I'm very sorry for being so loud on (date). The party at my house got a little bit out of control. I asked repeatedly for my guests to keep the noise down, but to no avail. I realize the noise they were making was disturbing to you and I apologize for the...
Dear (recipient's name),
I'm very sorry for being so loud on (date). The party at my house got a little bit out of control. I asked repeatedly for my guests to keep the noise down, but to no avail. I realize the noise they were making was disturbing to you and I apologize for the inconvenience.
You have my promise that all parties in the future will stay within normal noise limits. I now realize that a crowd as large as the one on (date) is too large for a neighborhood like ours. I appreciate you as a neighbor and am grateful for your kindness and understanding.
Sincerely,
(your name)