Dear Mr and Mrs Williams,
I am writing in regards to the complaint I have received from you recently. My sincere apology for the inconvenience and problem caused due to my actions and I assure you that I will be more careful in the future about it.
I started learning the piano recently. As you may know, I work full-time and the only free time I am able to dedicate to my classes is weekends. I have hired a piano teacher to teach me during the weekends and I am sorry that the noise reached your flat.
I am sorry about the inconvenience I caused to you and Mrs Williamds. I did not expect the sound of my piano to be so loud and reach your rooms. I totally understand your position and request you to accept my sincere apologies.
As a solution, I have decided that I will continue my piano classes at my tutor’s house instead of mine. This way I would be able to continue my practice and not disrupt you.
I hope this unpleasant situation hasn’t hurt our friendship.