From the Online Etymology Dictionary:
early 15c., of stitching, from Old French cuilte contrepointe “quilt stitched through and through,” altered from coute pointe, from Medieval Latin culcita puncta “quilted mattress,” from Latin culcita “cushion” + puncta, fem. past participle of pungere “to prick, stab” (see pungent).
Of music, mid-15c., from Old French contrepoint, from Medieval Latin cantus contrapunctus, from contrapunctum, from Latin contra + puncta, with reference to the indication of musical notes by “pricking” with a pointed pen over or under the original melody on a manuscript.
In music, counterpoint is the relationship between voices that are harmonically interdependent (polyphony) yet independent in rhythm and contour. It has been most commonly identified in the European classical tradition, strongly developing during the Renaissance and in much of the common practice period, especially in the Baroque. The term originates from the Latin punctus contra punctum meaning “point against point”.
Said, E. (1993) Culture and Imperialism. New York: Knopf.
Aida‘s peculiarities–its subject matter and setting, its monumental grandeur, its strangely unaffecting visual and musical effects, its overdeveloped music and constricted domestic situation, its eccentric place in Verdi’s career–require what I have been calling a contrapuntal interpretation, assimilable neither to the standard view of Italian opera nor more generally to prevailing views of the great masterpieces of nineteenth-century European civilization. 
This was in keeping with the mortuary aspects of the opera he was writing (making the mummies sing, he once said), which opens with a piece of strict canon writing; Verdi’s contrapuntal and stretto techniques in Aida reach a heightened intensity and rigor of an order he rarely achieved… A full contrapuntal appreciation of Aida reveals a structure of reference and attitude, a web of affiliations, connections, decisions, and collaborations, which can be read as leaving a set of ghostly notations in the opera’s visual and musical text. 
My point in this contrapuntal reading is to emphasize and highlight the disjunctions, not to overlook or play them down. 
To situate Camus contrapuntally in most (as opposed to a small part) of his actual history, one must be alert to his true French antecedents, as well as the work of post-independence Algerian novelists, historians, sociologists, political scientists. 
I shall proceed on the assumption that whereas the whole of a culture is a disjunct one, many important sectors of it can be apprehended as working contrapuntally together. 
To rejoin experience and culture is of course to read texts from the metropolitan center and from the peripheries contrapuntally, according neither the privilege of “objectivity” to “our side” nor the encumbrance of “subjectivity” to “theirs.” 
First, by a new integrative or contrapuntal orientation in history that. sees Western and. non-Western experiences as belonging together because they are connected by imperialism. 
At this moment [C.L.R] James accomplishes another contrapuntal, non-narrative turn. Instead of following Césaire back to West Indian or Third World history, instead of showing his immediate poetic, ideological, or political antecedents, James sets him next to his great Anglo-Saxon contemporary T. S. Eliot, whose conclusion is “Incarnation.” 
Instead of the partial analysis offered by the various national or systematically theoretical schools, I have been proposing the contrapuntal lines of a global analysis, in which texts and worldly institutions are seen working together, in which Dickens and Thackeray as London authors are read also as writers whose historical experience is informed by the colonial enterprises in India and Australia of which they were so aware, and in which the literature of one commonwealth is involved in the literatures of others… But this global, contrapuntal analysis should be modelled not (as earlier notions of comparative literature were) on a symphony but rather on an atonal ensemble; we must take into account all sorts of spatial or geographical and rhetorical practices–inflections, limits, constraints, intrusions, inclusions, prohibitions–all of them tending to elucidate a complex and uneven topography… But this global, contrapuntal analysis should be modelled not (as earlier notions of comparative literature were) on a symphony but rather on an atonal ensemble; we must take into account all sorts of spatial or geographical and rhetorical practices–inflections, limits, constraints, intrusions, inclusions, prohibitions–all of them tending to elucidate a complex and uneven topography. 
From this perspective also, one can see “the complete consort dancing together” contrapuntally. 
It is more rewarding – and more difficult – to think concretely and sympathetically, contrapuntally, about others than only about “us.” 
Said’s advocacy for contrapuntal reading is elegant, seeks harmony through rightful placement. When I read his analysis of Verdi’s Aida, my own personal histories come into play. The opera was commissioned by Ismail Pacha who, at the time, governed Egypt and Sudan as part of the Ottoman Empire. I think that the insertions of some histories and contexts into texts can be painful. I think that personal subjectivities can create universes of jarring and disharmonic counterpoints to original texts, and carried through, unsettling practice. This is sometimes necessary.