A compound of formula A, B, or C: wherein: ---- designates a single or double bond; n is 1, 2, or 3; each of PG 5 and PG 6 is independently a suitable hydroxyl protecting group, which taken with the oxygen atom to which it is bound, is selected from an ester, a silyl ether, an alkyl ether, an arylalkyl ether, and an alkoxyalkyl ether, or PG 5 and PG 6 are taken together to form a cyclic diol protecting group, which taken together with the oxygen atoms to which they are bound, is selected from a cyclic acetal, a cyclic ketal, a silylene derivative, a cyclic carbonate, and a cyclic boronate; W is CH-A or C; A is a C 1-6 aliphatic group, wherein A is optionally substituted with one or more Q 1 groups; each Q 1 is independently selected from cyano, halo, azido, oxo, OR, SR, SO 2 R, OSO 2 R, N 2, NR R, NR R, NR N 2, NR OR, OR, O R, N 2, O N 2, or OPG 1, wherein PG 1 is a suitable hydroxyl protecting group, which taken with the oxygen atom to which it is bound, is selected from an ester, a silyl ether, an alkyl ether, an arylalkyl ether, and an alkoxyalkyl ether, and wherein: optionally two Q 1 are on A and are taken together to form a 3-8 membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each R is independently selected from hydrogen or an optionally substituted group selected from C 1-6 aliphatic, a 5-10 membered saturated, partially unsaturated or aryl carbocyclic ring, or a 4-10 membered saturated, partially unsaturated or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, wherein: when Q 1 is independently selected from N 2, NR N 2, N 2, and O N 2, two R groups on the same nitrogen atom are optionally taken together with said nitrogen atom to form a 3-8 membered saturated, partially unsaturated, or aryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and wherein X B is O, and R B is TMS; X B is H and OH, and R B is TMS; or X B is H, OAc, and R B is Ac; and R 1 is -CH 2 CO 2 R 2, wherein R 2 is alkyl. ---- designates a single or double bond; n is 1, 2, or 3; each of PG 5 and PG 6 is independently a suitable hydroxyl protecting group, which taken with the oxygen atom to which it is bound, is selected from an ester, a silyl ether, an alkyl ether, an arylalkyl ether, and an alkoxyalkyl ether, or PG 5 and PG 6 are taken together to form a cyclic diol protecting group, which taken together with the oxygen atoms to which they are bound, is selected from a cyclic acetal, a cyclic ketal, a silylene derivative, a cyclic carbonate, and a cyclic boronate; W is CH-A or C; A is a C 1-6 aliphatic group, wherein A is optionally substituted with one or more Q 1 groups; each Q 1 is independently selected from cyano, halo, azido, oxo, OR, SR, SO 2 R, OSO 2 R, N 2, NR R, NR R, NR N 2, NR OR, OR, O R, N 2, O N 2, or OPG 1, wherein PG 1 is a suitable hydroxyl protecting group, which taken with the oxygen atom to which it is bound, is selected from an ester, a silyl ether, an alkyl ether, an arylalkyl ether, and an alkoxyalkyl ether, and wherein: optionally two Q 1 are on A and are taken together to form a 3-8 membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; optionally two Q 1 are on A and are taken together to form a 3-8 membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each R is independently selected from hydrogen or an optionally substituted group selected from C 1-6 aliphatic, a 5-10 membered saturated, partially unsaturated or aryl carbocyclic ring, or a 4-10 membered saturated, partially unsaturated or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, wherein: when Q 1 is independently selected from N 2, NR N 2, N 2, and O N 2, two R groups on the same nitrogen atom are optionally taken together with said nitrogen atom to form a 3-8 membered saturated, partially unsaturated, or aryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and when Q 1 is independently selected from N 2, NR N 2, N 2, and O N 2, two R groups on the same nitrogen atom are optionally taken together with said nitrogen atom to form a 3-8 membered saturated, partially unsaturated, or aryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and wherein X B is O, and R B is TMS; X B is H and OH, and R B is TMS; or X B is H, OAc, and R B is Ac; and R 1 is -CH 2 CO 2 R 2, wherein R 2 is alkyl.