PENTACHORDS IN MELODIES

A tonic pentachord may reveal itself both spatially and temporally. Spatially, tonic (formerly: finalis) and dominant (formerly: tenor) act as the tones from which the leaps begin and on which they end, and as turning-points of scalic motion. Temporally, tonic and dominant in a pentachord act as beginning and/or terminating tones, as temporally dominating tones, and as rhythmically stressed tones.197

In any heptatonic scale, pentachordal modal melodies may be divided into five classes according to their ambitus. As much as possible the D Dorian pentachord is used in illuminating these classes.

In the first class there are melodies that are based on the tonic pentachord (D E F G A; Fig. 4.2.3–1a). In this first class there are three groups. In the first group there are melodies that utilize the complete pentachord. In the second group of the first class fall those melodies where between tonic and dominant there is some degree that is not utilized at all (e.g. D E F _ A; Fig. 4.2.1–1b) [op. 73:5–10]. These kinds of tonic pentachord may be termed gapped (in the figures the gap is shown by a marker). In the third group of the first class lie those melodies where the tonic of the pentachord is not utilized (e.g. _ E F G A; Fig. 4.2.1–1c) in the line, but it is presented in accompaniment (D\E F G A). This kind of tonic pentachord is termed shared [cf. op. 114:II:1–3]. Yet a rootless tonic pentachord is never completed by another component. In order to differentiate it from a tetrachord, or from a short pentachord that always includes a tonic and thus is not rootless, the tonal context must be taken into consideration.

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Fig. 4.2.3–1 a–c. Complete, gapped and shared tonic pentachord.

In the second class are those melodies that are based on short pentachords. The tonic tetrachord (D E F G; Fig. 4.2.3–2a), as well as the tonic trichord (D E F; Fig. 4.2.3–2b) may be considered short pentachords. The missing degree or degrees do not prevent the tonic from ruling a short pentachord. Besides a minor (or Dorian or Aeolian) tonic tetrachord there may also be a major (or Ionian or Mixolydian) tonic tetrachord (Fig. 4.2.3–2c) as well as Phrygian (Fig. 4.2.3–2d) and Lydian (Fig. 4.2.3–2e) tonic tetrachords. Also, aside from a minor (or Dorian or Aeolian) tonic trichord there may be a major (or Ionian or Lydian or Mixolydian) tonic trichord (Fig. 4.2.3–2f), as well as the Phrygian tonic trichord (Fig. 4.2.3–2g).

Fig. 4.2.3–2 a–g. Tonic tetra- and trichords as short pentachords.

In the third class there are melodies where the tonic pentachord is extended by additional tones. In these extended pentachords the ambitus does not reach the octave (cf. section 4.1.1). This third class may be divided into two groups. The first group of the third class includes extended complete pentachords. A tone above the pentachord extends it to a hexachord (D E F G A + B; Fig. 4.2.3–3a). Two additional tones above the pentachord extend it to a heptachord (D E F G A + B C; Fig. 4.2.3–3b). This was the case that Sibelius presented in the lecture fragment (see section 4.1). Below the pentachord an extending tone is a subtonic (C + D E F G A; Fig. 4.2.3–3c; cf. Fig. 5.1.3–5 [op. 34:VIII:1–3]), or a leading-tone (i.e. C#) depending on the scale. Below the subtonic a submediant may be added further (B C + D E F G A; Fig. 4.2.3–3d; cf. Fig. 11.5–2 [op. 52:II:93–98]). The subtonic may also be located below a hexachord (C + D E F G A + B; Fig. 4.2.3–3e).

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Fig. 4.2.3–3 a–e. Extended tonic pentachords.

The extension of a gapped pentachord to a gapped hexachord, or the extension of a shared pentachord to a shared hexachord (cf. Fig. 7.3–4 [op. 114:II:8–11]) are rare.

In the second group of the third class are short pentachords that are extended. In the music of Sibelius there are numerous extended tonic tetra-, as well as trichords. In an extended tetrachord, or extended trichord either a subtonic (C + D E F G; Fig. 4.2.3–4a, C + D E F; Fig. 4.2.3–4b) is added, or both a subtonic and a submediant are added (B C + D E F G; Fig. 4.2.3–4c; see Fig. 5.3.3–1 [op. 18:IV:1–5], B C + D E F; Fig. 4.2.3–4d).

Fig. 4.2.3–4 a–d. Extended short tonic pentachords.

In the fourth class there are complete extended pentachords where extensions are made by means of octave-doublings. In this fourth class the ambitus does reach the octave. A pentachord may be extended by adding octave-doubling of its dominant below it (Fig. 4.2.3–5a; see Fig 8.4–1 [op. 70:1–5]), or adding octave-doubling of its tonic above it (Fig. 4.2.3–5b).

Fig. 4.2.3–5 a–b. Complete tonic pentachords extended by octave-doublings.

The fifth class contains melodies where there are “seven tones within an octave” (as Sibelius put it in his audition lecture; see section 4.1.1). Since in these melodies the tonic pentachord still rules, they may be viewed as combinations of both ways of extension dealt with above. An authentic mode

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contains conjunctively a tonic pentachord and a dominant tetrachord (Fig. 4.2.3–6a), while a plagal mode conjunctively contains a dominant tetrachord and a tonic pentachord (Fig. 4.2.3–6b).

Fig. 4.2.3–6 a–b. Tonic pentachords extended to authentic and plagal modes.

Recognizing the tonic pentachord is helpful in defining any heptatonic mode in the music of Sibelius. The ambitus as such will not suffice. There is the possibility that an authentic scale (Fig. 4.2.3–7a) and e.g. a heptachord extended by the subtonic (Fig. 4.2.3–7b; cf. Fig. 8.2.1–1 [op. 39:I:108–111; the collateral line), or a hexachord extended by the subtonic and submediant (Fig. 4.2.3–7c) share the same ambitus.

Fig. 4.2.3–7 a–c. Extended tonic pentachords that fill up the same ambitus.

Melodies where an authentic or plagal scale is extended beyond the octave in one way or another are not separately classified (see Fig. 11.3.1–5 [op. 7:II:93–96]).