I find the graphs informative, but music is not a frequency sweep.
I'm not informed about this, so please correct me if I'm wrong:
To me the graph shows the quantity, but not the quality.
For example, having bass, is not the same as having a good bass.
I leave these questions:
Do speakers respond the same way to music as they do to single frequencies?
Can we equalize the freq. sweep, to get the same graph of a better driver?
Do we get the same music quality using that equalization?
Your questions are really good ones. I will try and answer as best as I can, but I am not an expert.
Speakers/headphones will respond to music in the same way they respond to a FR sweep. As you said, the FR graph will show the quantity of SPL at any given frequency. If a speaker/headphone FR measurement shows elevated treble response as an example, then you will hear elevated treble in music as well. Having said that though, you still can't take any old FR graph and say something like oh there is a peak at 10kHz so when I listen to these earbuds there will be as well. It does depend on the measurement system used and whether the FR graph has been compensated. My graphs are raw measurements, so while I think they are useful for comparing differences between earbuds, you do need to have a real world reference point, in ear, to have a better understanding of how they really sound. For example, if you own a Vido and you know how that sounds, then you could look at my FR graphs of the Vido compared to any other mx500 bud I have measured and infer the difference between them based on your understanding of how the Vido actually sounds and my graphs. This would give you an understanding of sound signature differences, but not necessarily sound quality and detail retrieval differences. I hope that made some sense. If you are looking at more sophisticated graphs such as those at innerfidelity, then you could probably look at a given graph, see a peak at say 10kHz for example, and expect in real life to hear a peak at 10kHz as well, still with headphones its never guaranteed to be exactly where the graph says.
Can we equalize the freq. sweep, to get the same graph of a better driver?
You can do this, but the type of EQ will determine how well it will work in practice. Parametric EQ's are known to cause timing/phase issues and can really ruin the sound quality of a headphone or speaker. I have used parametric EQ to compensate speaker systems to measure perfectly flat in room, and the result was terrible. It can honestly be so bad that it sounds like you are listening to music out of a tin can. If you use FIR filtering (finite impulse response) then you can achieve really good sound quality even with lots of EQ. This is because FIR filters can implement linear phase filtering, which means the filter will have no phase shift across the entire frequency band. I am no expert in this stuff, but I have used both parametric EQ and FIR filtering to calibrate loudspeakers to have perfectly flat responses in room. The difference between the two is huge, absolutely night and day. This perfectly illustrates how FR graphs aren't the end all be all and don't say how good something actually sounds. The parametric EQ compensated speakers measured perfectly flat but sounded like garbage. If using parametric EQ it is best to stick to EQing the bass only since it is harder for the human ear to hear details down there compared to the mid range frequencies. It sometimes works alright for taming treble spikes as well.
Do we get the same music quality using that equalization?
I would say no, not really. You may be able to achieve a very high quality result when using FIR filtering, but how good the final result is still depends on how good your speaker system is. For example I could EQ a pair of transmission line loudspeakers with 4" full range drivers to have a flat FR down to say 40hz or so, but I couldn't expect the bass texture and quality to be on par with an open baffle system with 4x 16" woofers handling the bass. The same would go for headphones. Depending on what you are trying to compare to as a reference you may get really close, or may still have some large differences.