4x4 and 5x5 blindfolded
3-style on the big cubes: centres, wings, midges and corners, each by commutators, and their parities.
Big-cube blindfolded solving is 3-style applied to every kind of piece: each kind has its own buffer and its own letters, memorised and solved in turn. On the 4x4 that is the x-centres, the wings and the corners; the 5x5 adds the t-centres and the midges, the middle pieces of the edges, which behave like a 3x3's edges.
Centres
Centre pieces of one colour are interchangeable, so tracing follows colours: the piece in the buffer is red, so the next target is any unsolved spot of the red face (the first in letter order, by habit). Pieces already on their own colour are skipped. The usual buffers are Ubr for the x-centres and Ur for the t-centres.
X-centre letters, clockwise from the top-left of each face, as for corners.
T-centre letters on the 5x5, clockwise from the top one, as for edges.
Centres
506 cases · Every 3-cycle of the Ubr centre buffer: 506 cases.
X-centres
506 cases · Every 3-cycle of the Ubr x-centre buffer on the 5x5: 506 cases.
T-centres
506 cases · Every 3-cycle of the Ur t-centre buffer: 506 cases.
Wings
A wing cannot flip in place, so each wing has one letter: the sticker that comes first clockwise on its face. Most wing commutators use one inner-slice turn and outer turns. The usual buffer is UFr.
Wing letters: on each face, the first wing clockwise on each edge.
Wings
506 cases · Every 3-cycle of the UFr wing buffer: 506 cases.
Wings
506 cases · Every 3-cycle of the UFr wing buffer on the 5x5: 506 cases.
Midges
The 5x5's midges are lettered and solved like a 3x3's edges, from UF, with commutators that use the middle slice alone where a 3x3 commutator would turn M, E or S.
Corners and parity
Corners are solved as on the 3x3, from UFR; commutators that turn only outer faces work unchanged on the bigger cubes. Each kind has its own parity. On the 4x4 the corners' parity changes with each quarter turn of an outer layer and the wings' with each quarter turn of an inner one, so the two are independent: an odd number of corner targets ends with a corner swap, and an odd number of wing targets with a swap of two wings, which the 4x4's OLL parity algorithm does on its own.
2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2
A swap of two wings and nothing else visible: the pure OLL parity algorithm. (22 HTM)
Checked by the engine: 2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2 → 2 edges moved, 0 corners moved, 0 centers moved
On the 5x5 the midges move with the corners under every outer turn, so with the centres in place corner and midge parity come together, as on a 3x3, and the 3x3's parity algorithm handles both; the wings have their own parity, handled as on the 4x4.