PART TWO: THE STRUCTURE OF SIBELIAN
4. THE BASICS OF LAYERED TECHNIQUE
4.5 CHORD-FORMATIONS IN REFLECTION
All the various concepts and devices above are in some way related to the lecture fragment. This perusal offers us some points to be reflected upon. Firstly a glance is cast on how ninth, eleventh and thirteenth chords were explained in traditional harmonic theory. Then these explanations are weighed in connection with the lecture fragment (section 4.5.1). Secondly the analysis of layered Satz is discussed (section 4.5.2). Here the difference between the concepts of chord and column is also touched on (section 4.5.3).
4.5.1 NINTH, ELEVENTH AND THIRTEENTH CHORDS EXPLAINED
In the course of the history of music theory, ninth, eleventh and thirteenth chords have been either rejected or accepted as independent chords. In the eighteenth century suspension-formations, i.e. non-tertian harmonies were explained as inverted ninth, eleventh or thirteenth chords.204 Yet already in
the eighteenth century acceptance of the dominant ninth chord (e.g. G–B– D–F–A) emerged as a fundamental harmonic entity.
Ninth, eleventh and thirteenth chords were explained as supposition and superposition. In supposition a third (or fifth) is added below a seventh chord. In supposition the bass spatially above the added tone is still considered to be the root of the chord.205 In principle – though not in
204 Cf. Sheldon 1982:61.
205 Rameau in his Treatise on Harmony (1971 [1722]) explained ninth and eleventh chords as
resulting from a supposition where the root of a seventh chord is called “the fundamental of this chord”, or “fundamental sound” and the interval of a third or a fifth that as a fifth part is added below
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terminology – this resembles a three-voice framework (see section 4.3) that includes an assisting bass and bass.206 Supposition was the older way of
explanation and originated in the eighteenth century.207 In the Romantic era
chord-formations wider than seventh chords (i.e. wider chords) were often introduced.208 Explaining these as superposition where thirds are stacked on
top of a seventh chord began to gain more and more acceptance in the nineteenth century.209 An interesting transition stage was the moment when
different simultaneous suspensions over the sustained root and the seventh were regarded as independent eleventh chords (9–8 and 4–3 during 7/1), as well as thirteenth chords (9–8, 4–3 and 6–5 during 7/1).210 According to the
earlier practice in connection with the seventh chord the independent status for the eleventh and thirteenth chords should only have been allowed when the bass proceeds during the resolutions. In the twentieth century the (dominant-type) ninth chord – along with the triad and the (dominant-type) seventh chord – could be included among the “chords of nature” (Naturklänge).211
The description by Sibelius in the lecture fragment (cf. chapter 2.1.4, Tolonen) concerning “a ninth chord” G–B–D+D–F–A as “an upper
this root is called an “added sound” (Rameau 1971[1722]:292, Ex. III.81, ibid:294, Ex. III.85, ibid:299, Ex. III.91).
206 Before one of his examples Rameau even writes the signatures 7/5/3/1 and 9/7/5/3/1 in
succession. The topmost numbers of these signatures (7 and 9) are located in the same space in order to show how they (as well as the lower factors of the seventh chord) relate to the factors of the supposition-formation (Rameau 1971 [1722]:292, Ex. III.81). Rameau thus describes the twofold intervallic quality in the sum-chord (see section 4.3).
207 Besides Rameau (1722) supposition was represented by Marpurg who added the thirteenth
chord to Rameau’s chords constructed by supposition (Wason 1985:9, 165 note 36) and also by Türk (Wason 1985:63).
208 According to the Introduction of N. Rimsky-Korsakov 1930 [1886]:1–2 “Three chords are
considered fundamental chords: a triad, a seventh chord[,] a ninth chord”. The author offers three note-examples, the last of which is the same – though not layered – as that in the lecture fragment of Sibelius. This ninth chord is supplied with a footnote that refers to the note 1) on page 2. In this further note there reads: “At present more than five notes can be used to build up a chord. The eleventh and thirteenth chords are accepted and widely used …”.
209 Superposition was represented by Bruckner, who – unlike his teacher Sechter – considered the
ninth chord (also the non-dominant ninth chord) a “fundamental harmony”. Bruckner moreover conceived inversions of dominant eleventh and dominant thirteenth chords (Wason 1985:71–74, 165 note 36). Piston 1978 explains wider chords only by superposition.
210 See Rimsky-Korsakov 1930 [1886]:86. In the note to the paragraph 71 Rimsky-Korsakov says:
“The compound suspensions … are at present regarded as independent chords and are respectively described as eleventh-chords … and thirteenth-chords … with the third and fifth omitted”.
211 According to Georg Capellen 1903:15 these three chords “are the only true copies
(objectivations) of the Nature” [J. A.] (Da der Durdreiklang, Durseptimen- und Nonenakkord allein
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pentachord resting upon a lower one” (see section 4.1), may be understood either as superposition (i.e. added-ninth chord), or as supposition (i.e. added-root ninth chord). Sibelius began his text quoted above with the melodic (upper) pentachord and only then introduced the harmonic (lower) pentachord. This order of presentation may reflect which of these sub-triads was the starting-point in his layered technique (cf. chapter 1.3). Be that as it may, in the music of Sibelius sum-chords can be encountered that may be explained by means of supposition (see Fig. 5.2.3–2 [op. 9:30–35], Fig. 5.5– 2c [op. 49:16–17], 5.6–3 [op. 12:III:203], Fig. 6.1.3–4 [op. 66:I:27–30]), as well as others that may be explained by means of superposition (see Fig. 5.5– 3 [op. 82:III:195–200], 5.6–4 [op. 82:I:31], Fig. 6.1.6–1 [op. 112:612–614], Fig. 7.3–2 [op. 112:593–597], Fig. 10.4–1 [op. 74:II:35, 36, 37], Fig. 11.3.3–1 [op. 18:III:1–5]).
4.5.2 ON ANALYSING LAYERED SATZ
The conventional harmonic analytic notation was developed in order to analyse Satz mostly based on non-additive harmony. In the case of sum- chords the conventional analytic notation – even when it technically can be used – will only give an external, if not false, description (cf. Fig. 6.1.5–1 [op. 5:V:73–77]).
It is probable that without the guidance of the composer the conceptual division of the melody as well as the accompaniment into sub-triads (Fig. 4.5.2–1a) would not have been recognized (cf. chapter 3.1). Without this recognition the line in the lecture fragment would have been analysed in terms of a two-voice framework (see section 4.3), as a single part that dissolves a G-rooted dominant-type seventh chord (Fig. 4.5.2–1b).
Fig. 4.5.2–1 a–b. The same phenomenon understood as a three-voice framework a), or as a two- voice framework b).
In Sibelius’ music the situation where a dissolving line is a layer (a sub-chord or a sub-interval) is quite common (cf. Figs. 4.2.5–2 [op. 52:I:61–63] and 4.4.1–2 [op. 52:I:63–65]; see also Fig. 10.5.3–1 [op. 82:II:182–185], Fig. 11.5–1 [op. 46:III:1–15], Fig. 11.7–1 [op. 114:IV:11–17, 19–23]). Therefore in analysing the music of Sibelius it is always useful to begin with the melody (cf. Sibelius to W. Davies, chapter 1.3) and clear up its ambitus and harmonic content, in order to find out whether it is a layer, or merely a part in a non-
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additive harmony. This problem is also touched on later in connection with irregular sum-chords (see Fig. 10.5.3–1 [op. 82:II:182–185]).
With conventional analytic tools the additive harmony (see section 4.1.1) of the Satz of Sibelius can easily fail to be taken into consideration (cf. Fig. 4.5.2–1b), it is more likely to be rejected a priori. In analysis this distorts the overall picture. Harmonic reduction into sub-chords does not necessarily produce less or more complicated analyses than other analytic methods, but in this method economy of thought can also be strived for.
4.5.3 CHORD VERSUS COLUMN
There are some differences between the concepts of chord, sum-chord and column. A chord is either consonant or dissonant, while a sum-chord is always – in traditional terms – a dissonant formation (the term chord- formation covers both of these). Yet a sum-chord may contain a consonant layer, or be a sum of merely consonant layers (cf. Fig. 4.1–1c). To my mind it is exaggerated to consider a dominant-type sum-ninth chord a “quasi- consonant sonority”.212 As far as I know, Sibelius never expressed such an
opinion.
A chord may be described as a product of voice-leading in a two-voice framework (see section 4.3) ruled by the most important voices soprano and bass, while a sum-chord – being a sum of its sub-chords – establishes a three-voice framework (see section 4.3). Thus in connection with sum-chords the twofold intervallic quality (see section 4.3) of those components that lean on the assisting bass is always to be taken into consideration.
A column is a concept wider than a chord or even a sum-chord. Besides the sum-chord, a column as a stack of thirds also includes the temporal process that by means of increasing or decreasing, or both, leads to and from the sum-chord (see section 4.4). Thus there can be a sum-chord without it being a column (i.e. a sum-chord that is preceded and followed by chord- formations that do not increase the stack of thirds of the sum-chord). On the other hand, without a sum-chord there is no material for a column. With regard to Satz during a column there often is a pentachord-succession in the domain of an assisting bass, while the bass holds a sustained sub-tone (see Fig. 4.4.1–1 [op. 56:V:254–259]), sub-interval, or sub-chord (cf. Fig. 4.4–1, see Fig. 4.4.1–2 [op. 52:I:63–65]). As we shall later see, in the domain of an assisting bass increasing or decreasing a column may also be achieved by means of voice-leading typical to traditional figured bass (see Fig. 5.5–1 [op. 63:IV:158–162]). This may be called a columnal progression. Both it and columnal succession encountered earlier (see section 4.4) are the two main aspects of columnal technique.
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A chord is located on a certain degree. A sum-chord (e.g. the one in the lecture fragment) includes two different simultaneous degrees in terms of a three-voice framework, but only one in terms of sum-bass (see section 4.3). In a column an assisting bass may produce two or more successive degrees. Yet these degrees as sub-roots (see section 4.3) may lean on one sum-root (see section 4.3) held by the sustained bass (see Fig. 4.4.1–2 [op. 52:I:63– 65], Fig. 7.2.1–1 [op. 63:IV:178–182]). A column in its course may also embrace more than one sum-root, or degree. This will happen, if the sustained bass ceases (see Fig. 4.4.1–1 [op. 56:V:254–259]). The technique of entering and ceasing layers will be discussed later (see chapter 6.1). More than one sum-root, or degree, during a column will inevitably follow, if there is a motion in the domain of bass (cf. Fig. 5.2.3–2 [op. 9:34–37], Fig. 6.1.6–1 [op. 112:612–634]).