In traditional organ point Satz, besides the two harmonic situations where an organ point either did, or did not, belong to a harmony that leant on the assisting bass, in terms of this study (see chapter 4.6.1), a third harmonic situation emerged where smaller harmonic units together added up to a larger one (see chapter 4.6.2). Sibelius used this third additive alternative in shaping formations that outwardly resembled organ point-formations, i.e. traditional seven-four-two chords (see section 5.1.1).
In traditional seven-four-two chords – according to the very rubric of C. P. E. Bach – the seventh is a major one (ma7), while in Sibelian sum-seven- four-two chords (that may be called pedal point-formations) the seventh is a minor one (mi7). In connection with tonic pedal point this minor seventh is caused by the subtonic (see chapter 4.2.3), or by a flattened leading-tone in those scales not possessing a subtonic. Thus sum-seven-four-two chords are a specific group among dominant-type chords (see Figs. 5.2.2–2c, 5.2.2–3b, 5.2.2–4d, 5.2.2–5c).
In figured bass-practice the compound second was discerned from a ninth on harmonic grounds (see Fig. 4.3.1–3).234 Yet in order to show the analogy
between traditional and sum-seven-four-two chords, this classic practice of accuracy is relaxed in this section. Thus in the following figures (from Fig. 5.2.2–1 to Fig. 5.2.2–5) the sum-ninth may be marked by the signature “two”, the sum-eleventh by the signature “four” and the sum-thirteenth by the signature “six”.
232 C. P. E. Bach [1762](1985):293–299; on p. 294 a seven-four-two chord is characterized as a
“passing” or “retardation” depending on context. On p. 298 the factors of a seven-five-two chord (a variation of seven-four-two) are called “appoggiaturas”.
233 See e.g. Piston 1978:129–132.
234 Cf. C. P. E. Bach: 1985[1762]:302–303 “The ninth is and remains a ninth even when it is placed
directly adjacent to the bass. (…) Of course, (…), it is always better to place the ninth nine degrees above the bass.”
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Below the sum-seven-five-four-two chord (Fig. 5.2.2–1a) and the sum- seven-six-four-two chord (Fig. 5.2.2–1b) are viewed as the complete formations, while the others are considered their incomplete versions. Thus the sum-seven-five-two chord (Fig. 5.2.2–1c) is considered an incomplete version of the sum-seven-five-four-two chord (Fig. 5.2.2–1a). On the other hand, the sum-seven-four-two chord (Fig. 5.2.2–1d) may be understood an incomplete version of either of the complete formations. Because of this family resemblance in these formations and because of their importance in Sibelian Satz, in terms of both three-voice framework (see chapter 4.3) and modal dimension it is appropriate to scrutinize sum-seven-four-two chords in a way that some readers might find rather meticulous.
Fig. 5.2.2–1 a–d. Sum-seven-four-two chords.
Above the traditional seven-four-two chords were combinations of a chord and organ point (see Fig. 5.2.1–1). In these combinations the lowest tone of the chord – whatever it may be – functions as an assisting bass. In a similar way the sum-seven-four-two chords may be considered combinations of a sub-chord and a sub-tone below it (in all the Figs. 5.2.2 the sub-tone is c). In this combination the lowest tone of the sub-chord functions as the assisting bass. Thus a sum-seven-four-two chord also has several alternatives for an assisting bass according to which one of the factors of the sub-chord stands the lowest. In the closest positions of these alternatives the sum-ninth (as well as the sum-eleventh and sum-thirteenth) stands below the sum-seventh.
In Fig. 5.2.2–2 there are all the alternatives for the assisting bass of the upper sub-seventh chord of a sum-seven-five-four-two chord (mi7–5–4–2). In Fig. 5.2.2–2c there is a root-position sub-seventh chord in a regular sum- eleventh chord without a third, while in Figs. 5.2.2–2a, –2b and –2d there are irregular root-position sum-eleventh chords. This term is used here, even when the lower, supposedly regular, sub-chord is represented only by its root (cf. section 5.1). The three-voice framework of C Mixolydian: I mi7–5–4–2 in Fig. 5.2.2–2c would be C Mixolydian: V7+I1 and its sum-bass C Mixolydian: I1+11. The other alternatives can be deciphered accordingly.
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Fig. 5.2.2–2 a–d. Sum-seven-five-four-two chords.
In Fig. 5.2.2–3 there are all the alternatives for the assisting bass of the upper sub-triad of a sum-seven-five-two chord (mi7–5–2). In Fig. 5.2.2–3b there is a root-position sub-triad in a regular sum-ninth chord without a third, while in Figs. 5.2.2–3a (see Fig. 11.5–2 [op. 52:II:93–102]) and 5.2.2–3c there are irregular root-position sum-ninth chords. The three-voice framework of C Mixolydian: I mi7–5–2 in Fig. 5.2.2–3b would be C Mixolydian: V+I1 and its sum-bass C Mixolydian: I1+9.
Fig. 5.2.2–3 a–c. Sum-seven-five-two chords.
In Fig. 5.2.2–4 there are all the alternatives for the assisting bass of the upper sub-seventh chord of a sum-seven-six-four-two chord (mi7–mi6–4–2). In Fig. 5.2.2–4d there is a root-position sub-seventh chord in a regular sum- thirteenth chord without the third or fifth, while in Figs. 5.2.2–4a, –4b and – 4c there are irregular root-position sum-thirteenth chords. The three-voice framework of C Ionian-Aeolian: I mi7–mi6–4–2 in Fig. 5.2.2–4d would be C Ionian-Aeolian: VII7+I1 = I1+13 (sum-bass).
Yet it is also possible to understand this sum-seven-six-four-two chord as the 4th inversion of a sum-ninth chord (Fig. 5.2.2–4e) i.e. as a reverse sum-
ninth chord (see section 5.1). In this case the sum-ninth (C) stands as the sustained tone, while the sum-root (B flat) stands as the seventh from this bass. The three-voice framework of C Ionian-Aeolian: I mi7–mi6–4–2 in Fig. 5.2.2–4e would be C Ionian-Aeolian: VII7+I1 = VII7+9 in the 4th inversion
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Fig. 5.2.2–4 a–e. Sum-seven-six-four-two chords.
In Fig. 5.2.2–5 there are all the alternatives for the assisting bass of the upper sub-triad of a sum-seven-four-two chord (mi7–4–2). In Fig. 5.2.2–5c there is a root-position sub-triad in an incomplete regular sum-eleventh chord without the third or fifth, while in Figs. 5.2.2–5a and –5b there are irregular root-position sum-eleventh chords. The three-voice framework of C Mixolydian: I mi7–4–2 in Fig. 5.2.2–5c would be C Mixolydian: VII+I1 = I1+11 (sum-bass).
It is also possible to understand this sum-seven-four-two as the 4th
inversion of an incomplete sum-ninth chord without a seventh (Fig. 5.2.2– 5d). Moreover, in this case the order of the layers is reversed (see section 5.1) and the sum-ninth stands as the sustained tone and the sum-root as the seventh from this bass. The three-voice framework of C Ionian-Aeolian: I mi7–4–2 in Fig. 5.2.2–5d would be C Ionian-Aeolian: VII+I1 = VII5+9 without a seventh in the 4th inversion (sum-bass).
Fig. 5.2.2–5 a–d. Sum-seven-four-two chords.
The sum-seven-four-two chords were presented above on the tonic in order to emphasize their difference in relation to traditional ones in major keys. Yet often the sum-seven-four-two chords appear on dominant pedal points (cf. section 5.1.1). In this case there is no need to raise the seventh (i.e. the fourth degree) in major and minor scales either.
In Fig. 5.2.2–6 there is a spot of line-pedal Satz that is a musical realization of Fig. 5.2.2–4b. This sum-seven-four-two chord rests on
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sustained C (Fag., Cb.) over which there proceeds a dissolving thickening (Cor. I, II). This abundant line-pedal Satz is reduced (cf. Fig. 5.5–3 [op. 82:III:189–212]), but the lower horn parts (Cor. III, IV) that function as the orchestral artificial pedal effect (cf. chapter 8.3.2) in this dissolved sum- seven-four-two chord are still included.
Fig. 5.2.2–6. Line-pedal Satz including a dissolving thickening. Fifth Symphony op. 82 (1915/1916/1919) 3. mvt. bars 203–207.