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Over the course of his theoretical writings, Schoenberg issued many poignant judgments on the "tonality" of his serial and pre-serial music, but not without apparent inconsistencies and contradictions. One finds, for example, comments that the cyclic nature of serial procedures assured that no one tone would predominate over the others (1975: 219-220 and 246) or that the structural functions of chords in serial musicdo not derive from harmonic principles (1954: 194) and that complete recourse should be made to the structure of the row as the premise of tonal coherence (1975: 246-7). On the other hand, one finds a complete abhorrence of the term "atonal" when applied to any of his music, a strong belief in the eventual discovery of the "tonality" of his serial music (since "tonality" for Schoenberg was more an issue of aural understanding than of particular harmonic materials and idioms) and a conviction that critical/analytical judgments of this music should be made by listening rather than via observations of its technical peculiarities (1975: 283-4). Schoenberg's most clearly focussed discussion of issues of "tonality" and form is to be found in an article entitled "Problems of Harmony" where he associates organizational and functional impressions of "tonality" with particular harmonic principles, factors of cadence, form and modulation, and harmonic/motivic consistency. The very general but essential synthesis at which Schoenberg arrives is that One thing is certain: all chords that in any way may turn to a key, no matter how dissonant they may be, fall within the domain of the old harmony and do not disturb tonality. It might be further said that tonality does not depend upon the number of dissonances used or their eccentric effect, but rather: 1) on whether these chords may be referred to a key; or 2) whether these relations are convincingly enough worked out. [1975: 283] It is striking to see Schoenberg's reference to the common practice concept of a "key" in this generalized explanation of tonal comprehensibility. This is founded to a considerable extent on an appeal to the overtone series (1975: 271) as the natural basis for harmonic and melodic coherence. The tones or chords closest together in the overtone series form the most natural harmonic groupings or successions as in triadic structurings and progressions of the diatonic keys. Conversely, those which are farther apart in the overtone series form more forced or artificial associations which may nevertheless be involved in convincing expressions of tonal logic (as in chromatically altered scale degrees or the more complex pre-serial and serial tonal structurings). Although the second part of the statement is quite vague, Schoenberg has, elsewhere in the essay, revealed what he views to be relations which are "convincingly" worked out. Perhaps foremost among these is the sense of cadence and cadential emphasis relative to different tonal centres within the phrase and formal structure of a work (see 1975: 278) This will be termed "tonal form" here. Schoenberg terms this the "art means" of a piece (1975: 275) which is necessary for the perception of a particular tonal logic. Although it is never specifically mentioned, one must also assume that melodic or harmonic successions can be "convincingly worked out" by clearly directed voice-leading which creates a sense of motion and goal regardless of the nature of harmonic and melodic materials and regardless of whether there is a cadential or repetitive centering of a particular tone or sonority (1975: 248). This is most clearly illustrated in the following two chorale-style examples from "Problems of Harmony" (1975: 229 and 230). A series of consonant but non-key-related sonorities (in the first example which is Schoenberg's example 5 from "Problems of Harmony") is compared with a series of more dissonant chords which are nevertheless clearly organized with directed motions to stable sonorities on A and D. …

On Tonality and Tonal Form in the Serial Music of Arnold Schoenberg