Muestra B, sin precipitados
4.1 Introducción del Capítulo
Above there were cases of three-voice framework (see chapter 4.3) where the assisting bass proceeded above a sustained bass tone. In those cases the progression in terms of the sum-bass was columnal (cf. chapter 4.5.3) when all the chords in the domain of the assisting bass were – or could be considered to be – (harmonically) upper sub-chords of the same hypothetical sum-chord (see Fig. 5.5–1 [op. 63:IV:155–162], Fig. 5.5–3 [op. 82:III:189– 212]). On the other hand, in those cases the progression in terms of the sum- bass was non-columnal when at least one root in the domain of assisting bass suggested a sum-chord for which the sum-root was different from the sustained tone in the bass part. In a non-columnal progression this different sum-root formed an interval of a second in relation to the sustained tone (see Fig. 5.5–2 [op. 49:15–18]).
However, when a sum-root in the domain of assisting bass is different from the sustained tone, it is still possible to build up columnal progressions, if a different sum-root increases the would-be sum-chord downwards. This new (harmonically) lower sum-root may spatially stand above the sustained tone, but also spatially below it. In this latter case the assisting bass will cross the bass. In crossing, the assisting bass and the sustained tone may also meet in unison and then immediately diverge.
From the point of view of terminology in a situation where the assisting bass crosses the former bass and then stands below it, these terms should be exchanged. Yet due to the momentary quality of this new situation and the
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re-gaining of the original situation, the original terms should again be restored. This kind of terminological switch – that may reiterate – would easily lead to confusion. Therefore it should be decided that the assisting bass may keep its name even after crossing the bass. In this extraordinary spatial position the assisting bass bears a (harmonically) lower sub-chord, while the bass bears the (harmonically) upper sub-chord. Thus the terms assisting bass and bass are given for the components according to the spatial condition that prevails most of the time.
In Fig. 5.7–1a there is a Satz that is composed of two chordal layers. The structure and harmonic rhythm of them is different. One of the layers is a dissolved regular pentachord-succession (Vl. I, II, Vle., Vc.), which has already been encountered (see Fig. 4.2.5–2 [op. 52:I:61–64]).255 The pattern
in bars 61–63 (G: II–VII–V–VII–II–IV) is repeated in bars 64–66. The lower octave-doubling of this component ends in bar 62. Against this pentachord- succession in the strings enters a wind call (Fag., Cor. – Fl., Ob. Cl.; see chapter 6.1). The harmonic basis of the wind call – some passing chords neglected – consists of different forms of an F sharp-rooted half-diminished seventh chord (G: VII7–VII four-three). It includes the two F sharp- and A- rooted innermost pentachords of the pentachord-succession (G: II and VII). Thus only the two outermost pentachords (G: V and IV) will function as chordal layers in relation to the wind call.
In a regular adjustment of these components the assisting bass of the pentachord-succession would proceed above the bass, meet it in unison, then cross the bass and fall below it, again meet the bass in unison, then cross the bass and proceed above it, etc. (cf. Fig. 5.7–1b). Yet here due to the spatial relation of the components and the motions of the wind chord, the actual
255 According to Virtanen 2005:87 “Measures 61–67 are, again, built upon a single chord, the half-
diminished seventh chord F#–A–C–E, and the note D that appears in mm. 62 and 65 reinforces the dominant function of these measures”. It surely does, but Virtanen does not take into consideration the harmonic column (see chapter 4.4) the reach of which goes even beyond the dominant ninth chord. Virtanen also notices “the implied C-major chord on the first beat of m. 61; this chord, even if not unequivocally present on the surface, implicitly derives from an underlying voice-leading progression shown in Example 10–7” (Virtanen 2005:86). This implication may well be done, but in my opinion Virtanen overestimates the importance of this implied crotchet in bar 61 in comparison with the prolonged dominant in bars 61–67. Only in Ex. 10–8 (that illustrates an alternative approach indebted to Lauri Suurpää) the half-diminished seventh chord (replacing the implied C major triad) stands at bar 61 (ibid.:86), while in other respective examples the implied C major triad stands under number 61 and the half-diminished seventh chord after it seems a passing formation; see Virtanen 2005:76 (Ex. 10–1b), 81 (Ex. 10–4d), 82 (Ex. 10–5d; this letter “d” is missing, but the sketch comes after 10–5c), and 85 (Ex. 10–6; this marking is missing, but the sketch stands between Ex. 10–5 and Ex. 10–7). Both these decisions – excluding the added–root D from the sketches and neglecting the temporal weight in deciding the hierarchy of chords – seem to derive from the preconceived opinions of the “Schenkerian perspective” (cf. Virtanen 2005:76).
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columnal succession will mostly be irregular, although the crossing of the components indeed takes place in bar 62.
In bar 62 the lowermost D-rooted sub-triad (G: V) of the string figuration functions as the (harmonically) lower sub-triad that increases the upper F sharp-rooted sub-seventh chord downwards into a regular D-rooted added- root ninth chord in bars 61–62 (G: VII7+V = V9+5). In bar 65 the same sum- ninth chord is in reverse form (L + U inv; G: V+VII four-three = V9+5 in the 3rd inversion). The term “figuration” as used here does not imply the
contrapuntal nature of the string layer. Yet it hardly meets the demands of a “counterpoint” in the traditional sense of the term. The content of string “figuration”, or “counterpoint”, is repeated only once, so it does not truly fulfil the demands of an ostinato either. This difficulty in finding an appropriate term for this segment of a macro-component (see chapter 8.5) stems from the untraditional nature of Sibelian Satz.
In bars 63 and 66 the topmost C-rooted sub-triad (G: IV) of the string figuration functions as the upper sub-triad. It increases the F sharp-rooted lower sub-seventh chord upwards into an inverted added-ninth seventh chord (U + L inv; G: IV+VII four-three = VII7+9 in the 2nd inversion). Here
the sub-chords share the mutual bass C.
Taken all together, the irregular columnal succession is G: VII7 – V9+5 – VII7 – VII four-three – VII7+9 in the 2nd inversion – VII four-three – V9+1
in the 3rd inversion – VII four-three – VII7+9 in the 2nd inversion (cf. Fig.
4.2.5–2 [op. 52:I:61–64]). Furthermore all these may be considered sub- seventh and sub-ninth chords of a wider D-rooted dominant sum-eleventh chord D–F sharp–A–C–E–G (Fig. 5.7–1b).
In the surface level in bars 63–64 and 66–67 there is a filled dissolution 11–x–9 (G–F sharp–E). In bar 67 the entering horns suggest G: V2. This leads to a progression G: VII four-three+V2 – I/I6 = V9+1 in the 3rd
inversion – I6. During this progression the suggested (harmonically) lower sub-seventh chord (G: V2) is resolved, while the upper sub-seventh chord (G: VII four-three) in the woodwinds ceases (see chapter 6.1). In the string figuration the ninth E is also released by the motion 9–10 (cf. Fig. 5.3–5c).
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Fig. 5.7–1 a–b. Chordal layers put against each other. Third Symphony op. 52 (1907) 1. mvt. bars 60–67.
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