In the era of figured bass, ninth chords were accidental and therefore it was unnecessary to develop any kind of deciphering for them (cf. Fig. 4.6.1–1). The only inversion of a ninth chord that can afterwards be deciphered according to a traditional figured bass signature is the 4th inversion (see Fig.
5.6–1e). It would of course be possible to suggest new signatures for other inversions. Thus the 1st inversion (Fig. 5.6–1b) of a sum-ninth chord would
be a seven-six-five-three chord, the 2nd inversion (Fig. 5.6–1c) a six-five-four-
three chord and the 3rd inversion (Fig. 5.6–1d) a six-four-three-two chord (in
these signatures the location of the ninth is indicated by means of italics). Yet these signatures are longish and can easily be mixed up. Therefore in their tonal or modal harmonic context with all the inversions of a sum-ninth chord outlined below only the degree of the root (by Roman number) and the ordinal of its inversion are announced. In harmonic analytic notation the lowest factor of an inverted sum-ninth chord is marked below the roman number (cf. the sum-bass of Fig. 5.2–1). These practices are also followed in connection with inversions of sum-eleventh (see Fig. 7.2.1–1 [op. 63:IV:178– 182]) and sum-thirteenth chords. For the sake of conciseness the procedures are illuminated in connection with sum-ninth chords. The same devices are adaptable to the wider sum-chords as well.
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Fig. 5.6–1 a–e. Sum-ninth chord and its inversions.
In order to compare the other inversions of a sum-ninth chord with the fourth one, all the other inversions in Fig. 5.6–1 are selected from dominant- type ninth chords that include the tone C. In each figure the root is indicated by the breve and the ninth by a blackened note-head.
The regular sum-ninth chord presented in the lecture fragment was a sum of sub-triads (see chapter 4.1). More often than not in the music of Sibelius the inversions of a ninth chord also appear as sums of sub-chords.
In Figs. 5.6–2a, –2b and –2c the first, second and third inversions of the dominant-type sum-ninth chords seen in Fig. 5.6–1 include fifth-rooted sub- triads that share common tones. When presented in the closest position possible, one sub-triad is always in root-position, while another is inverted. In Fig. 5.6–2a there is the inverted type U + L inv, while in Fig. 5.6–2c there is the reverse type L + U inv (cf. Fig. 5.2–1e). In both cases there is an assisting bass over the bass. In Fig. 5.6–2b there is a situation not hitherto encountered. The lowest tone [C] is common to both sub-triads. The bass and assisting bass meet in unison. Both layers thus share a mutual bass (see chapter 4.3, chapter 6.1.6).254 This type could be considered either an
inverted (U + L inv), or a reverse (L inv + U). The more tones the sub-chords have in common, the more possibilities there will be open for mutual basses. In Figs. 5.6–2aa, –2bb and –2cc the same inversions include third-related sub-seventh chords. All their combinations lean on mutual basses.
254 A mutual bass may equally well be shared by sub-triads of a sum-seventh chord. Furuhjelm
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Fig. 5.6–2 a–cc. The 1st
, 2nd and 3rd inversions of sum-ninth chords as different combinations of sub-chords.
As well as on the layers of the same width, these inverted sum-ninth chords – as was the case with regular ones – may be based on layers of different width, e.g. on a sub-triad and sub-seventh chord (see Fig. 6.1.6–1 [op. 112:612– 634]), etc. In a situation where a single tone as a sub-tone (i.e. as a layer) appears above the bass of a sub-chord, by assuming a mutual bass it is possible to conceive a hypothetic sub-chord where this sub-tone belongs (see Fig. 5.6–3). If a single tone appears below a sub-chord, by assuming a mutual soprano it may be decided whether there is a mutual bass or a separate assisting bass and bass (see Fig. 5.6–4).
In Fig. 5.6–3a after a two-voice framework (see chapter 4.3) a mutual bass is assumed in connection with a single bass tone. Before this spot of three-voice framework (see chapter 4.3) in bar 203 the tonic F major triad and subdominant added-sixth triad alternate (cf. Fig. 5.3.2–3). In bars 200
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and 202 in the melody the tone E flat appears, which increases the F-rooted tonic triad to a secondary dominant seventh chord (F Harmonic major: V7 of IV). Then the seventh resolves to the third of the subdominant added-sixth triad (F Harmonic major: IV5+6). This is a resource well known before Sibelius.
However, the third appearance of the melody tone E flat differs from the earlier ones. In bar 203 it no longer occurs in connection with the tonic triad, but instead above the subdominant added-sixth triad (F Harmonic major: IV5+6). Against it this E flat at first seems to be a non-harmonic tone. Then in bars 203–204 the E flat proceeds by leap to the fifth C of the tonic triad.
Yet it may be assumed to be a sub-seventh chord (B flat–D flat–G–E flat) to which this tone E flat belongs as the lower root. This E flat-rooted dominant-type sub-seventh chord (F Ionian-Aeolian: VII four-three) leans on the same bass tone B flat as the added-sixth triad does (Fig. 5.6–3b). In the resulting added-root sum-ninth chord in the 2nd inversion (F Ionian-
Aeolian: VII1/IV5+6 = VII four-three+IV5+6 = VII9+1 in the 2nd inversion)
this E flat-rooted sub-seventh chord is the (harmonically) lower one, while the former sub-dominant added-sixth triad (that in bar 203 can also be written in F Ionian-Aeolian), would stand as the (harmonically) upper sub- seventh chord (Fig. 5.6–3c), if the sum-ninth chord is arranged into a regular stack of thirds.
According to this explanation (F Ionian-Aeolian: VII9+1 in the 2nd
inversion – I) there is no “leaping non-harmonic tone”, but instead the leaping sum-root E flat that perforce is a consonant tone (see section 5.3.4; cf. Fig. 5.1.3–2 [op. 82:III:147]). Thus in the middle of the plagal cadence (F Ionian-Aeolian: IV5+6 – I) a kind of passing progression is inserted (“1 ½ chord”) that corresponds to an authentic closure. This passing progression is also non-columnal.
Fig. 5.6–3 a–c. A seeming leaping dissonance interpreted as a factor of a sub-seventh chord. Sonata op. 12 (1893) 3. mvt. bars 193–204.
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In Fig. 5.6–4 a mutual soprano is assumed in order to conceive a sub-chord. Against a sustained dominant tone d1/d (Tr. III, Timp.) proceeds a line thickened by thirds (Fl., Ob., Cl., Vl. I&II). This line at first utilizes an F sharp-rooted diminished pentachord and then the dyad f1 sharp–a1. The collateral line of it initially utilizes a D-rooted major pentachord and then the dyad d1–f1 sharp. Together these overlapping pentachords at first form a dissolved D-rooted dominant-type seventh chord (G: V7) and after dissolution 7–x–5 (see chapter 4.4) in bars 32–33 they form a dissolved dominant triad (G: V).
A two-part ostinato proceeds below the thickening (Fag., Cor., Vle., Vcl.) where the parts in a one-bar pattern (d1–e1–d1–c1 … and d–c–d–e …) proceed in systematic contrary motion (see chapter 7.4). Against the sustained tone d1/d (Tr. III, Timp.) in bars 31–32 the ostinato-tones C and E function merely as neighbour notes (Fig. 5.6–4a). Yet in relation to the thickening the ostinato functions as a layer where the sub-dyads e1/c and c1/e are separated by the passing tone d1/d.
Below the dominant triad (G: V) the sub-dyads of the ostinato function as an added-seventh and an added-ninth. Assuming a mutual soprano (A), the sub-dyads may be included in a (harmonically) upper sub-seventh chord (F sharp–A–C–E) that alternates between its second and third inversions (Fig. 5.6–4b). Together these layers add up to a reverse combination (L + U inv). With the D-rooted (harmonically) lower sub-triad the tenth-dyad adds up to a dominant added-ninth chord in the 3rd inversion, while the sixth-dyad
presents the 4th inversion of it as a mi7–6–4–2 chord (cf. Fig. 5.2.2–4c). In
relation to the passing tone d1/d the added-seventh is released and the ninth resolved. Those inversions hold true on the condition that the low A at the beginning of bar 31 is considered ceased (see chapter 6.1).
At the beginning of bar 32 during the tone d1/d a passing chord occurs (G: I six-four) resulting from a passing dyad b1/g1 in the thickening. In bar 34 against the terminating tone of the thickening g1/g1 the ostinato tones C and E stand as the root and third of a major triad (G: V–IV). Now the former consonant passing tone d1/d functions as a non-harmonic passing tone between G: IV3 and IV6 without third. In C Lydian these chords (C Lydian: II– I) would form a closure (cf. Fig. 5.4.2–1c). This new situation appears again in bar 38, while before it in bars 36 and 37 the familiar situation from bars 31–33 returns. Thus the scalarly associated G major and C Lydian alternate in bars 31–40 (see chapter 4.2.2).
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Fig. 5.6–4 a–b. An assumed sub-seventh chord below a sub-triad. Fifth Symphony op. 82 (1915/1916/1919) 1. mvt. bars 31–34.