I wasn’t aware the dance was relatively recent–early 17th century from what I read. A favorite bit of music is the final movement from Luigi Boccherini’s Guitar Quintet (G448). I was listening on my morning walk–it really picks up your step.
Then I found this version by a youth string orchestra. In a church, no less.
From Grove’s Dictionary of Music on the dance:
Soon after its introduction, in the 17th century, it was condemned by the ecclesiastical authorities in Spain as a ‘godless dance.’ Just as the Consistory were about to prohibit it, one of the judges remarked that it was not fair to condemn anyone unheard. Two celebrated dancers were accordingly introduced to perform the fandango before the Consistory. This they did with such effect, that, according to the old chronicler, “every one joined in, and the hall of the consistorium was turned into a dancing saloon.” No more was heard of the condemnation of the fandango.
Catholic Sensibility 
Of the major/regional national schools of art music in Western European cultures, those of Iberia have the strongest apparent survival of medieval forms. The fandago may chronically be of the early Modern era, but to most ears it sounds rooted in older forms for that reason. This has a parallel in literary and especially musical Spanish (whose current spoken/written form modernized at nearly the exact time in the early Modern era as English), with a cornucopia of customary elisions and rhythmic meter, and much more vigorous residue of pre-Modern world views. Crossing from schoolbook conversational Spanish to literary/musical Spanish (and then the many national instances of Spanish on the ground in the Hispanidad) is to ford a much broader river than, say, French.