As can be assumed from his choice of terminology, Janeček's interest in "imaginary tones" lies not so much in the realm of tonal syntax but in the phenomenon of the individual sonority and its apparent perseverance in the ear until it is succeeded partially or completely by the next sonority. In addition to studying the harmonic state of chords as determined by "real" or "imaginary" pitches, Janeček cites the even richer possibility of characterizing the chords generated at the interphase of real and imaginary chords i.e. the lingering pitches with those that are newly arriving to the ear. He gives various examples (see Example 16) in which he employs a combination of the notated harmonic progressions with a superimposed typescript of the imaginary tones and the linear graphic representing their projected decay.

Example 16: Progressions Involving the Interaction of Real and Imaginary Pitches

Situations involving chords larger numbers of pitches pose less substantial impressions as imaginary pitches in Janeček theory since they will inevitably be "cancelled" in the dampening complexity of the ensuing chord. Similarly the interference of imaginary tones is much greater in the succession of consonant sonorities than in the succession of dissonant sonorities and hence the need for classical voice leadings to nearest adjacent pitches which will eliminate the accumulation of imaginary pitches. Janeček explores other implications of cancelled and uncancelled pitches in the silence following staccato chords or quick arpeggiating figures and the "dampening" affect of close-proximity dissonances as opposed to consonances or in widely spaced dissonances.

The situation of the "composite expression of chords in a single voice" (Janeček's expression for compound melody) provides a further dimension of Janeček's theory of the "imaginary" tone in the implied harmonic structure of a single-line melody (see Example 17).

Example 17: Harmonic Profile of Single-Voice Melody

In parsing more complex situations Janeček adheres to more or less intuitive preferences: for two (or more) simple chords as opposed to single, more complex sonorities, also for simpler metric parsings over more complex ones, and for harmonic segmentations that complement rhythmic motivic structurings. He acknowledges the ambiguity of many modern melodic situations where clear segmentations, even of just the real pitches, are not possible.

Janeček's discussion become particularly refined in the consideration of non-harmonic tones versus "counter-canceled" tones (which involve a dissonant harmonic structure) and "imaginary harmonic" versus "imaginary tonal" (essentially the common-practice non-harmonic tones) pitches. The latter are more transient, more linearly connected, less disruptive of the harmonic context (i.e. invariably "cancelled") and hence insignificant intrusions on dissonant formations. Among the more prominent effects of non-harmonic tones, he notes the very "penetrating" and de-tonicizing effect of passing (non-harmonic) tritones formed with whatever degree of the consonant triadic structure, and also the less structurally threatening effect of dissonances forming a whole-tone or a semitone (but not also a tritone) with whatever member of the triad. Janeček attributes this to the innate attraction of the tritone, as if the ear wants to keep it as part of the harmonic sonority. Only the major/minor third semitone alternation is judged to have comparable distracting qualities to the passing tritone. Generally, because of their inherent connectedness Janeček ascribes a greater "durability" in the overall tonal/harmonic percept to "tonal imaginary" pitches (passing tones etc.) as compared to "harmonic imaginary" pitches since they function at a lower, more sustainable level of our harmonic awareness.

The "incompleteness" of harmonic sonorities is also an aspect of their particular "expression" and one interesting consequence Janeček's concepts of "tonal" and "harmonic imaginary" tones is his conjecture that incomplete sonorities are more "inclined to take in spontaneously further components by which they can be enriched." Dissonant formations with few tones will conversely tend to take in pitches which will not complicate their dissonance characteristic and more consonant incomplete chords will strive toward completion via their transient tonal and imaginary pitches.

Speculations on Harmonic Motion, Function and Progression

Janeček's initial distinctions among possibilities of harmonic motion are those of "partial harmonic motions", between chords of similar pitch (but not dissonance) content and "fundamental harmonic motions" between two clearly independent harmonies. "Higher-ranked" harmonic motions are designated as the more pronounced motions between the end of one chord succession and the beginning of the next. "Links" are common pitches between adjacent chords, and can be single, double or multiple and even "complete" in the case of identical repeated chords in which there is no harmonic motion. A "direct link" is a direct pitch repetition or, interestingly, an octave transposition which does not "cross over" or take part in a major or minor second voice-leading ⁽¹⁹⁾ anywhere in the harmonic motion. An "indirect" or interrupted" link conversely involves an octave transfer which does not cross over a major or minor second voice-leading. Generally, direct links form stronger bonds between chords than indirect links and the fewer the pitches in the chord, the more effective the link (see Example 18).

Example 18: Examples of Direct and Indirect Links

Essentially what Janeček judges in his category of harmonic motion are effects of succession and continuity between tones related in purely harmonic terms. Partial harmonic motion lies between melodic motion (i.e. the absence of harmonic motion) on the one hand and fundamental harmonic motion on the other. Whereas melodic motion is seen to unfold harmonic structures via uncancelled imaginary tones, partial harmonic motion will result from the cancellation of some imaginary pitches in a first harmony via real pitches of a second. Fundamental harmonic motion, however, will result only from the simultaneous cancellation of all imaginary tones between successive chords.

Relative judgments as to the effectiveness of the link, and hence whether a progression is "fundamental" or "partial", depend on the number of tones involved in the link (a single tone for two voices, a double link for three or four voices, a triple link for five voices etc.) and the harmonic/registral strength of the link, i.e. whether it is in the bass, etc. What is judged to be an insufficient link between two harmonies gives rise to a fundamental harmonic motion or the succession of independent harmonies as opposed to merely successive states of the same harmony, or in Janeček terms, "interdependent chordal cross-sections". Janeček gives multiple examples of partial and fundamental harmonic progressions in which tones between chords involved in voice-leadings of 1 or 2 semitones present a "pronounced" form of harmonic motion. Uncancelled imaginary tones of course, complicate the situation but generally Janeček asserts that the "simpler intervals" formed between imaginary tones of the first chord and the real tones of the next will make the more effective harmonic function. Imaginary pitches (which, as such, form "imaginary" links between harmonies) will not effect the status of a progression as "partial" or "fundamental" except with wide ascending leaps in all voices (and hence multiple uncancelled imaginary tones) which would tend to link the chords as a single registrally unfolding harmony.

Interesting postulations emerge in Janeček's discussion of voice-exchanges or indirect links via register transfer of tones between chords. While the impression of a more fundamental progression involving these effects is difficult with three-note chords (see example 19a), he notes that it is possible with four- and five-note chords. Among indirect links the case of the common tone becoming part of a melodic interval 1 or 2 (as opposed to crossing it) is a more significant link. This case is weakened if it is part of a voice-exchange, i.e. the melodic movement of 1 or 2 semitones is reversed in another voice. Fundamental harmonic motion is said not to be possible between two different positions of the same transposition of consonant triads or dissonant three- or four-note chords that do not contain the interval 1 or 2 (i.e. 44, 33 or 333). But a fundamental harmonic progression is said to be possible between different chord types or different transpositions of the same chord type, and also with different registral dispositions of the same transposition of higher-class (4-, 5- or 6-note) chords containing the interval 1 or 2 (Example 19b and c). Especially interesting in the latter case are the voice-exchange progressions of two-triad combinations. Re-voicings of +2+ combinations (major triads separated by a major second) are not seen to produce fundamental harmonic motions to the same extent as, for example, the more complex +6+ re-voicings.

                                   
                                            Example 19: "Fundamental" Progressions Involving Registral Exchange of Pitches

In an essentially normative discussion, Janeček acknowledges the relation between rhythm, meter and fundamental harmonic progression and the role of effective modulatory chords in "higher-ranked" harmonic motion. Cadential progressions then become a standard for judging other progressions in terms of three factors: the "pure" tonic, the leading tone and the functional principle. The "pure" tonic as an ultimate sonority is free from imaginary pitches, or pitches that have not been connected to the tonic by half step or descending whole step. Janeček however, adds a further condition that the "pure tonic" be free from imaginary tonal pitches (i.e. unresolved non-chord tones) which form a tritone, the most "welcome" dissonance, with any of the real pitches of the chord. In other words, in C major, the chromatic tones of C#, F#, and B. Janeček does not discount the possibility of final cadences which are less tonally closed or which even end on dissonant sonorities, but rather asserts the pure tonic as a universal ideal operating on a higher level than stylistic convention.

Concerning the pre-cadential chord Janeček notes that of the nine notes of the negative of the major triad, three form tritones with the different degrees of the tonic triad (B, F# and C#, for a CEG tonic) of which one cannot be cancelled (B) in motion to the tonic triad. The other two, (F# and C#) can be resolved via semitone motion (and hence cancelled) into the tonic, but the F# is a less appropriate pre-tonic element since it forms a tritone with the tonic pitch itself. In the minor key, A natural is eliminated as a pre-tonic element since it would form a tritone with the minor third (E). Janeček asserts that there must be one semitone cancellation in cadential harmonic motion, with obvious preference for the one to the tonic pitch itself. A descending half-step motion (D - C), however, would evoke the tritone with the fifth (G) of the tonic sonority and a second leading-tone, to the fifth (F#) would similarly conflict with the tonic itself, as already noted.

Janeček's theoretical discussion of the functional principles of harmonic tonality echoes the symmetrical balancing of "pre-tonic" degrees above and below the tonic as seen in the dominant and subdominant of the theories of Riemann and Otakar Šín. Thus Janeček maintains that only the purely consonant and hierarchical (root/third/fifth) harmonic structures of triads are capable of defining a functional tonal space ⁽²⁰⁾ and that the only admissible pre-tonic triads should have equal but opposite functions and mutually exclusive pitch content among themselves. They should also fulfill a fundamental harmonic progression with no more than a single tone in common with the pure tonic. Thus, the voice-leading principle of the pure tonic, i.e. the resolution of all imaginary and melodic tones, will admit only the dominant and major and minor subdominants as pre-tonic sonorities (for major or minor), and so idealizing the "classical functional system of three members" which comprises the nine pitches (including E of the tonic minor, and the A of the minor subdominant) of the combined major and minor scales.

To accommodate the harmonic and tonal resources of new music, however, the classical three-member system is expanded to five members including the flattened supertonic (Phrygian) and major leading-tone sonorities (Lydian) which maximize the semitone voice-leading to the tonic. The new degrees are designated respectively as P (D-F- A in C major) and L (B-D#-F# in C major) for their contribution of the Phrygian second and Lydian fourth. The flaw, as Janeček sees it, in the new pre-tonic harmonies is in their tritone relationships with the tonic itself (the Lydian fourth to the tonic and the Phrygian second to the fifth). As a solution to the problem of integrating these harmonies into the syntax of the "pure tonic" Janeček proposes the progressions PLT (Phrygian to Lydian to Tonic) or LPT with the minor Lydian which eliminate unresolved imaginary tones through the voice-leading successions of semitones. Similarly, the new pre-tonic harmonies (P, L) are strengthened when they are joined to the classic pre-tonics S, D (Subdominant and Dominant), i.e. PST, PDT, LST, LDT, canceling the tritone imaginary pitch arising from P or L with the tonic itself.

The final portion of Janeček consideration of pre-tonic function concerns the ambiguity of dissonant two-, three-, four- and five-function combination chords (composed by combinations of the five major and minor T, D, S, P and L functions). From the multitude of all possible combinations, some (i.e. -+D/-T, -D/+T etc.) are eliminated because they "encumber" the progression of the pure tonic with too many imaginary tones. Others, such as -P/+T, are redundant as they result simply in a missing note from more complete combinations such as +P/+L. Further redundancies are eliminated between combinations of two functions (-L/T, for example) which produce an incidental third function (+D) thus significantly reducing the number of larger member combinations. Of the 74 admissible and non-redundant major and minor combinations, only 19 are seen to be unambiguous, i.e. referable to a single tonic and are listed with their orientation schemes. A subsequent list is then presented all of the ambiguous combinations with their orientation schemes and pitch examples with the keys to which each sonority can be referred as a combination of harmonic functions (see Example 20).

                                    Example 20: Excerpt from Janecek's List "Ambiguous Dissonant Functional Combinations"

As is often the case in this work, the attention given to the generation of the analytical typologies is far in excess of any discussion of their analytical significance. However, based on their typical frequency of occurrence and distribution, some integrative considerations of proximity and family relationship between the 5 functions are offered as in Example 21. The dots indicate closeness of relation as might be seen in Schoenbergian structural functions and tonal regions. Janeček notes additionally that factors of concrete disposition and completeness are essential determinants of functional intelligibility and proximity of these abstract schemata:                                  

 Example 21: Representation of Family Relation of Tonal Functions

Janeček further develops the notion of inter-function (IN) or chromatic triads which are viewed as combinations of both tonic and pre-tonic functions for which he suggests particular symbols to indicate which pitches are borrowed from which functions. He then proceeds to break down the inter-functions of all major and minor triads in relation to C major: thus in C major, the A major triad, or IN₃, would be an inter-function of subdominant and minor Phrygian functions. ⁽²¹⁾ The tonic can have direct or indirect relations to inter-functions, depending if they proceed to other chords before reaching the tonic. Ultimately, in Janeček's view, sonorities can be derived as combinations of elements from tonic and pre-tonic chords. With the inclusion of the minor dominant and Šin's P and L functions, all 12 tones would be available for this, and so any dissonant formation could be related to a tonic S a theoretical possibility, as Janeček admits at best. Nevertheless, another categorization of dissonant formations is proposed based upon four possibilities: superimposed complete functions (the dominant upon the Phyrgian, for example), triads supplemented with single pitches from another function (dominant plus the basic pitch of the subdominant), functional degrees merged with inter-functional triads (i.e. the dominant plus the major mediant, or +IN⁴) and finally a group like the inter-functions which combines single or double elements from various functions. While superimposed complete functions are clear in their implication, the actual functions of the more fragmented and mixed combinations can only be determined from the musical context (see Example 22).

                Example 22: Examples of Fragmented Functional Combinations (excerpt)

In his preliminary notions of harmonic progression, Janeček creates several categories and differentiations which can be schematized as follows:

Motion: quality of harmonic motion: primary and auxiliary functions / tonal direction levels of motion: lower, higher and intermediate
Function: "resolution": "lower" or "higher" levels "connection": "simple" or "compound" and "lower or "higher" level "transfer"

The "quality" of harmonic motion relates previously established primary versus auxiliary functions (Tonic, Dominant, Subdominant versus Phrygian and Lydian) to the notion of direction to or from the tonic, dominant or subdominant. ⁽²²⁾ "Higher" levels of motion are attributed to movements between primary and auxiliary functions (Pr - Aux or Aux-Pr) and lower levels to movements within primary and auxiliary functions. Intermediate functions are conceived for progressions between combinations of primary and auxiliary functions. "Resolution" refers to harmonic motion directed to the tonic, which can be "simple" (as in triadic motions) or "compound" for variations or derivations of this motion, with the possibility of harmonically imperfect resolutions to the tonic (added sixth sonorities, for example). "Lower level" resolutions involve motions of primary or compound functions to the tonic with "higher level" resolutions involving the auxiliary functions moving to the tonic. "Higher level" resolutions are thus said to be weaker than those involving S, or D, or elements of S or D.

"Connection" is the opposite of resolution; it refers to a motion to a function other than the tonic. It is "simple" if it involves only single functions and "compound" if it involves combined functions. "Lower level" connections, again, involve movement within primary or within auxiliary functions and "higher level" connections involve movement between primary and auxiliary functions. A "transfer" is a special case of harmonic motion where a composite sonority is reduced to one of its component parts, typically involving uncancelled imaginary tones. Janeček summarizes these relationships in terms of the functional degrees in the following diagram (Example 23):

Example 23: Janeček's Summary of Resolution, Connection and Transfer Relationships

Concerning harmonic syntax Janeček offers essentially common-practice intuitions by which the simplest and most intuitive analysis is the most desirable, and by which the awareness of the tonic is established both by its physical prevalence and its inherent "gravitational" relationship to the functional progressions. Having said this, however, he presents a number of passages of theoretical interest as "successions of complex chords with rich sounds and considerable kinetic tension". The examples which Janeček gives are worth representing in part here since they further illustrate the stylistic milieu which seems to have given rise to his concepts of progression and function. ⁽²³⁾ In one example (see Example 25 below), he substitutes different resolutions for the penultimate sonority as well as different openings, demonstrating the flexibility of his materials and providing interesting cases where the tonal context prompts different readings from what might be imagined for the chords in isolation.

Example 24: Janeček's Progressions Involving Complex Functional Relationships (excerpts)

                                    Example 25: "Modulation from D major to B minor Without Real Asserted Pure Tonics"

In a very interesting commentary, Janeček contemplates the effectiveness of modulation in terms of the variety of ways in which the tonic can be harmonically weakened and then disrupted, thus imparting not only a degree of uncertainty in the tonal orientation but also a certain "novelty" and "freshness" in the prevailing harmonic syntax. The typical weakening agents of the applied functions, the auxiliary functions P and L, the inter-functions (in isolation or combination) and bi-tonal or polytonal chords are integral to the essential "renewal" and maintenance of harmonic interest which Janeček describes in these transitional passages. This, he claims, gave rise to all of the increasingly ambiguous situations, systems and modulatory practices of the late Romantics such as the cadential use of the half-diminished sonority in the close of Debussy's Afternoon of a Faun and the use of the church modes in Vítslav Novák's "Prelecel sokol" from his Slovenske spevy. In Janeček's view the extreme case of the avoidance of the tonic obtains in "non-functional (atonal) music" ⁽²⁶⁾ where either the gravitational attractions of the tonic or the distinctiveness of the tonic itself are destroyed. It is perhaps no surprise, however, that Janeček insists that "reliable functional relations can be found in music intentionally created as atonal." He asserts, for example, a "masked" B minor in Example 26a and a C major with an elided final E-minor tonic in Example 26b, an upper G minor strata in Example 26c, and layered function in B major in Example 26d. Janeček's closing comments on the issue of atonality suggest parallelism, full chromaticism, non-combination (i.e. quasi-bitonal) chordal dispositions and limited diatonic progressions as means of supporting "non-functional comprehension".

In a particularly revealing discussion, Janeček seems to touch on his essential view of musical language. His notion of "styling ⁽²⁷⁾" in modern harmony refers to the conscious compositional choice of harmonic materials within classical harmonic idioms such as parallel motions, pedals, doublings, contrary chorale-style motions, imitative contrapuntal techniques, etc. Thus Janeček, as much as any other pre-war European composer, adheres to the pouring of the new harmonies into the neo-classical molds, and to the exploration of personally conceived recipes and definitions of materials, forms and harmonic syntax.

Example 26: Examples of Functional Relations in Atonal Contexts

In his chapter on "problems and applications" Janeček sketches a philosophical, and almost pan-historical perspective in which "modern harmonies" (the chord types themselves) created a radical divide between contemporary musical languages and those of the baroque, classical and romantic eras. Yet at the same time he sees that they are guided by the same principles of harmonic succession that evolved in the earlier styles. In essence, however, "modern harmony" is also a repository which also includes the chord structures from the past eras. Thus Janeček sees the necessity of distinction between universal laws, as best they can be expressed and which apply under all circumstances, and the evolving stylistic tendencies of certain eras and certain composers.

He takes the very engaging stance concerning the pre-eminence of the creative act that "the law of an artistic work is sufficiently autonomous that a discrepancy with established law in the realm of art is of no consequence to it; neither is a discrepancy with any natural law of any importance..." Janeček cites the historical discovery of perspective in visual arts as an obvious natural principle which invalidated neither any previous artworks nor subsequent works which were eventually independent of its principles. In the musical domain, he cites the Landini cadence in its indirect motion to the octave (scale degrees 7-6-8) which can be seen as an altered precursor to the more direct voice-leading of the DT "pure tonic" (leading-tone to tonic) formula, is also seen to persist in its own right as a distinctive cadential idiom in subsequent eras. Following this view, Janeček concludes that the chromatic and diatonic systems are natural systems, whereas whole-tone and quarter-tone systems are artificial or only partially natural etc.

Janeček expounds at length on the necessary integration of experience with theory citing treatises of Skuherský ⁽²⁸⁾ and Hába as examples of work dominated by the experiential without the organizing strength of conceptual insight. Primary experiences in Janeček's view must be transformed within reason into principles, and two or more principles, even apparently disparate principles, can be subsumed under a common denominator. The defining qualities of Janeček's "pure tonic", for example, are related to the particularly attractive and stimulating quality of the tritone in isolated chords which is avoided in a closing sonority. Thus phenomena which appear unrelated (i.e. the sensual quality of the tritone and the tonal stability of the perfect cadence) will eventually become fully or partially assimilated into more inclusive principles. Throughout the course of the treatise, Janeček inadvertently provides many such illustrations of this: his orientation versus harmonic scheme, the characteristic-maxima versus triadic combination families, etc.

Janeček provides a rigorous assessment of the dual nature of harmony as eminently static in quality and kinetic in effect, thus making it impossible to consider motion (functional progression, imaginary tones etc.) independently from the uniquely affective dissonant/consonant qualities of the chords involved: "their tension versus their functionality (i.e. their possibility instead of their necessity). Phenomena such as imaginary tones are at the inter-phase of tension in the succession of sonorities since they represent lingering, unresolved voice-leading tensions." Janeček even seems to raise elementary formulations of a "kinetic" concept of harmonic progression in the succession of dissonances:

This does not say that in actual cases conditions are not more favorable for one particular goal or direction (of a progression) than for other goals and directions. These favorable conditions depend on the measure of motion necessary to reach the goal.

Thus Janeček sees that in their ambiguity of dissonance and function, modern harmonies are particularly sensitive to the most subtle effects nuance and disposition. The extreme (and for Janeček, rare) case of non-functional harmony assumes that "internal and external tension, dissonance and the non-tonic quality are one and the same" and would give rise to a situation in which 'the most favorable' kinetic possibilities have disappeared and all possibilities are 'equally good'"

In his chapter on "Compositional Practice" for which he provides extensive examples, Janeček explores more deeply his compositional and pedagogical concept of "styling". His main concern here is for composers, and in general that "if they want to defy some traditional law, for example, they do so in a way that will not appear as lack of skill". His essential starting point is "harmonic phenomena that can be judged statically without considering their relation to their surroundings" to which he gradually adds "phenomena that are explainable kinetically."

Beginning with the creation of "modern melody" Janeček like many other compositional theorists, advocates recipes for avoiding the clichés of diatonic or chromatic melodies, i.e. resolution of leading tones, specific rhythmic figures, the typical connections between identifiable harmonic functions, etc. (see Example 27a). Then, broaching the harmonic context, melodies are written with counterpoints or accompaniments restricted to major or minor diatonic triads (Example 27b) or a specific interval (the perfect fifth, Example 27c) and with varying degrees of chromatic accompaniment, contrapuntal complexity and dissonance and focused on particular intervals or harmonic structures (with particular attention, as in Janeček's Chapter 5, to the disposition of all 1 intervals or 01combinations). Initial exercises explore simpler combinations followed by denser combinations (16, 016, then 126 etc.) and an "exercise on a given harmonic basis" makes a two-voice adaptation from the chorale passage of Stravinsky's Three Compositions for String Quartet (Example 27d). This is followed by the inverse exercise of deriving a 5- or 6-voice harmonic background from the opening measures of the third movement of the Suite for piano of Pavel Bokovec and then a recomposed imitation of the original from the harmonic sketch. An extensive exercise ensues in setting a short seven-note melodic fragment involving different harmonic skeletons (chordal regions, in legato sustained sonorities and in stacatto arpeggiations), different mid-register counterpoints, chord-stream accompaniments and descants - all hosting a variety of harmonic challenges and points of dissonance treatment but with the general goal of ensuring "that the sonic effect of individual chords was good and that there was an overall natural flow"

In his texture exercises Janeček provides two- and three-voice accompaniments for a simple flowing eighth-note phrase, with different harmonizations for each which nevertheless retain certain common harmonies. Accompaniments proceeding in wider leaps were seen to leave more residues of imaginary pitches than others and hence were deemed to be harmonically richer. The complex issue of the resolution of dissonant sonorities is approached with registrally distinct triadic components (i.e. "non-combination"  dispositions) and then through dispositions in which triadic components are intermingled (i.e. "combination" dispositions) with the aim of finding different solutions and classifying the results in terms of the harmonic function of the chord to be resolved.

                                                        Example 27: Examples of Compositional Exercises

In the resolution of combination dispositions we see various principles at work including the unfolded 11 group in Example 28a which obviates the normal voice-leading resolution (ascending major second resolution for the D natural). Other aspects of resolution involve inter-function sonorities which in principle are obliged neither to obey pure-tonic voice-leading nor to be balanced by primary functions (Example 28b).
                 

                                        Example 28a: Unfolding of a 11                  Example 28b: Example of Inter-Function  

                                               Voice-leading Resolution                                 Voice-leading Resolution

The pursuit, on the other hand, of a pre-tonic chord for resolution must ideally balance components of D or L with S or P. Disposition become paramount in Janeček's sampling of instances (see Example 29) in which the single leading tone counterbalances the entire S, as well as a complex 6-note chord in the third case and a particularly harsh sonority in the third and fourth examples.
                                     

Example 29: Various Pre-tonic to Tonic Resolutions

Resolution is strengthened by altered or closely related repetitions of pre-tonic chords successions (Example 30a) and by strings of pre-tonic chords, each suitable to resolution on the ultimate tonic, which may be strung together with only the final chord providing the actual resolution (see Example 30a and b).
                                                           

Example 30: a) altered versions of the same pre-tonic chord b) succession of pre-tonic chords to the ultimate tonic c) possible resolutions to final tonic of the pre-tonic chords in b)

The actual progression from the pre-tonic sonority to the final tonic may be "strong" with pronounced linear or harmonic motions in the bass (i.e. clearer DT functions without "uncancelled " "imaginary" tritones in the voice leading) or "loose" or less clearly defined (Example 31).

                           

Example 31: Example of "Strong" (a) and "Loose" (b) Relations to the Tonic

Chords with clear tonic resolutions will dominate a passage at the peril of becoming too obvious and hence the value of controlling the more obscure functional relationships. Janeček attributes a particular "centrifugal" value to chords that can be favorably resolved into "other" tonics and as such stand close to the category of "chords that defy the tonic completely." The discussion grows particularly inventive in its consideration of "functional variations in a chord progression" where Janeček provides a very rich and varied series of cadences or pre-tonic sonorities and resolutions (Example 32).

Example 32: Variations on Dominant-Tonic Formula

Despite the sensitivity of their voice-leading and functional balance in their resolutions, it is curious that few of these resolutions are acceptable to the ear because of the simplicity of the pure tonic triad in contrast to the remarkable richness of the pre-tonic sonorities. Janeček's subsequent variations applied to harmonic phrases, however, involve initially complex tonics, followed by complex subdominants, dominants etc., but once more, resolve to inappropriately simple, and perhaps only theoretical tonics. A final set of variations adds chromatic bass lines to the functional formulas defined in the upper voices.

In turning to "free composition" Janeček offers an interesting example from his own composition Variations op.25 in which clearly combined functions as well as a pure tonic enclose a 10-measure arch of the melody with certain resolving complications. Subsequent, more refined examples come from his Sonata for piano op. 25, but with surprisingly little commentary apart from remarks on foiled harmonic expectations, "open-ended phrases" and bitonal interventions of a remote tonality (F minor) against the tonic (D major) in one of the more transparent and lyrical passages. It would appear that other passages are left for the reader to make his own observations concerning technique and harmonic function.

In an example which must be close to his own harmonic thinking Janeček demonstrates the accessibility of atonal chorale styles to the tabulation of orientation scheme and dissonance characteristics (Example 33).

Example 33: Application of Orientation Scheme and Dissonance Characteristic Analysis to a Chorale-Style Excerpt

Example 34: Application of Orientation Scheme and Dissonance Characteristic Analysis to Two-Voice Excerpt

Two of the analytical goals which Janeček sets for his theory are the elementary discernment of whether particular chord-, or characteristic-types, or dispositions appear exclusively or pervasively in a particular passage and whether the expression of the essential chords has any metric ambiguities. This is accomplished in obvious ways in the preceding chord- and dissonance-characteristic profiles beneath the harmonies but also in the study of transient or non-harmonic chords among the analyses which are listed with commentary in Appendix B. Janeček's closing overview of the issue of the "tonally functional plan of a composition" asserts an essentially normative distributional view of modulation, affirming the tonic at the beginning and end of a composition as an essential framework within which secondary keys can be expressed in various degrees of clarity or complexity and functional (primary or auxiliary) representation. He then hypothesizes cases in which remote modulations could involve keys expressed in essentially primary functions in contrast to very close modulations involving keys expressed by very complex and auxiliary functions.

Commentary

Although it has been possible to do little more than skim the surface of Janecek's work, it is hoped that the preceding overview of the Foundations of Modern Harmony will prove of some introductory value in our expanding historical and technical understanding of twentieth-century theory and composition. Its significance is obviously unquestionable in the development of Central European compositional esthetics and while the details of Janeček's theories may be unique and personal, they clearly complement the fluid and intuitive harmonic languages not only of Martin, Isa Krejčí, Vítêslav Novák, and Janeček himself but also the comparable languages of Roussel, Hindemith and Honneger, to say nothing of the subsequent generations who has been influenced by Janeček's own teachings.

Other aspects of the treatise's unique cultural "location" referred to at the onset of this study can be seen in its legacy of functional tonal analysis in the line of Riemann via Šin, its (albeit disavowed) adaptation and development of Leoš Janácek's concept of the "imaginary tone", and the apparently original inception of a harmonic prime form (the "orientation scheme") long in advance of the analogous and eventually paradigmatic concept of the prime form of classical set theory. Similarly, Janecek's more abstract notions of harmonic progression offer an interesting complement to those being promoted on the North American continent by Schoenberg (Structural Functions of Harmony) and Hindemith (The Craft of Musical Composition).

Yet given its orientations to developing mid-century philosophical and analytical directions, Janeček's work is uniquely situated at the heart of even larger and deeper intellectual directions in its continuous modeling of classical harmonic theory, its almost high-Medieval dedication to the sensory evaluation and description of harmonic quality, and a truly obsessive structuralism for exhaustive definition and categorization of theoretical schemata. Of these, it is perhaps the second, and most basic of these propensities of Janeček's work that bears the most promise to contemporary theoretical analysis. Indeed, one of the most striking consistencies of recent twentieth century atonal harmonic theory has been its neutrality to perceptual realities of harmonic formation, progression and processes of dissonance alternation, fluctuation, accrual, etc., perhaps in deference to the many abstract and even arbitrary compositional techniques for which it is so well adapted.

It has probably also not escaped the reader's attention that Janeček makes an impressive number of contentions and classifications of relevance not only to practical compositional pedagogy but to the study of music cognition. The distinctiveness, for example, of "increased" and "merged" dissonances and the similarity of chords within the dissonance maxima families, appear to make verifiable claims on our capacities of harmonic intuition. The perceptual reality of imaginary tones and their "cancellation" could similarly be explored as an aspect of short-term auditory memory and harmonic perception, and Janecek's differing criteria for ascending and descending whole-step cancellation seem to provide hypotheses about our perception of linear melodic continuity. Janeček's theory also bears clearly on our perception of harmonic complexity in its attribution of acute sensitivity to different dispositions of 313 structures and apparent indifference, in perceived dissonance, to different harmonic dispositions of 213 structures

In closing, an important interdisciplinary example can be taken from Janeček's later chapter on "Problems." Janeček makes no obvious attempt, despite the scope of many of his preambles, to provide a definitive and all-encompassing theory of harmonic structure. The concept of characteristic-maxima based on the association of dissonant elements was pursued to a point of complexity where it was clearly no longer operative and it was supplanted by its converse, a theory of triadic combination, itself with obvious limitations. The equal acceptance of bitonality and monotonal composite functions and even of functional and non-functional expressions of tonality itself (although Janeček is obviously much more interested in the former than the latter) further define his interest in the integral relationship of compositional and esthetic concerns to systematic theoretical insight. For Janeček  theory and analysis take a clear stance at the intersection of the universal principal and the creative will:

Older music theorists strove to establish a binding and universally applicable system of compositional rules or norms. These efforts could not lead to a positive result, because they were futile. Living creation always broke through all elaborately constructed normative systems and worked its way to a new and a different compositional technique, ignoring theorists' rules. The impermanence of theoretical requirements and rules bears witness to the fact that their roots do not reach as deep as theorists might wish.

...Music theory takes universal law over from the natural sciences. It then creates artistic law based on artistic practice. Compositional practice tends to become stabilized for a time with certain idioms and procedures and, it is for music theory to capture, classify, and evaluate the essential practical gains so established.

....As long as universal law affects the attitude of practical artists, it must be reflected in the results of theoretical investigation. A precept that has been derived from practice can be more far-reaching and need not be merely an expression of temporary artistic custom. Thus it is an important task of music theory to define the role of universal law in practical artistic (technical) rules.

Appendix A: Janeček's Foundations of Modern Harmony Table of Contents

Appendix B: Commented List of the Examples in Chapter Twelve of Foundations of Modern Harmony

Paul Hindemith: In the String Trio op. 34, final movement, fugue, an essentially tonal melodic ostinato is set against intentionally harsh dispositions of the minor ninth.

Albert Roussel: In the op.45 String Quartet excerpts are taken from the slow movement and last movement. In the former a prolonged iiø6/5 before a closing cadence involving transient sonorities on theorder of dominant sevenths (see Example 35). More dissonant transient chords are seen in the final movement before a closing sonority defined more its repetitive insistence and preceding chromatic bass line than by its intervallic qualities.

Arthur Honneger: In Pacific231 the "locomotive" chords are taken as an example of an arbitrary dissonance structure within an obvious compositional repetitive sequential processes and extra-musical reference. In Prelude, Arioso, Fughetta sur le nom de BACH, a passages from the fughetta which presents a complex combined Lydian/Phrygian pre-tonic sonority harmonizing the "C" of the B-A-C-H motive at its final cadence

P Bokovec: The close of the Chorale in which the relatively "loose" functional motion is balanced by repetitive arrivals on the tonic. The beginning of the Wind Quintet presents a superposition of diatonic fragments in which strata-defining semitones and dissonant chordal cross sections are indicated.

Vítslav Novák:: A cadence from the Third Quartet provides an example of Janeček's adage of the effectiveness of a pre-tonic chord which has strong possibilities for resolution to a completely different tonic (see Example 36).

Isa Krejci: The Trio-Divertimento provides a further example of extended functional relationships to a C major tonic. In a somewhat difficult analysis Janeček characterizes the ambiguity of the opening as pertaining to either F# major, A major and possibly B major for which he gives a table relating the various functional degrees (DSPL) to the number of beats the pertinent degrees are heard. C major emerges based largely on the prominence of its dominant (second and third measures) and the relative weakness of its auxiliary functions. Janeček then concentrates on the passages where C major functions are clear amid apparently parenthetical passages of textural and chromatic complexity.(Example 37)

Bouslav Martin: A short excerpt from the opera Julietta provides an example of intentional ambiguity where the tonic G minor is weakened by non-dominant linear motions and quasi modal progressions such as -D +S en route to D minor.

František Picha: In the Suite for String Orchestra and Gong the surprising B minor ending of the first movement is explored in a quasi-statistical manner, asserting a durational prominence of B minor (25 quarters) but in a relatively weak sense of the tonic in relation to G major which gives way via the D-S-S to B minor which is presented only in any degree of stability in the last four measures.

Example 35: Roussel: Closing Measures of the Slow Movement of String Quartet op. 45
                              

Example 36: Vítslav Novák: Excerpt from Third String Quartet

© 1939 by Breitkopf und Härtel, Leipzig, used by permission

Example 37: Isa KrejčiTrio-Divertimento, Introduction

© Czech Radio

1. See "An Interview with Rudolf Komorous," ex tempore , III/2 (Fall/ Winter 1985-86), p. 57.

2. In the original Czech: Základy moderni harmonie, Prague: 1965. At the point of completing this article, the translation of Foundations of Modern Harmony by Jana Skarecky and Anne Hall had yet to find a publisher. It is with their permission that passages from their translation are cited here.

3. From the original preface of the book entitled Modern Harmony. Although Janeček began this book in 1942 and finished it in 1949, important parts of the treatise were published in a variety of periodicals (Tempo and Rhythmus etc.) as early as 1931 and as late as 1947. Individual chapters of the treatise were revised and re published until the final version of the work was published as Foundations of Modern Harmony in 1965.

4. See Appendix A which presents the table of contents for the entire treatise.

5. While in his preface Janeček distinguishes between his "imaginary tones" and the "pseudo-sensed" (in the Skarecky-Hall translation) tones of Janáček, it is fairly clear that he builds on the concept of the earlier composer and theorist.

6. It is interesting to note that Janeček apparently evolved (but does not describe) a very systematic listening process of comparison and evaluation of the "chord-" or "characteristic-types":

Each of these nine combination possibilities can be illustrated by concrete examples of chord-types, of which we can study the sound and which we can compare with each other, evaluate, and characterize. This indispensable process, demanding detailed and intimate knowledge of the extensive material, knowledge supported by living practice, cannot be described here step by step.

7. Although by no means systematized, Janeček makes numerous interjections of a statistical nature from his unique perspective of chord types defined by dissonant elements. On the near omni-presence of the semitone he notes that it occurs in ten of the nineteen three-note chords, also in 10 of the 43 4-note chords but in only three of the 66 five-note chords, as presented in his charts in §25.

8. Janeček thus hears the dissonant effect dominant seventh and half diminished sevenths sonorities as "softer and more integrated than that of the dull and unrefined minor-minor (seventh) chord."

9. There is a potential confusion here which is never graphically resolved since 11 refers to both an orientation scheme for a three-note chord as well the semitone clash of semitones which arises from the four-note orientation scheme 111.

10. The hyphen which does not appear in the Skarecky-Hall translation, is intended here to alleviate the potential English-language confusion of "characteristic" as a noun and "characteristic" as an adjective.

11. Janeček obviously does not subscribe to the adage of the origin of the half-diminished and diminished seventh chords in rootless dominant major or minor ninth sonorities. We might also assume problematically from Janeček's discussion that the dominant seventh (GBDF), the minor-minor seventh, GBDF, the augmented-minor seventh, GBD#F, and the flat-fifth dominant seventh, GBDF, are quite different classical "harmonies" of which the chords G-B-F or G-D-F would represent various ambiguously incomplete forms.

12. Once again from his charts in §25.

13. Janeček acknowledges Leos Janáček's as having coined this term.

14.  Janeček also provides graphs for the subgrouping of each maxima family. The subgrouping of maxima and nuclei family for 2 is represented in chart form as the following:

where, as in his orientation schemes for 3-, 4-, 5-, and 6-note chords, the bracketed numbers refer to the octave complement interval.

15. To a certain extent, the inventory of dissonance maxima has already been introduced in the preceding exploration of unmerged (i.e. increased) dissonance elements. In this chapter the maxima of merged dissonance elements as well as those containing the tritone and semitone clashes (11 and 66) are added.

16.  More specifically Šin's theory combines functions of Tonic, Dominant, Subdominant, which Janeček extends to the Phrigian and Lydian. While these latter functions are not observed in Janeček's triadic combinations, they are later applied his analysis of chord progressions.

17.  Janeček's designation of "combination" and "non-combination" is somewhat counter-intuitive since the former refers to a registral separation of the two triads and the latter to combined mixing of the two triads or triadic elements.

18.  The issue of Janeček's "imaginary tones" is probably worthy of a study in itself in the broader context of tonal coherence. Janeček makes no attempt to find (Schenkerian) layerings of voices over the broader cancellations of harmonic tones and he similarly does not seem to recognize such phenomena as cross-registral voice-leadings.

19. Janeček differentiates here between the voice-leading of classical harmony and mere pitch succession which applies independently of the part motion.

20.  Dissonant chords are excluded as pre-tonic chords since the essence of a functional relation for Janeček's is that "the substantial characteristic of gravitating to the tonic is separate from inner sonic tension." In other words the pre-tonic chord must be a pure "extract freed from the secondary characteristic of real dissonance."

21.The superscript or subscript represents the root of the inter-function chord in number of semitones above or below the tonic.

22.  With the annotation that the progression DS (Dominant to Subdominant and its derivations) is historically avoided as unnatural but its opposite, SD, is common and completely natural.

23.  The dots in the example show the completeness of the functional degrees (two dots to the right of the function symbol indicating the presence of two of the three tones of the triad) as well as the seventh (the dot above the functional symbol) and any added tertian elements (the horizontal dots above the tertian symbol). Altered tones in any of these sonorities are indicated via commas instead of the dots. Thirds added below the root of a function are indicated by dots (usually one or at most two) beneath the function symbol.

24. The symbol (d) is used for an applied minor dominant.

25.  The brackets indicate the function of the chords as applied subdominants and the small (s) for the D minor sonority represents the fact that it is a minor, and hence altered subdominant in A major.

26.  Janeček actually recognizes three case:s "music in which the meaning of the chords is definite and unambiguous, (b) music in which the functional relations are loosened, and (c) music in which no functional relations between chords can be objectively and reliably determined."

27. As noted in the Skarecky-Hall translation, "styling" is their term for stylizace which is more literally rendered as "stylization" or "conventionalization".

28.  F.Z. Skuherský, Theory of Harmony with Scientific Foundations in its Simplest Form 1885.