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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.

Bela Bartok's six string quartets are generally regarded as the next most significant works in the medium after the quartets of Beethoven. Unlike some of his contemporaries in the field, e.g, Hindemith, Milhaud, and Schoenberg, Bartok's quartets are representative of his musical growth and, as such, are worthy of equal status with those of such recognized masters as Haydn and Mozart, as well as Beethoven...

What is generally referred to by the public-at-large as “modernism” is thought (by it) to be based upon the denial and contradiction of the fundamental principles of musical art. But it would be a grave error to assume from this that the present age differs in the attitude toward modernism very considerably from any other, except perhaps in degree. The general intellectual or artistic niveau of any period whatsoever is almost inevitably a low one, apart from a few outstanding figures -- rarely exceeding two or three in any single generation -- who impart most of the significance to it. One is too prone to forget that art is somewhat different from other human activities in that the achievement of one man of genius far outweighs that of any number of mediocrities put together, even though he may be outnumbered by them in the ratio of a thousand to one. Even though it is rare, if not impossible, to find a man of solitary genius who is not indebted to at least one or several lesser men for his achievements it still holds true that a thousand noughts added together only amount to nothing in the end. It is the inability to recognize this simple truth that is primarily responsible for the all-too-familiar charge of decadence which is increasingly brought by each successive generation against its contemporary artists, even in the most incomparably fertile periods of artistic activity. In Bartok’s music one can feel a rich humaneness. The mechanization of music as found in Stravinsky, and the constructivism of Schoenberg in later years, are equally alien to Bartok. No matter how new his music, no matter how far he ventures into unexplored tonal spheres, his music never loses its inherent warmth. His keen mind, thinking clearly and surely, does not chill the emotion and does not allow the soul to freeze, as do the intellect of Schoenberg and the calculated objectivity of Stravinsky. Regardless of how much Bela Bartok condenses music and reduces it to the very essential of tone and rhythm, and even when he seeks heights where the atmosphere becomes thin and cold, music remains an art of the soul, of its grief and sorrow. The songs of the people, from whom Bela Bartok is descended, still resound into the lonely spheres in which the spirit of a great composer sought a new truth

Various approaches to rhythmic analysis have been produced by recent research. Many of these are most suitable for tonal musical compositions; when other methods of tonal organization are present, these theories are less useful. This study uses accent based criteria in order to establish a set of analytical procedures which are applicable to a wide range of musical compositions. Four accent types (contour, agogic, dynamic, and motivic) are identified in two string quartet movements. These are Beethoven's Op. 18, No. 1, movement four, and Bartok's String Quartet No. 4, movement five. The study finds great differences in accent placement between the two works. In both works accents affect phrase grouping and meter. Accent patterns and composite accent profiles, which represent all the accent types in a particular passage, are compiled for important themes. Large fluctuations in accent use are evident between the formal sections of each work.

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