The Mystic Whistle (イタコ笛 , itako fue, literally translated as Itako Whistle) is item number 4 of the Spirit Detective tool kit. The name is a pun, given that the term itako is usually written as いたこ.
This device is something of a dog whistle for demons/apparitions, emitting a soundwave that only their kind can hear. The stronger the Spirit Energy of the person who blows into it, the louder the noise it makes. Also, the stronger a demon's energy, the louder the sound is.
Botan claims to be capable of making this peculiar sound wave travel at least sixty miles, and describes it as "rather annoying," in her words.