This paper is an aitempt to utilize the theoric operations of the set theory in mathematics.It is assumed to bring selection and formation of the total vacalic elements of the cardinal vowel some clearness to the system . Some abstract aspects of the set theory like, tuiality, property and functional relationship are used to help to realize some confusion and inproper formation within the two sets of the system. Each of them is attested to contain vaguely a 'set of sets' which is thought to be the cause of the inconsistency and insufficiency of their application. The revision revealed the possibility of formulating a refined basic system, which contains one intelligible set of eight different vocalic variables (elements). This basic system,unlike before, can be extended to include two or more sets, once onc changes the identicat relative phonetic property of all the vocatic clements of the set within the basic systems.