CANON
, in Algebra, Arithmetic, Geometry, &c, is a general rule for resolving all cases of a like nature with the present enquiry. Thus the last step of every equation is such a canon, and if turned into words, becomes a rule to resolve all cases or questions of the same kind with that proposed.
Tables of sines, tangents, &c, whether natural or artificial, are also called canons.
Canon, in Ancient Music, is a rule or way of determining the intervals of musical notes. Ptolomy, rejecting the Aristoxenian way of measuring the intervals in music by the magnitude of a tone, formed by the difference between a diapente and a diatessaron, thought that they should be distinguished by the ratios which the sounds terminating those intervals bear to one another, when considered according to their degree of acuteness or gravity; which, before Aristoxenus, was the old Pythagorean way. He therefore made the diapason consist in a double ratio; the diapente consist in a sesquialterate; the diatessaron, in a sesquitertian; and the tone itself, in a sesquioctave; and all the other intervals, according to the proportion of the sounds that terminate them: wherefore, taking the canon, as it is called, for a determinate line of any length, he shews how this is to be cut, that it may represent the respective intervals: and this method answers exactly to experiments in the different lengths of musical chords. From this canon, Ptolomy and his followers have been called Canonici; as those of Aristoxenus were called Musici.
Pascal Canon, a table of the moveable feasts, shewing the day of Easter, and the other feasts depending upon it, for a cycle or period of 19 years. It is said that the Pascal Canon was the calculation of Eusebius of Cæsarea, and that it was made by order of the council of Nice.
