I’m continually amazed at how frequently I encounter the practice of using three triple swings of the thurible to incense the Blessed Sacrament. This was the case just a few days ago at Benediction in a local parish. Despite years of searching, the best explanation I’ve found is that it’s either a complete invention or a mistaken interpretation of the governing documents (Caeremoniale Episcoporum (1984), nn. 92-93; Institutio generalis Missalis romani (2000), n. 277). I’m still convinced there is no way to justify the practice according to the current liturgical law.
The Mass of Paul VI is governed primarily by the Institutio generalis Missalis romani, usually referred to by its English name General Instruction on the Roman Missal (GIRM). For our purposes, the 1975 and 2000 versions are most relevant. All the editions of the GIRM prior to 2000 did not contain any instructions on how incensations were to be carried out. A temporary solution was given by the Congregation for Divine Worship and the Discipline of the Sacramentes (CDW) in 1978 (Notitiae 14 (1978), 301–302, n. 2.). The first clear legislation in this regard was the 1984 Ceremonial of Bishops (CE) typical edition (nn. 92 and 93). The 2000 Latin typical edition of the GIRM adopted CE nn. 92 and 93 verbatim with only two minor editions (cf. 2000 GIRM 277) indicated below by underlining. It reads (emphasis mine):
 Tribus ductibus thuribuli incensantur: Ss.mum Sacramentum, […] oblata, crux altaris, […] presbyter celebrans, […] et populus […]. Duobus ductibus incensantur reliquiae et imagines Sanctorum publicae venerationi expositae[, et quidem initio tantum celebrationis cum incensatur altare].
 Altare incensatur singulis ictibus thuribuli, […]. Oblata thurificantur [incensat sacerdos tribus ductibus thuribuli], ante incensationem altaris et crucis[, vel signum crucis super oblata thuribulo producens].
Even if one does not understand the distinction between the Latin wrods ductus and ictus, it is immediately evident that whatever three ductus (tribus ductibus) means, the Blessed Sacrament (Ss.mum Sacramentum) along with the priest (presbyter celebrans), the cross (crux altaris), and the people (populus) all get the same incensation. Nowhere in the lists for two ductus (duobus ductibus) or single icutus (singulis ictibus) does one find the words for the Blessed Sacrament, the cross, the priest, or the people. There is nothing in the 1984 CE or the 2000 GIRM to justify giving the Blessed Sacrament a different incensation than the priest, cross, or people.
I’ll address how we can definitively conclude what ductus and ictus each mean in a subsequent post.