Hi, music degree here, I’ll do my best to answer your question within the scope of my knowledge of the music of medieval Europe.

Much of the music you hear that is marketed as “medieval” is a contemporary recreation of what the public perceives as medieval, and much of it is often simple percussion with recorder; we don’t have much information on music that was performed on instruments, as much of it was not written down at the time. The system of musical notation was not as developed then as it is now with modern (post-Renaissance) musical notation.

In reality, the musics of Europe were quite diverse, from sacred compositions of various kinds to secular folk songs and other types of music. Musical flavors and genres became even more impressive and interesting as polyphony developed into the modal system of harmony, rather than the monophonic (one melodic line) style of music that came before. I’ll give you a few different samples of the varieties of interesting compositions that showcase various techniques of harmony, melody, rhythm, and instrumentation.

In France during the 8th and 9th centuries, troubadour songs were quite common and popular, which were monophonic tunes that set poetry in Occitan, the “langue d’oc,” to a single melody. These songs would often be sung alone, or with instrumental accompaniment. Here’s a good example: https://youtu.be/ydsCLsXjNVo

In the sacred realm around the same time, you would likely hear plainchant throughout the Catholic mass when you went to a church. The standard chants included the Kyrie, Gloria, Credo, Sanctus Spiritus, Agnus Dei, and Ite, Missa est. Here’s an example of plainchant: https://youtu.be/TufmraHIh14

Later on in the medieval period, polyphony, starting as something called organum, would begin to further diversify the types of music you would hear. At first, the music was very simple, two lines and only using perfect intervals: https://youtu.be/SgHzH5iDcGQ

Eventually, though, it would become much more complex, with the late medieval and early renaissance providing examples like this, where the modal system has become much more developed as well as the rhythmic complexity as the notation improves: https://youtu.be/ZWLsLAujZzI

Around this time, different musical forms became apparent as well, even among folk music, as things like motets, rondo form, and others began to emerge as independent styles of their own. Folk music began to be sung in rounds; one of the oldest examples we have is a Middle English folk song you may have heard before about the coming of summer, sung in rounds. https://youtu.be/b4FU8yz4BYY

Many folks think that medieval european music was not particularly diverse because much of it is centered around vocal music, but that does not mean that styles and genres were not diverse, especially as polyphony emerges.