@mahgister
You seem to be saying there exists a sort of Jazz "blueprint" that has been absorbed/integrated into many other genres, worldwide. You also seem to acknowledge that these other genres have, in turn, influenced Jazz.
I cannot describe what is at the core of jazz which is such that all musicians in the world in many different culture had begun to adopt it and used it to improve even their own innate musical language or their traditional instruments...
Observe that this is a fact not my opinion or my invention. there is jazz influences in Russia, as in japan or South America or in mid-eastern countries. Everywhere almost... There is jazz using oud for example in a mix which is some mideastern music instrument used in a jazz way...
But i can gave my explanation...
In jazz i felt a specific musical flowing time and timing sense a freedom which is related to the way musicians feel what a good improvisation is and must be and if it is successful one...
In other musical culture the importance of the specific instruments timbre and chords traditionally used act as a restraint because the final goal is more linked to specific traditional chosen instruments playing than to the improvisation with many non specifically chosen instruments as such as in jazz ( hammond or tuba or etc)...
The rules in traditional musics are more constraining than in jazz concerning the chosen instruments in use and concerning the rules over the improvisation session itself.
For example in India the veena is revered as a gift from Saraswati, his improvisations are heavily codified and the way to play the sound go with rigid rules.Same for the tabla. As it is for the Yoruba talking drums...
The way to play instruments are not so heavily codified in jazz... It is why jazz expressions styles had changed so much from so many different names,( bop , hard bop etc of style in 70 years golden age.
Jazz spirit is more free more easy to adopt even in the confine of other music traditions.
It is why i claimed that Jazz improvisation is universally influential in a way no other world music ever be save european classical written music tradition. this is less my claims than well known observable facts.
Also these two western music styles goes together, jazz and classical, with the same chords language and with some common background. ( negro spirituals, folk music & hymns of the pilgrims for example ) and had more influence all around earth together than any other musical traditional cultures on earth.
( japan music, Indian music and African music, Chinese music , Turkisch music has not that much in common as jazz and classical has)
I am not a musician and yes i need frogman here to correct me or to validate in a more professionnal way what i try to convey ...