The Music III is a sound synthesis software that belongs to the family of Music N. It marked a first turning point in the history of computer music with the introduction of Unit Generators.
Background – The innovations introduced by the Music III were not many in quantitative terms, but were so substantial that probably does not make sense to talk about the new version but rather a completely new software, although there are still the most distinctive features of the Music N. What spurred Mathews in the definition of the new program is not only a willingness to establish a flexible and well-set tool, suitable for professional use by composers, but also the technological innovations of those years, as the placing of CPUs transistor technology and the availability of the new IBM 7090, provided the right conditions for the emergence of more complex software. The new software was completed in 1960. In 1961 Max Mathews wrote an article that gives some reflections on the state of affairs of computer music and possible future prospects. This paper, along with issues identified, also illustrates the characteristics of the new program for digital synthesis.
Unit Generators – The real novelty of Music III, a turning point for the subsequent development of computer music, was the introduction of the Unit generator concept (from now simply UG). In computer terms UG are macros, sort of small pieces of software complete with instructions, which perform specific functions and are invoked by simple commands, very quickly. In Music N computer music language, construction of instruments is done by connecting together the various UG. In Csound UG are defined Opcode. In some cases this term was used, in general, to replace the term UG. But this is an improper use as Opcode are not machine-level instructions. The UG allows you to work in a very sophisticated and specific manner when they are connected to each other. For this reason, the UG were often treated as modules of analog synthesizers.
Connections – The basic principle that determines the effectiveness of UG is the fact that these units not only allow us to obtain an output data but also to accept input. In this way, linking the UG, it is possible to build both simple and more elaborate tools, able to perform complex functions. In fact, the operation of UG allows you to pass data from one unit to another. Compared to the analogy between UG and analog modules, which we mentioned earlier, the same Max Mathews argued that understanding the operation of the analog modules could be useful, in an educational perspective, to understand the operation of the digital corresponding introduced by the Music III. The UG (such as Csound Opcode today) could carry out different functions: UG are oscillators, capable of generating sinusoidal sounds; amplitude envelopes, which also define the attack and decay transients; others allow sounds filtering, and so on. The introduction of UG, then, contributed greatly to making the computer very similar to a musical instrument, with good flexibility and able to allow work on the sound to a level of detail hitherto unthinkable even for analog instruments. In this way, also, UG gave back a software with a reasonable degree of generalization.
Limits – Is true, though the importance of the UG was evident immediately, that their ability to enhance the musical use of the computer does not like getting with the Music III but with the software developed later. In fact, beyond the UG, the Music III did not look like a complete tool, Mathews himself was aware that he continued to develop its own research to arrive at the realization of Music IV. Even today, professional software for music, we think Max/Msp as an example, make use of UG concept introduced by Mathews in the early sixties. As for the Music III, however, the importance of it in those years also witnessed by the arrival at Bell Labs of figures such as James Tenney, and Jean-Claude Risset, which would help to expand the horizons and possibilities of computer music also in the aesthetic sense.
For this topic I’ve read.
 Max Mathews, An Acoustical Compiler for Musical and Psychological Stimuli, Bell Telephone System Technical Journal, 1961.  Curtis Roads, Interview with Max Mathews, Computer Music Journal, Vol. 4 , 1980.