What is Haunting Melody?
Haunting Melody is a [General] feat; no special rules govern them as a group.
The Book of Exalted Deeds says that These feats are thus supernatural in nature (rather than being extraordinary abilities, as most feats are) (BoED page 39) concerning Exalted Feats. This strongly implies that all feats are extraordinary abilities, but there may be table variance.
As for extraordinary abilities,
Using an extraordinary ability is usually not an action because most extraordinary abilities automatically happen in a reactive fashion. Those extraordinary abilities that are actions are standard actions unless otherwise noted.
Thus, if one's Dungeon Master allowed them to use Haunting Melody on its own, it would be a standard action.
But Wait, There's More!
While using Haunting Melody "counts as one of your daily uses of bardic music," it is not a "bardic music effect"—those are those abilities listed under "Bardic Music" with their names italicized. Unlike those effects, Haunting Melody may be used within an Antimagic Field, as it is a [General] feat and Bardic Music itself is not listed as a Supernatural or Spell-Like Ability.
Now, see the link to the description of an Extraordinary Ability up there? According to the text of Haunting Melody, the feat is a reactive ability with the triggering condition "When you sing or use some other Perform skill". Thus, whenever you meet the triggering condition you may opt to expend one usage of bardic music in order to 'inspire fear in your enemies'. Nothing in the feat description states or even implies that this is a standard action. If you can use Perform as a move-equivalent action, for example, the Gladiator's Roar of The Crowd (Sword and Fist page 21), you may use Haunting Melody then. If you can use Perform as part of casting a spell, as Music of Making implies is possible (but does not explicitly grant the ability to do so), you may use Haunting Melody then. In fact, if you possess Melodic Casting (Complete Mage page 44) or Chord of Distraction (Complete Scoundrel p. 75), you may even use Haunting Melody off-turn! Dragonsong (Draconomicon p. 105) increases the saving throw by 2, and there are many other feats and spells it can be used as a part of.
Too Long? Didn't Read? No Worries!
In summary:
- Haunting Melody is a reactive, extraordinary ability.
- It is triggered "when you sing or use some other perform skill"
- It can be triggered at any time, even during another character's turn, as long as the triggering condition is met
- It can be triggered when casting any bard spell (see the Players Handbook, page 26)
- It expends one use of bardic music upon activation
- Your DM may houserule to allow it to be used as a Standard Action
