The purpose of this paper is to present the non-traditional theo- retical techniques of Erno Lendvai and introduce the application of these techniques in a detailed analysis of the Fifth String Quartet of Bela Bartok. The theories of Lendvai are based on the Fibonacci Series, a series of integers which he assigns to consecutive half-step gradations of the chromatic scale. The numbers 1,2,3,5,8... are manipulated to produce two important cornerstones of his theory, namely mi-pentatony and alpha harmonies. According to Lendvai, mi-pentatony, directly related to the Hungarian folksong idiom, is the basic scale used by Bartok. Alpha harmonies are derived by the intervallic relationships created through the use of Fibonacci numbers. Erno Lendvai's theories, although not widely known, are a partial answer to the analytical problems Bartok's music presents. His con- cepts allow for tertian chords as well as non-tertian harmonies. By basing his theories on the intervallic relationships which comprise the folksong idiom, Lendvai's theories can account for much of Bartok's music. Lendvai's theory, in contrast to traditional tonality, not only allows the tritone interval between roots of chords, but relies heavily upon it. The axis system and relative chord structures establish polar relation- ships which give the same function to chords whose roots are a tri- tone apart. Through the use of polar exchange, it is possible to shift the tonal center by six key signatures, yet never alter the function of the two polarly related chords. The analysis portion of this paper is designed to give a struc- tural, tonal and harmonic overview of each movement, giving particular attention to three areas: pentatony; relative, modally related and substitute chord harmonies; alpha harmonies. These areas assume varying degrees of importance depending on the particular movement. The theories of Lendvai are too new and untried to place them into any kind of perspective at this time. Lendvai's own writings are concerned more with a few specific pieces of Bartok's works which conform neatly to golden section principles, clear cut use of models (1:2, 1:3, 1:5), or alpha harmonies. His writings avoid thses portions of Bartok's music which defy explanation using this methodology.