Vatican website translation:
39. Within the limits set by the typical editions of the liturgical books, it shall be for the competent territorial ecclesiastical authority mentioned in Art. 22, 2, to specify adaptations, especially in the case of the administration of the sacraments, the sacramentals, processions, liturgical language, sacred music, and the arts, but according to the fundamental norms laid down in this Constitution.
39. Intra limites in editionibus typicis librorum liturgicorum statutos, erit competentis auctoritatis ecclesiasticae territorialis, de qua in art. 22 § 2, aptationes definire, praesertim quoad administrationem Sacramentorum, quoad Sacramentalia, processiones, linguam liturgicam, musicam sacram et artes, iuxta tamen normas fundamentales quae hac in Constitutione habentur.
Slavishly literal translation:
39. Within the limits established in the typical editions of the liturgical books, it will be for the competent ecclesiastical territorial authority (concerning which see article 22 § 2) to define adaptations, especially concerning the administration of the Sacraments, as well as the Sacramentals, processions, liturgical language, sacred music and arts, nevertheless according to the fundamental norms which are held in this Constitution.
In a remarkable departure from earlier practice in which almost all regulation of liturgical practice for the Roman rite was controlled by the Sacred Congregation of Rites, with a few issues left for the determination of a local Ordinary, here the Council Fathers relegate to territorial bishops’ conferences the competence to deal with issues of liturgical adaptation, presumably because they would have first-hand experience concerning how liturgical sign systems would best communicate the meaning of the gospel in the cultures in which they live. It would be interesting to gain some sense of how the various territorial authorities have exercised their competencies in adapting the editions typicae of the liturgical books to their own areas for the sacraments and sacramentals, how they have promoted or curtailed liturgical processions in the light of cultural norms in their areas, what they have learned about translation of liturgical texts into the vernacular, and how they have promoted and overseen the development of sacred music and arts. Pray Tell readers may wish to discuss whether and how this norm has been lived out over the past fifty years and what we might suggest for the future in the light of this experience.