Understanding FM Implementations: A Call for Common Standards

Abstract

In recent years there has been much effort to standardize music representation so as to allow musical pieces to be transferred freely between systems. These efforts have dealt largely with music at the level of notes and scores. In such endeavors there is an unspoken assumption that the elements of discourse have the same semantic meaning for everybody, and this is certainly true of things like equaltempered scale, quarter-note, middle-C, etc. We have a long musical history that defines these concepts in an unambiguous way. If, however, we should ever want to extend this representation effort to include timbral propertiesand I think we should-we are in a rather bad position if the state of our synthesis implementations is anything like that which currently exists for synthesis via frequency modulation (FM). Because of ambiguous notions of what constitutes correct FM, a situation has developed in which sites have implemented incompatible FM algorithms, thus precluding the possibility of distortion-free migration of FM patches between platforms. This article is an attempt to set the record straight about this issue, and to identify and clearly define some of the different forms of FM that have emerged over the years. Please note that I have normalized the notation used in all the equations that follow, so they may be different from the original source from which they were taken. This also applies to the nomenclature surrounding the table lookup oscillator, which varies from author to author. Throughout the paper I have called it Frequency Increment Table Lookup oscillator, or FITL for short. The Source of Ambiguities