Kárpáti’s “Mistuning” Theory Re-considered in the Context of Bartók’s “Supradiatonicism” and Friedrich Hartmann’s Fully-Chromaticized Scales
The Hungarian musicologist, Bartók scholar and music bibliographer, János Kárpáti, in a wide array of publications expounds the concept which purports that mistuned perfect octaves and fifths form an integral niche within Bartók’s melodic and harmonic vocabulary. This supposition extends to the so-called mistuned interval of a major third.
The phenomenon of mistuning may roughly be defined as small scale augmentation or diminution of perfect structures, or – in a more definite form – one semitone augmentation or diminution of the structures based on a perfect octave or fifth. Measured in semitones it gives 13 or 11 instead of 12, 8 or 6 instead of 7, and – since the major third has been codified by Rameau as perfect in his basic triad chord called “harmonie parfaite” – 5 or 3 instead 4.
This article will consider Kárpáti’s “mistuning” theses and related analyses in the context of Bartók’s own “supradiatonic” pronouncements and Friedrich Hartmann’s (1900-1972) explications of expanded, synthetically constructed fully-chromaticized scales. In this regard Kárpáti’s assertions regarding the mistuning of dominant structures in tonic-dominant harmonic alternations, bitonality with semitonal representivity, “mistuned” major triads as well as double-degree chords comprising major and minor thirds will be appraised. In this article the formulation of an appropriate response to Kárpáti’s analytical contentions will reside especially with those analyses drawn from Bartók’s Fourteen Bagatelles (1907-8), Allegro barbaro (1911) and the Suite, Op 14 (1916) as portrayed in Kárpáti’s paper ‘Perfect and Mistuned Structures in Bartók’s Music’ and published as part of the Proceedings of the International Bartók Colloquim, Szombathely, July 3-5 1995. These three works cover a period of eight years, ranging from Bartók’s twenty-seventh year to his thirty-fifth year and they represent the time-frame when ‘the appearance of Bartók’s original musical language’ (Sadie ed.1980/2:208) can be discerned. In this instance “original” denotes the germinal stage resulting in the prototype of Bartók’s mature compositional style with the Fourteen Bagatelles marking the period when, as Elliot Antokoletz observes, the typically Bartókian “voice” makes its entrance.
virtually all the elements of Bartók’s musical language that he was able to absorb and transform throughout his career were already contained in microcosm in his Fourteen Bagatelles…his post-war [WW1] compositional and pianistic techniques…ultimately have their roots in this early set of fourteen masterpieces.
Notwithstanding the phenomena of natural progress and increasing musical maturity, a unity in Bartók’s composition style is discernable, which can be traced to this “germinal decade” where initial explications have been presented of his most salient compositional characteristics, especially those which remained at the core of his idiom until his death in 1945. Bartók’s statement in 1945 lends credence to this point of view: ‘As later developments indicate, the Bagatelles  inaugurate a new trend of piano writing in my career, which is consistently followed in almost all of my successive piano works …’  Halsey Stevens amplifies Bartók’s remarks as follows:
Now that Bartók’s work may be perceived in its entirety, its evolutionary line becomes its most striking aspect. In no other recent composer is there to be observed such an undeviating adherence to the same basic principles throughout a career … With Bartók there were frequent additions to his creative equipment, but seldom subtractions …
Bartók’s tonal language is a particular case in point, especially his eloquent enunciation of harmonic premises from 1908 onwards. In this regard consider correspondence between himself and Edwin von der Nüll:
From Opus 6  on; he [Bartók] wrote to Edwin von der Nüll, ‘I always tried to use the supradiatonic tones with the greatest possible freedom.
quotation is derived from correspondence between Bartók and von der Nüll. This
correspondence forms the basis for von der Nüll’s study of Bartók’s piano music
for the period 1908-1926, published in 1930 and entitled Bartók:Ein Beitrag
zur Morphologie der Neuen Musik (
The concept of “supradiatonic” tones with their sense of going beyond, above and below diatonic constituent scalar members is grounded in the notion clarified by Stevens (1993:200) that Bartók’s compositions evidence the use of augmented scales, “in which what might be …considered chromatic inflections are actually an integral part of the mode.” This supposition receives endorsement from Yates (1967:179) who articulates the understanding that “Bartók [employs], by notation and implication, a scale … which includes more than twelve notes.” The historicism inherent in the idea of a developmentally expanding scalar compound is borne out in the writing of Leon Dallin:
By the end of the romantic era chromatic tones were employed to such an extent they rivalled the [diatonic] tones of the scale in importance and frequency … [leading] to a greatly expanded concept of tonality. Carried to its logical conclusion, chromaticism leads to an all-inclusive scale … 
Thus, traditional common-practice tonality is expanded through the incorporation of “supradiatonicism” creating a compositional infrastructure whereby tonally gravitating and diatonically recognizable procedures are obscured in astringently decorated harmonic constructions and part-writing. “Supradiatonicism” results, therefore, in the simultaneous evasion and establishment of tonality within an expanded chromatic idiom.
According to a review by Colin Mason (1953:564) Steven’s The Life and Music of Béla Bartók represents “the first serious book on Bartók’s work, in any language, since Edwin von der Nüll’s study of the piano music, published in 1930.’’ Interestingly, Mason’s review comments on, in his opinion, Stevens’ lack of attempt to define Bartók’s conception of tonality and provide a general analysis of his melodic and harmonic language yet he notes that
From this angle von der Nüll’s book remains, in spite of its sometimes far-fetched explanations of chords, more valuable.
Von der Nüll’s analytical theses are based upon the
premise that the music of Bartók is diatonic, tonal and tertian in its
conception with Bartók extending the concept of harmony through added-note
technique, ellipses, unresolved chromatic neighbor notes, suspensions and modal
mixtures (Waldbauer, 1995:95-96). These analyses were followed by a 110-page
treatise on expanded tonality, published in 1932, entitled Moderne Harmonik (
…there is no doubt that Herr von der Nüll has taken great pains with his work: his discussions are very detailed, and he has read very widely, both in the music itself and in the international literature about it.
It becomes clear, when Bartók’s “supradiatonic” allusions are taken into consideration that in the Fourteen Bagatelles he asserts his creative and original understanding of tonality and harmony (in which he designated keys to individual movements) which, notwithstanding camouflaging surface details and the frequent emergence of dissonant textures, is fundamentally tonal in conception. Bartók’s “supradiatonic” tones moreover, form part of the same harmonic philosophy which governs the formulation of Hartmann’s fully-chromaticized scales and reflect the philosophical stance adopted by Joseph Yasser in 1932 with regard to his own “supradiatonic” scalar theories (Austin, 1953:30). They provide a platform for articulating conclusions regarding Bartók’s tonality and, in this study, a framework for re-considering the “mistuned dominant” contentions of János Kárpáti. Furthermore, they place Bartók’s harmonic language within the primary tenets of traditional tonality where procedures of obscuration nevertheless shroud the diatonic tonal pillars.
Hartmann’s Fully-Chromaticized Scales
The Austrian theorist-analyst and composer Friedrich Helmut Hartmann was clearly aware of von der Nüll’s work and with regard to analyses of Arnold Schoenberg’s Drei Klavierstücke Op 11/1 (1909) and Max Reger’s piano work Aus meinem Tagebuch Op 82 (1904-1912) he makes the following acknowledgement in his Harmonielehre (1934), published two years after von der Nüll’s Moderne Harmonik:
The above comparisons (Schoenberg opus 11 and Max Reger opus 82) are taken from the Moderne Harmonik of this author [von der Nüll], whose excellent analyses were used on several occasions in this book
Thus, it can be safely assumed that Hartmann doubtlessly had knowledge of von der Nüll’s analyses of Bartók’s piano music and the theoretical base from which von der Nüll developed these expanded, “supradiatonic” considerations.
The historical evolutionary process pertaining to the organic growth of additional chromatic scalar members, alluded to by Dallin, resulted in Hartmann’s formulation of the fully-chromaticized scales as:
indicative of the increasing knowledge that musical notes and chords – hitherto considered as not belonging to the same key system – are in fact members of the same key system, and governed by the same central power, the system’s tonic.
In this idiom the harmonic palette is widened to include new harmonic colors and tonal shadings with the shape of chord structures including constituent chordal elements within the mold, reflecting the expanding harmonic vocabulary and sound-world of this twentieth-century manifestation of tonality. Hartmann considered his fully-chromaticized scales as being guiding elements in analysing twentieth-century tonal compositions:
…the term “expanded tonality” should be used with regard to music employing the modern [fully-chromaticized] mixed scale material [with the] melodic and harmonic applications characteristic of it.
The composition of Hartmann’s fully-chromaticized scales and the historical process with regard to the incorporation of chromatic notes has been delineated by Socrates Paxinos:
The standard major scale added to its coloristic and harmonic resources those notes from its tonic [natural] minor which the two scales did not have in common. By a similar process, the minor scale was likewise enriched with borrowings from its tonic major. To these were added other chromatic notes, such as the Neapolitan second and the raised (or gypsy) fourth.
In the fully-chromaticized major scale of C, for example, this justifies the existence of five chromatically inflected notes: E♭, A♭ and B♭ (added from the tonic natural minor), D♭ (Neapolitan second) and F# (Gypsy fourth). In addition five further chromatically notated notes C#, D#, G♭, G# and A# are the result of the historical process of either increasing semitone support from above or below the seven diatonic degrees as explained by Hartmann.
By systematic continuation of the chromatication [sic] of the diatonic scales, that is by the insertion of semitones between all those degrees of the pure major and minor scales which still are separated by wholetone steps, the so-called fully chromaticized major and minor scales were obtained.
Thus, the fully-chromaticized major and minor scales comprise seventeen constituent members which through the nature of their design are an illustration of the widening harmonic vocabulary and “sound-world” of twentieth-century expanded tonality. Consider the following examples of the fully-chromaticized major and minor scales with seven diatonic representations, five chromatically raised degrees and five chromatically lowered degrees.
Example 1: Fully-chromaticized major scale of C
Example 2: Fully-chromaticized minor scale of C
Hartmann (1956:20-21) has identified the cumulative step in the historical evolution of the fully-chromaticized major and minor scales as being the fully-chromaticized mixed scale. This scale is a composite resulting from the fusion of both the fully-chromaticized major and minor scales.
It is notated in the following example and evidences no bias towards either the major or minor, representing an amalgam of both major and minor modalities. Each degree is represented thrice, except for the mediant degree, which possesses only two representatives for this, the genus-defining degree. ‘What applies to man, applies to music: there are only two genera’ (Hartmann, 1956:21).
Example 3: Fully-chromaticized mixed scale on C
In this way, the fully-chromaticized major and minor scales through the nature of their design are indeed a reflection of the widening harmonic vocabulary and sound-world of twentieth-century expanded tonality. The premises propagated through Hartmann’s analyses reveal, how obscured diatonic tonal props and chord functions within dissonantly constructed textures, are based upon the tonicization procedures and harmonic syntax derived principally from the Classic-Romantic continuum, with the diatonic and chromatic scalar members all being dominated by the same, diatonic, tonic. In this regard the use of Hartmann’s fully-chromaticized scales, in presenting specific formulae for analyzing expanded tonal works, amplifies other analytical approaches, especially those prevalent during his epoch. To this end, the analyses in this article are further proposed as a demonstration of the viability, and in South African musicologist Bernard van der Linde’s words, the “stroke of genius” of Hartmann’s fully-chromaticized scales in perceiving tonal coherence in Bartók’s expanded tonal compositions.
Bitonality: Kárpáti’s Bitonal Pronouncements in Allegro barbaro, mm. 76 - 80
Kárpáti’s (1995:373) assertion that in Allegro barbaro examples of transitory bitonality exist for ‘in Bartók’s case we cannot speak about … bitonality extending for the whole composition’ is entirely accurate though the examples, analyses and conclusions he draws are not concomitant with the philosophical basis pursued in this article. According to Kárpáti the passage in the following example, mm. 76 - 80, represents an example of ‘semitone bitonality [F major-F# minor] ‘… concomitant with the ambiguity of the dominant’ (1995:379). In Kárpáti’s scenario the C major chord represents either a mistuned dominant with F# minor being the perfectly tuned tonic or F# minor is regarded as a mistuned tonic with the C major chord being the perfectly tuned dominant of F major (1995:373). Kárpáti does not consider the chromatic-diatonic juxtaposition (C-F#) as being representative of a single, all-embracing expanded “supradiatonic” context, where chromatic and diatonic elements form a single scalar entity.
Example 4: Bartók: Allegro barbaro, mm. 76 – 80
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“mistuned dominant” theory does not take cognizance of Bartók’s knowledge of
late-Romantic harmonic procedures resulting from the compositional influence of
Richard Strauss (1864 – 1949) which includes tritone root movement at cadential
points. The Australian-based Bartók exponent, Malcolm Gillies states in the New Grove Dictionary of Music and Musicians (2001/2:788,789)
that Bartók was roused as by a lightning stroke after attending the first
With regard to the influence of Strauss upon Bartók’s harmonic language, Strauss’ employment of tritone root movements between a chromatically lowered dominant and a diatonic tonic to enunciate perfect cadences with juxtaposed chromatic and diatonic functions is significant. The following example from Strauss’ opera Feuersnot (1901) serves as an example of such a tritone root movement within a cadential context.
Example 5: Strauss: Feuersnot, commencing 8 measures after figure 159
While Bartók’s employment of a tritone root movement (m. 78 - 80) probably represents the influence of late-Romantic harmonic procedures, it also depicts the historical unfolding of the twofold properties of diatonicism and chromaticism simultaneously inherent within “supradiatonicism.” The ensuing discussion will re-consider Kárpáti’s “semitonal bitonal” supposition and draw conclusions with regard to bitonality as a “process and product” concomitant with Bartók’s “supradiatonic” commentaries.
Bitonal “Process and Product,” in Allegro barbaro, mm. 76 - 80
This passage represents a case of bitonality with the bass part depicting an expanded tonal “supradiatonic” F# minor tonality through the juxtapositioning of chromatic and diatonic root movement while the upper strand constitutes a unique modal combination: a synthetic scale based on the Mixolydian mode starting on A with a chromatically raised Lydian fourth degree. Thus, two horizontally represented tonalities prevail from which the bitonal process arises with the aural result being an intricate monotonal product in F# minor much in the way that Vinton ed. notes that “the pitch content of [bitonality] can be analyzed (though not necessarily heard) in terms of more than one key.”
In outlining the bitonal “process and product” hypothesis codified by Friedrich Hartmann Bernard van der Linde (1969:7) contends that “as far as the listener is concerned, polytonality [or bitonality] is monotonal” thereby representing an approach akin to that of Vinton. Furthermore, Waldbauer (1996:96) states that von der Nüll’s analytical methodology and terminology lead to bitonal analyses, in the sense of the term that would probably be acceptable to Bartók, “for in all cases the listener’s ear can reduce the resulting sound complex to a single tonality.” This point of view is upheld further by Bartók himself:
‘… polytonality [bitonality] exists only for the eye when looking at the music. But our mental hearing … will select only one key as a fundamental key and will project tones of the other keys on this selected one. The parts in different keys will be interpreted as consisting of tones of the chosen key …’
Waldbauer’s observation receives poignancy when Bartók’s statement with regard to the first of his Fourteen Bagatelles is considered. Bartók clearly embraces the phenomenon of a monotonal product resulting from a bitonal process:
The first [Bagatelle] bears a key signature of four sharps (as used for C# minor) in the upper staff, and of four flats (as used for F minor) in the lower staff. This semi-serious and semi-jesting procedure was to demonstrate the absurdity of key signatures in certain kinds of contemporary music … The tonality of the first Bagatelle is, of course, not a mixture of C# minor and F minor, but simply a Phrygian colored C major.
The first ten measures of this Bagatelle serve as an example (see Example 6); the bitonal process is led visually (horizontally) through Bartók’s simultaneous utilization of two different key-signatures for the diatonic representation of each strand – the upper in C# natural minor and the lower in C Phrygian. However, through an application of the fully-
Example 6: Bartók:Bagatelles Op. 6/1, mm. 1 – 10
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chromaticized major scale, and focusing upon the vertical, harmonic aspect, the music can be placed within a single, monotonal perspective, whereby Bartók’s “Phrygian colored C major” can be viewed as an analytical formulation of a bitonal monotonal product.
The “amalgamation” of C# natural minor and C Phrygian into a tonal product represented by the fully-chromaticized major scale of C displays the result of including chromatic degrees as constituent scale members subordinate to the same tonic as their diatonic counterparts. Derived from the Phrygian scale D♭, E♭, A♭ and B♭ are added to the diatonic major scalar system of C, with D♭, E♭ and A♭ receiving enharmonization as C#, D# and G# respectively. The Lydian fourth, F#, represents a further chromatic addition. Only three members of the fully-chromaticized scale are not used by Bartók in this instance, namely the diatonic supertonic, chromatically lowered dominant and the chromatically raised submediant.
The existence of a strong element of notational compatibility between the Bartók example and the fully-chromaticized major scale is of its own accord not of primary musicological importance. However, the fully-chromaticized scale not only provides an analytical substantiation of Bartók’s “Phrygian coloured C major” characterization of the music, it furnishes the analyst with a valid basis for harmonic analysis of this piece within the context of an expanded C major as expressed by Bartók. Thus, a tonal analysis can proceed within an unforced, natural musical environment.
Therefore, when re-considering the five measures from Allegro barbaro, mm. 76-80, the musicological plausibility of a monotonal product of F# minor receives endorsement when consideration is given to Hartmann’s fully chromaticized minor scale. The product of the bitonal harmonic enunciation of the cadential ♭V-I in F# minor (mm. 78-80) becomes recognizable within the realm of the “supradiatonicism” of Hartmann’s fully-chromaticized scale revealing assertions of “mistuned dominants” to be not founded upon tonal principles of the Classic-Romantic continuum. In the following example arrows indicate the notes utilized in the Allegro barbaro example (mm. 76-80) where Stevens’ (1993:200) supposition regarding Bartók’s augmented scales is realized with chromatic inflections actually forming an integral part of the mode.
Example 7: Fully-chromaticized minor scale of F# with arrows indicating the notes utilized in the Allegro barbaro example, mm. 76-80.
“Mistuning” of Traditional Chord Alternation
With regard to the mistuning of chordal structures Kárpáti elucidates the possibility of “…the notes of the perfect chord [being] substituted by chromatic - or mistuned - variants.” The first example, to be considered in this article, Kárpáti’s analysis of the initial four measures of the Bagatelle No. 14 requires examination:
Here the melody, transformed into a waltz rhythm, is accompanied by the stereotypical two-function chord alternation of waltzes – but in place of the dominant we get an “out of tune” chord: the most important components of the dominant are substituted: instead of A, B♭, instead of G, F# and G#.
The chord in question (mm. 2 and 4) comprises augmented sixth properties insinuated through Bartók’s positioning of the notes B♭ and G#. At this juncture it is invaluable to note that Bartók’s oeuvre constitutes frequent examples of orthography whereby, in the development of principles derived from the “common-practice” period, the notation and tonality form a cognate unit. In this regard Bartók’s systematic selection of pitches reveals his concern with relating all notes in a composition to a single tonality (Stevens, 1993:120). Therefore, his choice of the notes B♭-F#-G# can be considered deliberate especially in respect to tonal function within this work.
Example 8: Bartók: Bagatelles, Op. 6/14, mm. 1 – 7
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The construction is an incomplete representation of a tetrad formed on the raised subdominant of D major: G#-B♭-[D]-F# appearing in first inversion with the note B♭ in the bass. While this chord could be construed as a German augmented sixth with a raised fifth (F# in lieu of an F) it also constitutes a whole-tone tetrad (half diminished seventh, G#-B-D-F# with a flattened third, B♭) with, as we shall see, some orthographical similarity to instances in Strauss. In this regard consider the following example from Strauss’ lied Heimkehr Op 15/5, at m.263 (B-D#-Fx-A) and m. 333 (G-B- D#-F) where altered dominants arise, comprising a raised fifth, in the keys of E and C majors respectively.
Example 9: Strauss: Heimkehr, Op 15/5, mm. 21 – 37
For perfect orthographical correspondence between the Strauss examples and the Bartók chord in question, the Bartók construction ought to have embraced the notation B♭-D–F#-A♭. However, with reference to Bartók’s notation a plausible re-consideration of Kárpáti’s analysis is the chord progression, D: I - #IV7 with a whole tone tetrad on the raised subdominant with the chromatic “supradiatonic” notes B♭ and G# being constituent members of the fully-chromaticized major scale of D. The tritone root movement, D-G#, is in lieu of a traditional tonic-dominant alternation with the eschewal of dominant harmony through the representation of a strongly suggestive pre-dominant harmonic function chord. It is thus preferable to consider the chord in question as formulated upon a raised subdominant and not as a “mistuned dominant.”
A second example of a so-called “mistuning” of traditional tonic-dominant alternation is found during the opening measures of the first movement of the Suite op 14 where “instead of the traditional alternation of tonic and dominant we have alternating B♭ major and E major chords.” This point of view is explained in The Bartók Companion (edited by Malcolm Gillies) with Kárpáti (1993:156-7) arguing for the raised subdominant (an E major chord) as an enharmonicized lowered dominant in a synthetic scale: B♭ C D E F# G A B♭. According to Kárpáti this represents a scale in which
the fifth degree has now been sharpened, leaving now no perfect fifth above the tonic B♭ … the chords accompanying the tune have no perfect fifth intervals either, so instead of the traditional alternation of tonic and dominant we have alternating B♭ and E major (instead of F major). E major is a mistuned or substitute dominant …
Example 10: Bartók: Suite Op 14/1, mm. 1 – 12
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The triads found at m. 8 and 10 respectively, constructed above a non-diatonic root, are placed in juxtaposition with the diatonic tonic triad, thus causing both tonal instability and adding a sharp, biting harmonic angularity with the tritone root separation. At m. 10 the double-degree construction clearly epitomizes the expanded tonal idiom in the melodic decoration of the genus-defining third: E – G(♮)G# - B. Kárpáti probably implies that this “mistuned dominant” is an enharmonization of the orthographically complex F♭ - A♭♭A♭ - C♭. However, when Bartók’s orthography is considered as an accurate reflection of the macro-tonality it becomes obvious that another clear reference to the raised subdominant is being made, especially when “supradiatonic” notations are considered.
Kárpáti’s synthetic scale (which is a subset of the fully-chromaticized major scale) is based on the melodic content of the first eleven measures and does not take cognisance of the melodic C♭ found in m. 12 nor the triads which form the harmonic accompaniment to the melody which includes, for example, numerous references to the diatonic dominant degree, F, as a member of the tonic triad: B♭-D-F and also the appearance of the diatonic altered dominant ninth on F in mm. 21-26 (see below in Example 12); and the raised submediant degree, G#, as a member of the major quality triad formed on the raised subdominant degree, E. In the following example the notes which are utilized by Bartók during the opening twelve measures are indicated through the use of arrows depicting their presence within the “supradiatonic” fully-chromaticized major scale of B♭. Each note, diatonic or chromatic, has a place within the fully-chromaticized major scale with only five degrees not being utilized: the raised supertonic, lowered supertonic, lowered dominant, lowered submediant and the diatonic leading note. Thus, the seventeen member fully-chromaticized scale provides a basis for formulating comprehensible conclusions concerning Bartók’s “supradiatonic” tones and objectifies the rationale for disregarding the notion of a “mistuned dominant” in favor of a chromatically raised subdominant construction. It is clear that when Bartók’s orthography is considered to be an accurate reflection of his tonal processes his harmonic intent is revealed without the necessity for notational manipulation.
Example 11: Fully-chromaticized major scale of B♭ with arrows indicating the notes utilized in the Bartók Suite Op 14/1, mm. 1-12.
Within the next seven measures Bartók’s orthography does reveal two appearances of similar melodic-thematic material which employ the chromatically lowered dominant as a root. In this regard Kárpáti makes no mention of “mistuned dominants”; however, in my ensuing analysis these chords are construed as chromatically modified dominants (not “mistuned dominants”) which disguise the diatonic intent and represent a widened harmonic vocabulary, thus reflecting Bartók’s “supradiatonic” inventiveness.
The two appearances of this phenomenon are to be located at mm. 13 – 16, F# minor (alternation of I and ♭V) and mm. 17 – 19, D# minor (alternation of I and ♭V). The two tonalities presented in these seven measures represent, respectively, raised dominant and raised mediant relationships in a descending sequence from the tonic B♭. In each instance the tonic triad is notated diatonically with the modified dominant in the F# minor tonality being a major/major seventh chord (C-E-G-B) and the modified dominant in the D# minor portion being a similarly constructed minor/major seventh (A -C-E - G#).
Example 12: Bartók: Suite Op 14/1, mm. 13 – 24
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“Mistuned” Chord in Root Position
The concluding example to be considered in this article concerns the final chord in the Suite op 14 (mm. 34 and 35 from the fourth movement). The following example drawn from the final four measures portrays the issue under consideration.
Example 13: Bartók: Suite Op 14/4, mm. 32 – 35
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With regard to mm. 34 and 35 Kárpáti states that
Upon the basic B♭ chord, C# is a colouring adjacent note of the major third, A has the same function beside B♭, while G♭ substitutes the fifth, i.e. F, F♭ and C♭ are further colouring adjacent notes … In my interpretation this is the substituting type of mistuned major triads because the major third is substituted by a minor one [C# = D♭], the perfect fifth by an augmented one [G♭ = F#], and the octave by a diminished one [A = B♭♭].
A “supradiatonic”-oriented analysis of the tonic function harmony which concludes the Suite reveals that the diatonic tonic triad of B♭ major is represented by an irregularly constructed tetrad which simultaneously comprises both “chord of addition” and “chord of omission properties.” According to Dallin,
A simple chord to which is added one or more notes normally foreign but used as an integral part of the sonority is designated a chord of addition. A more complex chord from which one or more normally essential elements is omitted is designated a chord of omission.
Bartók presents the tonic structure B♭-D–F in a diatonically construed but “camouflaged” major seventh, B♭-D-F-A with the tonic degree receiving unequivocal diatonic presentation with its impact heightened through octave doubling and the C♭ representing semitonal support from above obscuring the primary harmonic intent. The genus-defining major third apart from diatonic representation receives semitonal support from below through the incorporation of C#; while, the fifth degree is omitted and is replaced with coloring minor seconds, G♭, from above and F♭ from below. Thus, the following tetrad is constructed: B♭-D–[F]–A [+ (C♭; C#; F♭; G♭)] with each of these notes being constituent members of Hartmann’s fully-chromaticized “supradiatonic” major scale. C♭ and C# represent chord of addition properties while F♭ and G♭ highlight chord of omission properties. This is indicated in the following example.
Example 14: Fully-chromaticized major scale of B♭ with arrows indicating the notes utilized in the Bartók Suite Op 14/4, mm. 34 and 35.
Considered within this scenario this tetrad with chord of “omission” and “addition” properties does not constitute the substitution of mistuned major triads but a tonic-inspired representation synthesising diatonic and chromatic properties which both simultaneously propagate and evade the diatonic enunciation of the tonic triad.
Furthermore, the quartal construction (C♭-F♭) which coloristically accompanies the tonic tetrad (mm. 34 and 35) is directly related to the linear quartal melodic profile in mm. 32 and 33 with the vertical intervallic presentation during the final two measures acting as a final reminder of the tritone dichotomy which, from the opening measures of the first movement discussed above, permeates this movement and the Suite as a whole. Enharmonicized, they represent the dominant (B) and tonic (E) of E major though their presence does impinge upon the strength of the B♭ major key at the close; in this regard it is interesting to note that both B and E are constituent members of Hartmann’s fully-chromaticized major scale of B♭.
In conclusion it should be noted that while Bartók would prefer the label of “polymodal chromaticism” in his later reflections, his earlier “supradiatonic” pronouncements reveal that his compositions, notwithstanding surface details, have a clearly tonal foundation based upon “common-practice” principles. In the case of the Fourteen Bagatelles, Allegro barbaro and the Suite Op 14, this is clearly identifiable and negates assertions of “mistuned dominants” and other analytical approaches which are not founded upon Classic-Romantic tonal postulations. The analyses presented in this article reveal Bartók’s well-ordered tonal organization representing a developmental growth grounded in the dissonant textures of the early twentieth-century.
Orthographically Bartók develops a concept of tonality which is complemented through Hartmann’s formulation of the fully-chromaticized scales. Hartmann’s fully-chromaticized scales allow firstly, for the development of a harmonic perspective within an inclusive tonality which contains both diatonic and chromatic tones and secondly, through their construction, harmonic orientations and enharmonization procedures become observable. Furthermore, they are a vehicle whereby Bartók’s intuitions regarding “supradiatonicism” and “bitonalism” can be understood and harmonically contextualized. The musical and theoretical integrity inherent within their construction makes them a relevant basis from which a perspective on the true nature of Bartók’s harmonic imagination can be gleaned.
Each of the aforementioned aspects act interdependently upon each other within Bartók’s remarkable aptitude for assimilating ideas and then reproducing them within the expanded tonal idiom. In conclusion, Graf’s comments on this are perhaps the most pertinent.
He [Bartók] possesses not only the fantasy of genius, but the lucidity of a genius as well. The music … that Bartók created, his harmonies and his rhythm, were studied with intelligent keenness. His artistic world is not just a sphere of fantasy, but a world of logic. Bartók’s artistic development … is without any arbitrariness, clear and sure … Imagination, intelligence and morality are united in Bartók’s work, as they are in every great art.
Antokoletz, E. 1993. The Bartók Companion. Edited by M.
Bartók, B. no date. Allegro barbaro (1911), Universal Edition Nr 5904.
_______ 1971. Fourteen Bagatelles for Piano, Op 6.
_______ no date. Suite, Op 14.
Essays, ed. Benjamin Suchoff,
Bukofzer, M. 1947. Music in the Baroque Era.
Dallin, L. 1974. Techniques of Twentieth Century Composition: A Guide to the
Materials of Modern Music. 3rd. ed.
E.W. 1932. ‘Reviewed Work: Moderne Harmonik by Edwin von der Nüll’. Music and Letters 13/2, 235-236.
Gillies, M. 2001. New Grove Dictionary of Music and Musicians Vol 2 Edited by
Graf, M. 1978. Modern Music, translated by B. Maier.
Hartmann, F. H. 1934. Harmonielehre.
Hartmann, F. H. 1956. Musical
education in the University.
Kárpáti, J. 1993. The
Bartók Companion. Edited by M. Gillies.
1994. Bartók’s Chamber Music
_________ 1995. ‘Perfect and Mistuned Structures in Bartók’s
Music’. Proceedings of the International Bartók Colloquium,
Mason,C. 1953. ‘Reviewed Work: The Life and Music of Béla Bartók by Halsey Stevens.’ The Musical Times 94/1330, 564.
Paxinos, S. 1975. ‘Hubert du Plessis’ Elegie Op.1 No. 3.’ Musicus 3/2, 40-43.
Simms, B. R. 1986.
Music of the Twentieth Century.
Stevens, H. 1993. The Life and Music of Béla Bartók, 3rd. ed. Edited by M. Gillies.
Strauss, R. 1964. Lieder-gesamtausgabe, Vol. 1.
Van der Linde, B. S. 1969. Polytonality: Another case of Atonality?
Van der Linde, B.
S. 1993. Study Guide for HARMPO-W, 2nd.
Vinton, J. ed. 1974. Dictionary of Contemporary Music.
Vinton, J. 1966. ‘Bartók on His Own Music’. Journal of the American Musicological Society 19/1, 232-243.
Yates, P. 1967. Twentieth Century Music.
 Kárpáti, 1995:367.
 Antokoletz,1993: 122.
 Foreword to Béla Bartók: Masterpieces for the Piano (unpublished) cited by Vinton, 1966:234.
 Stevens, 1993:306.
 cited in Stevens, 1993:111.”Von Op. 6 an trachte ich immer, die außerdiatonischen Töne möglichst frei zu gebrauchen” (as cited by von der Nüll, 1930:75).
 Dallin, (1974:44), italics belong to the present author
 Mason, 1953:564.
 Music and Letters ,Vol. 13/2.
 “Die vorstehende Gegenüberstellung (Schönberg opus 11 and Max Reger opus 82) ist der Modernen Harmonik dieses Autors [von der Nüll] entlehnt, deren vortrffliche Ausführungen in diesem Buch verschiedentlich Verwendung fanden,” Hartmann, 1934:215. Translation by Bernard van der Linde and the author.
 Friedrich Helmut
Hartmann (1900-1972) was born and educated in
Hartmann’s compositions are currently being studied by
Timothy L. Jackson (Director of the Lost Composers and Theorists Project,
University of North Texas); who is also exploring the concepts and theories
postulated by Hartmann in theoretical and analytical writings published in
Vienna during the 1930s, including Harmonielehre
(1934) published by Universal Edition and Kontrapunkt
(1936) published by M. Springer Verlag. A later unpublished harmony
treatise, which was completed after Hartmann’s return to
 This observation is reinforced by Bukofzer: “the profound effects of tonality persist in the present-day search for a new and wider concept of tonality” Bukofzer,1947:12.
 To this end postgraduate studies in the Department of Musicology, University of South Africa, have demonstrated the applicability of this methodology through analyses of works by amongst others Paul Hindemith (1895-1963), Reger, Joseph Marx (1882-1964), Michael Tippett (1905 - 1998), Walter Lang (1896-1966) and Bartók (1882-1945).
 Van der Linde, 1969:8.
 Consider the following: ‘…the superimposing of the various modes led … [to] a kind of restrict-
ed bimodality or polymodality. Bimodality again led towards the use of diatonic scales or scale-portions [that were] filled out with chromaticized degrees … They are not altered degrees of a certain chord leading to a degree of a following chord. They can only be interpreted as the ingredients of the various modes used simultaneously – a certain number of these seemingly chromaticized degrees belonging to one mode …’ The New Hungarian Art Music’, unpublished lecture notes prepared in 1942-43, page 57 cited by Vinton, 1966:239.
 Vinton ed. 1974:581.
 ‘The New Hungarian Art Music’, unpublished lecture notes prepared in 1942-43, pages 39 and
41 cited by Vinton, 1966: 238.
 Foreword to Béla Bartók: Masterpieces for the Piano [unpublished] cited by Vinton, 1966:238.
 This chord has also become known as the “Bebop” seventh frequently encountered in Charlie Parker, Dizzy Gillespie and Thelonius Monk revealing the emergence of same sounding harmonic constructions within a wide array of twentieth-century musical genres and styles.
 This conclusion is further supported by Bartok’s reservation of the structural dominant (a major seventh sonority on A natural) until measure 171 resolving to the tonic (as in the opening) at the beginning of the coda in m. 179.
 Kárpáti, 1995:371.
 Kárpáti, 1993:156-7.
 Dallin, 1974:82.
 Consider, for example the following: “As the result of superimposing a Lydian and Phrygian pentachord with a common fundamental tone, we get a diatonic pentachord filled out with all the possible flattened and sharpened degrees. These seemingly chromatic flat and sharp degrees, however, are totally different in their function from the altered chord degrees of the chromatic styles of the previous periods. In our polymodal chromaticism, however, the flat and sharp tones are not altered degrees at all; they are diatonic ingredients of a diatonic modal scale: Bartók Essays, 1976, 367, cit in Kárpáti, 1994: 175.
 Graf, 1978:229.