Could we trace in medieval music ancient origins of folkloric music from germanic peoples, celts, romans etc..? If not, how did it transform into such a different style and what are the origins of it? My questions may be open to origins of later gregorian chants etc.. Thanks!
I hope this helps to answer your question, while the music of those specific ancient cultures is not my specialty, I am a music theorist and I can approach the change from ancient music to medieval music from a theoretical and musicological standpoint. I'll start from the end: there are a few markers that set the beginning of "Medieval" period music, which we place around 500 A.D. These markers include:
The beginnings of music notation: before the Medieval period, there wasn't really a standard for music notation. Much of the earliest Ancient music is now impossible to recreate as the early notation was so vague. These civilizations also often passed down music entirely orally, with slight variations between each generation. With a standard notation system (slowly approaching today's), it became easier for people to share music between communities, regions, and countries; as well as to start standardizing the rules of music theory and tonal systems.
The advent of music theory practices. The Medieval era laid the foundation for a system of rules and practices for tonality that was utilized and expanded upon by composers from the Baroque to the Romantic period (not that it stopped existing after the Romantics, but there was a serious breakdown in tonal structure that is enough material for an entire Theory course). As these systems developed, music became more polyphonic rather than monophonic, and songs began to break away from mostly pentatonic scales towards minor and major modes.
To go back to the beginning of your question, modern Western music came together from a few ways: the notation system I mentioned previously, the Church, and, most often, from societies absorbing the musical customs of societies they had conquered. Most Roman popular music was actually "borrowed" from earlier societies - a lot of it is a mash-up of Greek harmony, Etruscan music, even some African and Middle Eastern influences can be found in the surviving Roman music we have. Over time and enough passage of musical traditions between cultures, music theory standards began to settle around Europe, often encouraged by the Church. Usually, you see more regional differences that reflect back on older cultures in secular music (folk songs, work songs, etc.).
So, in short, no, there's no direct link between ancient music to Western medieval music. In fact, we don't have any direct link to Ancient Greek and Roman music notation even to know exactly how to interpret it, and the reconstructions have been educated guesswork.
As for the evolution of music notation, and other forms of notation, I'm going to link you to another post I made on it. Have a look if that answers your question, and feel free to follow up if you want additional information.
Edit: Please follow up here and not in the linked thread.