Density and Form in NoaNoa

Arlene Ducao | 14 May 2001

On a first look at Kaija Saariaho’s 1992 piece NoaNoa for solo flute and electronics, the form is not very apparent.

FLUTE ATTACK DENSITY

Of all of the graphical analyses produced for this paper, a graph of flute attack density (example 1) reveals the strongest sense of formal order. The overall shape of the graph is that of one and a half arcs: one arc from mm. 1 to 137, and a half-arc that starts high at m. 137 and descends to m. 175. Two high points (of 23-24 attacks) divide the graph into three major sections: mm. 1-60, mm. 61-136, and mm. 137-175. Section I (mm. 1-60) and Section II (mm. 61-136) are rough mirror images of each other. Both of these sections are bisected by secondary high points: in Section I, mm. 29 and 32 contain 14 attacks, and in Section II, m. 87 contains 17 attacks. Sections I and II are not exactly symmetrical, and Section II even has an additional set of fifteen measures (mm. 115-130) tacked to its end. In this added section, there are very few attacks.

Section III (mm. 137-175) is a little shorter than the first two sections and is the densest part of the piece in terms of flute attacks. Even in measures where there are few flute attacks, there are many vocal attacks. As a result, the last section is truly the most rhythmically active and makes an effective climax for NoaNoa.

The flute attack density graph shows that NoaNoa is full of continual attack contrast. There are no long periods of many attacks or few attacks per measure—instead, measures of many attacks (scales or oscillations between few notes) continually cut into passages of few attacks (sustained notes). Even the relatively homogeneous measures at the end of Section II (mm. 115-130) contain some attack variation in mm. 116, 117, and 124.

Example 1. Flute Attack Density in NoaNoa.

GESTURES OF SUSTAIN

Primary Gestures: NoaNoa opens with a 32^nd note C5 that leaps into a sustained E6. This haunting gesture is repeated (with the E6 glissing up to an F6). The short note followed by a sustained note is the most prominent gesture in NoaNoa. By delineating between formal sections and transitions, this gesture acts as an aural guide for the first-time listener to begin making sense of the piece.

The most significant occurrences of the short+sustained note gesture occur in mm. 1-2, 41-42, 61-63, 88-92, 111-113, and 141. Example 2 shows how these occurrences fall on or near attack density high points:

Measure #	Section	Relation to Attack Density Form
1-2	I	introduction of primary gesture; opening of Section I
41-42	I	occurs near secondary high point of Section I (mm. 32)
61-63	II	occurs at opening of Section II (m. 61)
88-92	II	occurs at secondary high point of Section II (m. 87)
111-113	II	occurs right before the added measures at the end of Section II (mm. 115-130)
141	III	occurs right after opening of Section III (m. 137)

Example 2. Occurrences of the Primary Sustained Gesture.

(As we will see in later sections of this discussion, significant events seem to fall around m. 60 and m. 137, so for convenience’s sake, I will continue to use these measures to delineate between sections. However, it is sometimes impossible for significant events to occur simultaneously. For instance, a sustained primary gesture cannot occur where a period of dense attack occurs. Consequently, sections are divided more by transitional periods than by individual measures. This will be discussed further when I examine the frequency spectra.)

The primary gestures within each section have common characteristics. In mm. 1-2 and 41-42 (Section I), the gestures are nearly identical; the only difference is the terminal articulations of the high E6.

Section II contains the next three occurrences of the primary gesture (mm. 61-63, 88-92, 111-13), and these are loud variations on the original C5-E6. In mm. 61-63, the gesture is dropped an octave and repeated twice—only the sustained notes are B4 and G-flat4 in the repetitions. This occurrence is made especially conspicuous since the flutist must vocalize on the sustained pitch and gliss up as high as possible. The gliss is emphasized by an infinite reverb. In mm. 88-92, the gesture is returned to its original register, but the short C5 is dropped. The gesture is repeated 4 times and is strongly emphasized by loud dynamics, tremolos, and crackling electronic sounds. Mm. 111-113 contains the gesture in its original register and with the short C5, but on each of its two repetitions, the sustained E6 inches up a half step.

Measure 141 is the only occurrence of the primary gesture in Section III. This occurrence is hardly noticeable since it has been dropped an octave and played at a relatively low dynamic (mezzo-forte decreasing to pianissimo).

Secondary Gestures: The primary gesture plays a less significant role in Section III so that two other sustained gestures can assume more prominence. Both of these gestures involve chords. One gesture (which we’ll call S1) is a chord that takes a note from all the registers that the flute uses in NoaNoa (G#4, F#5, D6, B-flat6).

The second gesture (S2) seems to be a synthesis of the original primary gesture and S1. It is similar to the original primary gesture in that it starts with a 32^nd C note. However, this C is in register 4, and the sustained note is actually a chord: C#5, F#5, and D6. This chord shares two notes with S1. The occurrences of S1 and S2 are charted in Example 3.

Measure #	Section	Gesture	Occurrence in Relation to the Primary Gesture
33	I	S1	7 mm. before
37	I	S1	4 mm. before
55	I	S1	5 mm. before
66	II	S2	3 mm. after
68	II	S2	5 mm. after
114	II	S1	1 m. after
135	II	S2	6 mm. before
156	III	S1	NA
163	III	S1	NA
169	III	S2	NA
172	III	S2	NA

Example 3. Occurrences of Secondary Sustained Gestures.

As shown in Example 3, occurrences of the secondary gestures are always near primary gestures in Section I and II. If there is a gap between primary and secondary gestures, it is filled by gestures of frequent attack. In Section III, the secondary gestures do not occur near primary gestures since there is only one primary gesture at the opening of Section III. By Section III, the secondary gestures have become the most prominent gestures of sustain. Rather than having gestures of frequent attack cut into longer periods of sustained gestures (as is the case in Sections I and II), Section III uses S1 and S2 to cut into periods of frequent attack. By the NoaNoa’s end, S2 has become so important that it concludes the piece.

Sustained-note gestures act as sectional markers, but at other points in NoaNoa, sustained notes in the flute allow the vocal and electronic lines to emerge. Saariaho always uses a sustained gesture to introduce a new element, whether it be vocal or electronic. For instance, at m. 22, the vocal line is introduced while a sustained note is held in the flute. The first occurrence of sampled sounds in the electronics coincides with the first occurrence of S1 (m. 33). Pre-recorded voice sounds and filtered sounds also first occur (in m. 46 and m. 119) with a sustained note in the flute. Saariaho eventually pairs all of these sounds with gestures of frequent attack, but only after introducing them with a gesture of sustain.

GESTURES OF FREQUENT ATTACK

As mentioned earlier, gestures of frequent attack serve to interrupt gestures of sustain in Sections I and II, but in Section III, gestures of frequent attack comprise most of the music. The flute attack density graph also shows that gestures of frequent attack begin as less dense and gradually become denser until the densest gesture at beginning of Section II (m. 60, which contains 24 attacks). The gestures then become more sparse until the end of Section II. At the beginning of Section III (m. 137), the density of the gestures spikes up and then thins out to the end.

There are two kinds of general gestures: those that outline a set of pitches, and those that are more scale-like. Both kinds of gestures occur within a single measure. The outlining gestures occur more frequently in Section I, and then gradually give way so that the scale-like gestures are the most common by Section III. Both kinds are gestures tend to ascend in steps or small intervals and descend in leaps or large intervals. This kind of intervallic motion, combined with the leaping motion of the C’s in the sustained gestures, creates an impression of continual ascension. Downward leaps seem more like registral transfers than actual changes in direction.

Outlining Gestures: The first outlining gesture arises as a mere extension of the primary gesture of sustain, but by adding differing pitches in differing registers, the outlining gestures soon develop apart from the sustain gestures. In doing this, NoaNoa’s outlining gestures contribute to a sort of pitch/register hierarchy by emphasizing certain pitches in certain registers. These pitches gradually alter through each section: Section I’s outlining gestures (O1,O2, O3, O4—see Example 4) emphasize the lower half of Octave 4, the lower third and upper third of Octave 5, and the lower half of Octave 6. Section II’s outlining gestures (O5, O6, O7) continue to use these pitches, but in addition, they fill in the middle third of Octave 5 and more of the lower half of Octave 6 (namely D6). The outlining gestures of Section III are a special case: instead of expanding that section’s pitch language beyond its gestures of sustain, O8 simply outlines the secondary sustain gesture S1. By acting as an extension to a sustain gesture, O8 is returning full circle to the function of O1. The occurrences of the outlining gestures are charted in Example 4.

Gesture # for ID purposes	Measure # altered pitch sets are in [ ]	Section #	Pitch Set Outlined grace notes are in ( )	Comments
O1	10, 13, 15, [39], [78],	I	F4, Gb4, C5, A5, D4, (Db5), E6	contains C5 and E6—extends the original primary gesture
O2	14, 16, 31, [32], 34, [79], [108]	I, II	E6, Db5, Bb5, A5	fills in the lower third and upper third of Octave 5
O3	17, 38, [45], [64], [72], [133]	I, II	D4, C#5, (A#5), A5	--
O4	43, [44]	I	E6, F6, C#6, G5, A#5, B5, D#6	fills in much of the upper part of Octave 5 and the lower part of Octave 6
O5	70	II	F4, (F#5)	--
O6	102	II	F#5, D6, A5, C#5, Bb5, D#5, E5, Eb6, B4, G5, Eb4, C#4	introduces D6 as a note in a gesture of frequent attack (before, this note only occurred in sustained chords)
O7	137	II/III	C4, D4, Eb4	ends Section II/ opens Section III by synthesizing notes to be used in an altered gesture of sustain? (m. 141)
O8	154, 155, 160, 161, 162, 167	III	G#4, F#5, G#5, D6	outlines S1

Example 4. Occurrences of Outlining Gestures.

Scale-like gestures: Scale-like gestures occur less frequently than outlining gestures, but they are usually quite noticeable because of the speed and dynamic at which they are performed. In Sections I and II, there is only one scale-like gesture, and it always occurs as a lead-in to a sustained note or chord; in Section III, scale-like gestures are combined with percussive vocal sounds to create several measures of rapid rhythmic activity.

Gesture #	Measure #	Section	Pitch Set	Comments
C1	29, [56], [68], [85-87],	I, II	C4, Db4, F4, G4, B4, C#5, D#5, E5, G5, A#5, B5, C#6, Eb6, F6	This gesture touches on many of the notes presented in the outlining gestures, but it fills in Octaves 5 and 6 a little more. C1 also avoids the use of C5 and E6—the notes used in the original primary gesture.
C2	143, 144, 145, [146]	III	Eb4, F4, G#4, C5, E5, F#5, G5, A5, B5, D5, C#5	This gesture is similar to C1, but it starts to condense, acting as a transition from C1 to C3.
C3	148, 149, 150, 151, 153	III	F4, G#4, A4, F5, F#5, G5, B5, C#6, D6	With the exception of a few neighbor notes, this gesture outlines S1.

Example 5. Occurrences of Scale-Like Gestures.

With their more limited presence, the scale-gestures perform some of the same pitch functions as the outlining gestures. In Sections I and II, they expand a pitch hierarchy by emphasizing pitches in certain registers. In Section III, the scale-like gesture condenses and then acts with O8 to outline the secondary gesture of sustain S1.

It is clear that all gestures undergo some kind of evolution over the course of NoaNoa. The primary gesture of sustain is varied throughout Sections I and II, but by Section III, it is laid to rest in favor of gestures S1 and S2. These secondary gestures appear sporadically throughout Sections I and II before they become the most prominent sustain gestures in Section III. In Sections I and II, the outlining gestures arise from the notes of the original primary gesture, then they become independent and help to form a pitch hierarchy. In Section III, the outlining gesture returns to outlining the notes of a sustain gesture. The scale-like gestures play a similar role: in Sections I and II, they expand NoaNoa’s pitch language, but by Section III, they are very closely related to the sustain gesture S1.

VOCAL ATTACK DENSITY

Like in the flute attack density graph, the vocal attack density graph (see Example 6) has two obvious high points (mm. 28 and 147). Unlike the flute graph, the vocal high points do not act to divide sections. Since the vocal line acts as counterpoint to the flute line, measures of frequent vocal attacks coincide with measures of few flute attacks. In mm. 28 and 147, the measures of densest vocal attack, the flute has only one attack in that same measure. Counterpoint is not the only reason that the flute has few attacks when the voice has many: the demands of simultaneously playing the flute and vocalizing necessitate that the flute cannot have too complex of a line!

Example 6. Vocal Attack Density in NoaNoa.

In Section I, the vocal line acts coincides with gestures of sustain. In

Section II, the vocal line coincides with gestures that gradually become more active. The exception to this is the last fifteen measures of Section II, where the vocal line occurs again in conjunction with sustained flute gestures. In Section III, the both the flute and vocal lines are extremely active—the last forty measures are the densest in both the flute and vocal graphs.

Like with the flute attack density graph, the vocal attack density graph shows that starting in m. 23, there is continual attack contrast, though it occurs in a slower pattern (at least in Sections I and II). Measures of many vocal attacks regularly cut into periods of few vocal attacks, though this interruption takes place less frequently than in the flute. As for Section III, the many/few attack juxtaposition pattern is about as rapid in the voice as it is in the flute, though the overall level of frequent attack measures is a little lower in the voice than in the flute.

The contrapuntal addition of the voice fills in some of the attack frequency gaps left by the flute. This does not mean that the voice fills in every gap or that that NoaNoa is full of constant attacks—there are still moments that contain sustained gestures only. However, the voice adds a softer quality to the attack levels in the piece: on one level, there is the flow of harder attacks from the flute, while on another level, there is a slower flow of softer attacks from the voice.

FREQUENCY SPECTROGRAM

NoaNoa’s frequency spectrogram (see Appendix A) divides up along the same lines as the flute attack density graph. For the most part, the spectrograph shows purer sounds (with upper partials only) or sounds with just the slightest bit of noise. Areas in the spectrograph with heavy noise bands—all of these areas coincide with prominent gestures of sustain. Areas of heavy noise are charted in Example 7.

Measure / approx. time	Section	Gesture/ Comments
30-32 / 1:10 (see Spectrog. pg. 3)	I	variant on original primary gesture of sustain
59-64 / 2:30-2:50 (see Spectrog. pg. 6)	I/II	-sustained F4 (with overblown harmonics) -scale-like gestures of sustain -variation on primary gesture (with voice glisses)
88-93/ 3:55- 4:10 (see Spectrog. pg. 9)	II	variation on primary gesture of sustain (with pre-recorded voice in the electronics)
99-103/ 4:32-4:44 (see Spectrog. pg. 10)	II	agitated outlining gesture (with sampled flute in the electronics). The electronic sounds are contributing a great deal to the slight noise.
119-120/ 5:29-5:39 (see Spectrog. pg. 12)	II	high sustained notes—part of “tail” to Section II (with pre-recorded, filtered sounds in electronics). The electronic sounds are contributing a great deal to the noise.
137-146/ 6:37-6:55 (see Spectrog. pg. 14)	II/III	-outlining gestures -final variation on original primary of sustain -string of vocal consonants -agitated scale-like gestures -(with pre-recorded, filtered sounds in electronics). The electronic sounds are contributing a great deal to the noise.

Example 7. Occurrences of heavy noise bands in the spectrogram.

As shown in Example 7, major sectional divides (~ m. 60-63, m. 137-142) are areas of heavy noise. Some of the subsectional divides (~ m. 30, ~ m. 88-93) are also areas of heavy noise. One of the remaining areas of heavy noise (mm. 119-120) are agitated gestures of sustain, while the remaining area of noise (99-103, the noise is not as heavy as in other areas) is an outlining gesture where the vocal line first turns entirely into strings of consonants.

In highlighting major sectional and subsectional divides, the spectrogram adds an additional level of support to the plan first laid out by the flute attack density graph and then supported by the gestural map. The spectrogram also emphasizes other significant events, including the part where the vocal line transforms itself from actual words to strings of consonants.

PITCH

A pitch graph (Example 8) does not reveal as much of a formal structure as other graphs previously examined. However, the pitch graph does reveal some important formal points.

In Sections I and II, areas where pitch is spread out over several registers seem to alternate regularly with areas where pitch is constrained to one octave, usually Octave 4. This alternation is observed in Example 8 and charted in Example 9.

Measures of pitch spread	Section	Measures of pitch constraint
1-21	I	22-28 (Octave 4)
29-45	I	46-53 (Octave 4)
54-70	I/II	71-76 (Octave 4)
77-87	II	88-92 (Octave 6)
94-124	II	124-131 (Octave 4)
132-136	II	137-141 (Octave 4)

Example 9. Alternating levels of pitch spread/constraint.

The alternation of pitch spread and constraint seems to reflect the continual alternation of opposing techniques that has been so prevalent in this discussion of NoaNoa. Flute and vocal attack density, flute gesture, pitch, and as we will see later, vocal gesture—all of these aspects carry patterns of continual opposition and evolution.

In addition, like with gestural elements in the flute and voice, pitch reaches a kind of stasis in Section III. As discussed earlier, gestures of frequent attack served to create a kind of pitch hierarchy, but by Section III, pitches are so stratified that each register has a set of pitches that are nearly locked into place. These pitches change over the course of Section III—some are added, some are dropped—but there is a high level of stratification nevertheless. This stratification is charted in Example 10.

Measures	Locked pitches in Octave 4*	Locked pitches in Octave 5*	Locked pitches in Octave 6*
137-152	D4, D#4, F4, G#4, A4 (E4, F#4, G4)	C5, F#5, G#5, B5 (E5, F5, A5)	C#6, D6
154-167	F#4, G4 (F4)	F#5 (D5)	D6, Bb6
168-175	C4	C#5, F#5	D6

Example 10. Stratified pitches in Section III.

*pitches in ( ) are infrequently used, like neighbor notes

The reason that the pitch seems to reach a level of stasis is because opposing flute gestures—that of sustain versus that of frequent attack—converge on each other in this section. In this section, they outline the same set of pitches, so the pitches do not change.

ELECTRONICS

The electronics of NoaNoa uses much reverb. It

TEXT AND VOCAL GESTURES

The vocal line was added for its ability to be both percussive and breathy. Clearly, the voice is not meant to convey textual meaning, for the flute never stops completely and allows the voice to make a straightforward reading. In addition, the text is a series of fragmented words and consonants that all tie to the piece’s subtitle (“Fragrant”), but Saariaho’s text choices still seem like they were selected more for the way they sound than what they mean.

There are three ways that the voice is used: to impart actual words, to impart hard consonant sounds, and to act as a pitched continuation of the flute sound. In Section I, the voice is used to convey two series of actual words (mm. 22-28, mm. 48-53), and hard consonant flutters are used as accents (m. 28). In the transition from Section I to Section II (mm. 61-63), the voice takes its most prominent role in the piece: it continues the sustained flute pitches (E4, B4, G4) and loudly glisses them into the stratosphere.

Like in Section I, the vocal lines of Section II begins start with strings of actual words that are accented by consonant sounds (mm. 71-74). There is also an inconspicuous moment where the voice sings at the pitch of the flute (m. 77). In mm. 94-109, consonant sounds appear more frequently alongside the actual words, preparing us for Section III. But like with other performance aspects already discussed, the last fifteen measures of Section II are a break from the vocal flow of the piece. This section marks a return to sustained, actual words, though it is interesting to note that sometimes there is only one note value for more than one syllable. On the tape, the flutist seems to be whispering these words as softly as possible so that sometimes it is impossible to hear the last syllables.

Section III marks a return to the flowing, percussive direction that the music had been taking. The vocal sounds are almost exclusively hard consonant strings that arrive at the beginning of a scale-like gesture or in the gaps between flute gestures. The only actual words in this section come at the piece’s conclusion, when the flute returns to a gesture of sustain (S2).

Though vocal sounds fall in the flute gaps where there are few or no attacks, the way that the vocal sound is produced tends to follow the flute gesture that is being used. When a gesture of sustain is being used in the flute, the vocal sound is an actual word or a sung pitch. When a gesture of frequent attack is being used in the flute, the vocal sound is a percussive consonant sound.

CONCLUSION

An examination of attack density, gestures, spectrogram, pitch and electronics show that NoaNoa is built on an evolutionary form that still manages to maintain more traditional elements of repetition.

In her inscription, Saariaho says that she is interested in first juxtaposing then superimposing several elements.

Mention: articulation, meter