This passage from St. Pius V’s Quo Primum seems to give the Holy See the authority concerning local liturgical tradition:
"Let all everywhere adopt and observe what has been handed down by the Holy Roman Church, the Mother and Teacher of the other churches, and let Masses not be sung or read according to any other formula than that of this Missal published by Us. This ordinance applies henceforth, now, and forever, throughout all the provinces of the Christian world, to all patriarchs, cathedral churches, collegiate and parish churches, be they secular or religious, both of men and of women - even of military orders - and of churches or chapels without a specific congregation in which conventual Masses are sung aloud in choir or read privately in accord with the rites and customs of the Roman Church. This Missal is to be used by all churches, even by those which in their authorization are made exempt, whether by Apostolic indult, custom, or privilege, or even if by oath or official confirmation of the Holy See, or have their rights and faculties guaranteed to them by any other manner whatsoever.
This new rite alone is to be used unless approval of the practice of saying Mass differently was given at the very time of the institution and confirmation of the church by Apostolic See at least 200 years ago, or unless there has prevailed a custom of a similar kind which has been continuously followed for a period of not less than 200 years, in which most cases We in no wise rescind their above-mentioned prerogative or custom. However, if this Missal, which we have seen fit to publish, be more agreeable to these latter, We grant them permission to celebrate Mass according to its rite, provided they have the consent of their bishop or prelate or of their whole Chapter, everything else to the contrary notwithstanding.
All other of the churches referred to above, however, are hereby denied the use of other missals, which are to be discontinued entirely and absolutely; whereas, by this present Constitution, which will be valid henceforth, now, and forever, We order and enjoin that nothing must be added to Our recently published Missal, nothing omitted from it, nor anything whatsoever be changed within it under the penalty of Our displeasure.
We specifically command each and every patriarch, administrator, and all other persons or whatever ecclesiastical dignity they may be, be they even cardinals of the Holy Roman Church, or possessed of any other rank or pre-eminence, and We order them in virtue of holy obedience to chant or to read the Mass according to the rite and manner and norm herewith laid down by Us and, hereafter, to discontinue and completely discard all other rubrics and rites of other missals, however ancient, which they have customarily followed; and they must not in celebrating Mass presume to introduce any ceremonies or recite any prayers other than those contained in this Missal."
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