A mitre or miter joint is a joint made by beveling each of two parts to be joined, usually at a 45° angle, to form a corner, usually a 90° angle. It is often used in making picture frames. For miter joints occurring at angles other than 90°, for materials of the same width and height (i.e. pieces of a picture frame border) the proper cut angle must be determined so that the two pieces to be joined meet flush (i.e. one piece's mitered end is not longer than the adjoining piece). To find the cut angle divide the angle at which the two pieces meet by two. Technically two different cut angles are required, one for each piece, where the second angle is 90° plus the aforementioned cut angle, but due to angular limitations in common cutting implements (hand circular saws, table saws) a single angle is required and is used to cut the first piece in one direction and the second piece in the opposite direction. In woodwork, it is one way of joining two pieces of moulding that meet at an angle. (Compare the cope cut.) It is a popular method of joining as it is easy and attractive. By itself, it is one of the weakest joints to choose, but it can be strengthened with a spline. It is also done in pipe work, to take ducts around a corner, or in pipe organs, to fit a large bass pipe into a small space. (The same cut is used to shape of the resonators of certain reed ranks—e.g. see Great ranks and Pedal reeds of Ashton Hall organ—but only the other kind are called "mitered pipes". And, "mitered pipes" are sometimes constructed without miter cuts. The joints of bicycle frames built with lugs are said to be mitred, but in this case the ends of the tubes are carefully cut or filed to fit the radius of the tube against which they are held. The joints are then brazed with brass or silver brazing rods.
