Touy said: Correct. Tenma's a Daitengu. Daitengu are the long-nosed, red-faced tengu.
Actually this is what Perfect Memento said: There are various types of tengu, including: the tengu boss, Tenma the management types, Daitengu the nimble information corps, Crow Tengu (Aya) the ones who specialize in office work, Hanataka Tengu the mountain's defense force, White Wolf Tengu (Momiji) and the printers, Yamabushi Tengu.
Touy said: Actually, Nitori's design is quite clever when you think about it.
Its clever, but it also means she should be bald under that hat or she has some sort of dent in her head full of water and if she bows she'll die. I'll take Gensokoyu's "spitting on mythological accuracy-Rule of Cool/Cute" approach any day!