I did personally not notice a huge shift in flavor between Gen 3 and 4 specifically. While I can notice that things have changed in the series between most if not all generations, I don't feel like the differences between Gen 3 & 4 stand out above the others. Here are the general impressions I got from all generations and how they compare to the previous generation:
Gen 1 felt very basic which is expected as it was the starting generation. They were trying to see if the Pokemon concept could work, and it did! The games didn't have much in terms of post-game or content but the gameplay was solid enough for its time. The third version in terms of Yellow didn't do things a whole lot differently compared to the first pair, but as said, they were just starting out.
Gen 2 felt very much like an expansion pack to Gen 1. New Pokemon, but the main focus was still on the old Pokemon. Several of the new Pokemon were also related to the old ones. I felt that the games improved upon Gen 1 in terms of content, features, mechanics, physics, graphics as well as being less glitchy, but the overall gameplay wasn't as solid as in Gen 1. Crystal took the concept of a third version to a higher level than Yellow but there was still a long way to go.
Gen 3 was more of a reboot. Now that Pokemon was successful, they could afford to take some risks as the games would still sell like crazy. Which they did. The focus this time around was mostly on the new Pokemon, not all old Pokemon were available from the start. Connection with the older generations had been cut off which made many fans angry at first but allowed the games to expand on a technical level. This generation also brought FR/LG which allowed players to revisit the original games in an updated version that also fixed several problems with the original games. Emerald then took the concept of a third version even further than Crystal in terms of story changes as well as new features and content.
Gen 4 is hard to describe. I get the feeling that they wanted to recreate the original feeling of the first Pokemon games with D/P, but without really succeeding. They didn't showcase all of the new Pokemon during the main game, but they had a lot of content for a first pair. They also improved upon past games in terms of battle mechanics. Platinum then fixed most of the mistakes with D/P as well as continuing in the tracks of Emerald, being another great third version. Fans of the older generations then got to revisit both Kanto and Johto which had been updated in HG/SS.
Gen 5 aimed for another reboot, with only new Pokemon before you had beaten the main game and more new Pokemon than any previous generation! They also had a lot of content just like D/P and had a bigger focus on story and characters than previous generations. They then continued with B2/W2 - sequels instead of a third version, something we hadn't seen them do before (and not afterwards either, so far). These games had a completely new story set after the events of B/W, not to mention a ton of content, the most in the entire series to date. This generation didn't introduce any new major game mechanics, it just focused on improving the games as much as possible in terms of gameplay and content. And that is honestly something I personally value higher than introducing any new major mechanic.
Gen 6 was the series 3D debut, it had less new Pokemon than before but introduced some major new mechanics with the Fairy-type and Mega Evolution. Sadly, X/Y were a step down in terms of content compared to B/W and D/P. Hoenn fans also got their long-awaited remake in terms of OR/AS. There wasn't a third version or sequel this time around though, which I personally feel is a shame as that is one thing this generation really would have benefitted from.
Gen 7 really tried to change things at their very core, with the Gyms being removed and the trials taking their place. New mechanics in forms of Z-moves and Alola forms were also introduced. Still, there isn't a whole lot of content in these games either. It is hard to say something about this generation on the whole at this moment since it hasn't ended, we'll have to see what US/UM brings to the table.
...just some short thoughts on each generation so far.
As for the music, which is what the first post really asks for, I'm not sure. I guess there might be some major differences in terms of music between some, most or even all generations, but that's nothing I have ever thought about. I like most of the music in the games and I never reflected on the music being different from one generation to the next. I guess you could make a very deep analysis of the music in the games, but I'm not the right person to do that.
Anyway, in terms of flavor shifts between the generations. For me personally, I think there biggest flavor shifts happened in Gen 3 and Gen 6.
Gen 3 was vastly different compared to Gen 1 & 2, it felt a bit weird at first but I eventually got used to it and came to prefer it over the previous generations.
Gen 6 was the start of something new for the games. Starting with this generation, they have been putting a higher focus on fan pandering as well as having less content than previously. Which I'm not super happy about, even if I still like the new games a lot. As for Gen 7, despite everything Sun and Moon try to do differently, they only managed to feel like a second X/Y to me. Which is weird, but that's the way I feel. I think this was because of the fan pandering to Kanto, the low number of new Pokemon, the low amount of content and the removal of many useful features that the previous generation had. All of those were things X/Y also did. I still like S/M though, and I like X/Y as well. I have high hopes for US/UM but not as high expectations since I don't want to be disappointed.
Overall, Pokemon have changed a lot during the years, but it is still largely the same on the whole. I have found most of the games enjoyable despite their differences and similarities.