In reply to my query to Ed Greenwood about Tellsongs, he had the following to say. (Note the reply below is paraphrased from a longer response.)
A tellsong is an alarm spell, triggered under specific conditions (like those governing a magic mouth), that is invisible, and its “alarm” is a chiming tune, audible only to the caster (unless the caster desires otherwise and sets it so during casting), that sounds whenever the caster comes within range.
It either chimes one way, to signal its continued presence and active status, or another way, to tell the caster whatever it was set to detect has happened.
If touched by detection magic or by any powerful unleashed magical effect, the tellsong is instantly and tracelessly destroyed (i.e. the person detecting magic wouldn’t detect it, because their attempt to detect it would destroy it).
The name of the spell came from its earliest form, devised long ago, when Myth Drannan casters (usually elves, but this was the [[first]]time of the City of Song open to all races) sang something or magically “recorded” someone else singing something, and used it as the audible alarm part of the spell.