the patterns.
if you have the same density overall, then the lower keymode would probably be quite a bit more difficult due to the fact that you have a lot more strain on less fingers.
In a situation where there are no repeated notes over a given even interval, a per-lane density would prove that the higher key amount gets more difficulty because there are a lot more keys to handle at once. If you were to spread patterns out in such a way on 4K with a per-lane density of 4 n/s, you would have a 16 n/s stream assuming that the patterns are evenly distributed. If the same were to happen in 8k, well... you'd likely be in big trouble, haha. These are very extreme and unlikely circumstances, though.