This section is from the book "An Illustrated Flora Of The Northern United States, Canada And The British Possessions Vol1", by Nathaniel Lord Britton, Addison Brown. Also available from Amazon: An Illustrated Flora of the Northern United States, Canada and the British Possessions. 3 Volume Set..
Bulbous herbs, odorous (alliaceous); bulbs solitary, or clustered on short rootstocks. Leaves narrowly linear, rarely lanceolate or oblong, sheathing, basal, or sometimes also on the stem. Stem (usually a scape) simple, erect. Flowers white, purple, pink or green, in a terminal simple umbel, subtended by 2 or 3 membranous separate or united bracts. Pedicels slender, not jointed. Perianth persistent; segments 6, separate, or united by their bases. Stamens on the bases of the perianth-segments; filaments sometimes toothed; anther-sacs introrsely dehiscent. Ovary nearly sessile, 3-celled; style filiform, jointed, deciduous; stigmas small; ovules 1-6 in each cavity. Capsule loculicidal. [Latin for garlic]
Leaves oblong-lanceolate, absent at flowering time. [Validallium Small.]
Leaves linear, present at flowering time.
Bulb-coats membranous, not fibrous-reticulated.
Umbel capitate; pedicels shorter than the flowers.
Umbel looser pedicels much longer than the flowers.
Flowering umbel nodding.
Perianth campanulate, white or pink, its outer segments acute.
Perianth urn-shaped, purple, outer segments obtuse or notched.
Flowering umbel erect.
Leaves flat or channeled, all nearly basal.
Leaves terete, hollow, some on stem; flowers often replaced by bulblets.
Filaments with a tooth on each side.
Filaments simple, not toothed.
Capsule not crested.
Flowers mostly replaced by bulblets; scape 8'-2° tall.
Flowers rarely replaced by bulblets.
Scape 1°-2° tall; pedicels 8"-12" long; perianth-segments thin.
Scape 4'-8' tall; pedicels 4"-6" long; perianth-segments rigid in fruit
Capsule-valves with 2 short crests.