One positive benefit from Schenker's work, particularly appealing to readers with a preference for visual information sources, is his invention of a graphical notation to summarise large scale contrapuntal and harmonic structure. This appears in several different forms in his own writings, and proposals for its improvement have been made by others also. At present, the clearest definition of a notation for Schenkerian analysis appears to be that of Salzer.

Failure to prove an assertion is not proof of its contrary, and although Schenker's claim of the ubiquity of his fundamental structure does not appear to be proven by the arguments he advances, it remain a plausible hypothesis which deserves further investigation. Objective investigation requires that both Schenker's method and its range of applicability be more precisely expressed than they are in Free Composition. In particular, his hypothesis would have greater value if it were clear how it might be falsified. Given these two clarifications, independent workers could test it by fair sampling from the works of composers to which it might apply.

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Unfortunately, Schenker's proponents do not appear to have thought such action necessary. Some, indeed, share with him the unwarranted assumptions and cavalier attitude to facts that suggest to this writer the need to gloss over severe defects in the argument. For example, Jonas follows Schenker in referring to the overtone series as “natural”, even though it is demonstrable only on human artifacts;[29] he asserts that “The strongest partials in the overtone series are those shown in example 20” (the example shows the first five notes of the harmonic series, C, c, g, c', e'), which suggests that he is unaware of the characteristics of the clarinet or of closed organ pipes, on both of which even harmonics are very weak;[30] and, in order to counter an assertion of Schoenberg's, he writes, “Mere habituation - and this is what Schoenberg's assertion reduces to - can never establish or alter qualities.”[31] whereas it is a commonplace of psychology, known to Helmholtz, that it does exactly those things - so much so that it is a standard tool of experimental psychology. [32, 33] Such errors are minor details of an argument but serve to warn the reader that an author is ignorant or untrustworthy. A more fundamental difficulty of many expositions of Schenker's analytical method, including his own, is a failure to define its range of applicability. To say that it applies to tonal masterpieces does little to improve this state of affairs, since neither of the words in this phrase has a single agreed meaning. The more inclusive of the current meanings of tonal, applying to any work in which one note seems to have more importance than the rest, would include works by Debussy and Ravel, both of whom are strikingly absent from Schenker's examples. On the other hand, the nowadays less usual definition restricting the term to works which establish a key by the usual cadences at frequent intervals would save nearly all of Schenker's examples, with possibly only Josquin at risk. Greater difficulties arise with “masterpiece”. Of the two current meanings, “one's greatest achievement” has to be rejected, since it would allow Schenker examples from only one work of each composer, while “a piece of work worthy of a master” is clearly so subjective as to be useless.[34] The original, unambiguous meaning of the word, the piece by which the masters of a guild judged whether a journeyman was fit to join them, is now, unfortunately, obsolete. The difficulty with which this leaves us is that without this definition, Schenker's thesis concerning the fundamental structure lacks the status of a objective statement concerning the nature of music and can be regarded only as an elaborate definition of his personal aesthetic. The analytical components of most other disciplines have strict practices and criteria for correctness. Schenker not only asserts that “Music is always an art - ... Under no circumstances is it a science”, (for which it is possible to make something of an argument):[35] he and his followers seem content that musical analysis also should not be a science. Clearly many musical analysts agree with this view. This writer, in contrast, seeks for musical analysis the same epistemological status as has been achieved by the activities called “analysis” in most other disciplines. As presented by its inventor, Schenkerian analysis appears to inhabit the same intellectual limbo as the writings of the interpreters of Marx and the psychoanalytical theories of Freud, Jung and Adler: like them, it is a system whose protean nature protects it from refutation but substantially reduces the usefulness of whatever meaning can be derived from it.

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