Schenker's Free Composition is a curious document, in which assertions, of a more or less obscure character, greatly outnumber arguments.[23] Such a document depends for its credibility upon the authority of the author. To some extent this can be assessed by consideration of those arguments he deigns to supply, but for lack of many of these, the accuracy or otherwise of his assertions in areas of which this writer has substantial knowledge carries much of the weight.

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An example of Schenker's style of argument appears in his Introduction, where he purports to counter the question: “But did the masters also know about all this?”[24] His first response is an ad hominem attack (“This objection ... only betrays a lack of education”). He continues to argue that the masters had no need to write about the “laws of art”, which is true enough, but scarcely to the point, since some of them did, and finally suggests that the reader “must concede” that conformity of a composition with Schenker's ideas shows that the masters had a keen awareness of such relationships. The last seems to this writer not to follow at all, because of the many examples of human behaviour which stem from unconscious motives. The entire paragraph is consistent with the view that the masters' ground plan for music was substantially different from Schenker's, which is why he is unable to find a good answer to the question.

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Schenker's description of his fundamental structure is introduced by the curious phrase “In nature sound is a vertical phenomenon”[25] Since in the open air, and in the absence of wind, sound is a radial phenomenon, this is a peculiarly unfortunate phrase, which, this writer has been told, sounds no more plausible in the original German. The figure to which the phrase refers shows the first five notes of the harmonic series, so what Schenker appears to mean is that the occurrence of the harmonic series as a chord in music is a natural phenomenon. Unfortunately, this is still not true, at least not in the sense that Schenker intends, in two aspects. The trivial one is that on the majority of vibrating objects, it is much easier to demonstrate multiple resonant frequencies sequentially than simultaneously. The more serious objection is the one demonstrated above, that those musical instruments which sound harmonic, or approximately harmonic, do so because of the efforts of their designers and the choice of musicians, not because of the inherent nature of music, either in the human central nervous system or in the universe at large. Indeed, in a culture in which only percussion instruments existed, it is conceivable that a completely different art of music might have arisen, based on a dominant instrument with non-harmonic partials. The latter would have been the foundation for a completely different harmony and counterpoint, and the design of all other instruments would have had to conform to it.

Schenker appears to have had some difficulty in finding a reason to exclude the interval of the fourth from consideration as candidate in some part of his fundamental structure. His basic thesis requires him to find a way to deny to the interval of the fourth the same status in the fundamental line as that given to the octave and the fifth. [26] His argument appears dangerous to this writer, for whom the chord generated by the harmonic series reveals both the fourth and the fifth more readily than it reveals the double octave, and for whom any argument concerning the fourth applies equally well to the fifth. Moreover, if one attempts to derive harmonic laws from the harmonic series, one could as reasonably derive melodic ones; but this leads to the embarrassment of finding two minor thirds of different sizes before one finds the tone, and of the latter the lowest one in the harmonic series is larger than any tone used in conventional Western music, despite Kirnberger's attempt to introduce the harmonic seventh in 1771. [27]

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These three examples do not seem, to this writer, to demonstrate that Schenker is an author whose accuracy one can reasonably take for granted. On the contrary, he appears to be ignorant of many of the characteristics of sound which are of importance in music and contemptuous of the means by which they can be discovered. He is also inconsistent in the application of his arguments.