"Of Resonance" for string quartet

Kirsten Soriano Broberg

OF RESONANCE

String quartet 9 minutes

Resonant Strands Program Note: The works of the Resonant Strands cycle instrumentation: piano, bowed piano and string quartet (34'). For Resonant Strands, the ensemble is treated as a hyper-instrument that explores how the piano and string instruments may function both as string and as percussion instruments. Throughout, the piano is prepared with bows made from fishing line. The bows are woven around strings for seven pitches that are structurally important to the work, which are all drawn from an overtone series based on a low C fundamental. The title Resonant Strands has a double meaning. The nylon fishing line woven through the piano strings are literally strands that produce resonance when used as bows. The cycle also focuses on resonance as a structural feature and each work begins with the pitch, or pitches, on which the previous ends: as if there is a thread woven through from beginning to end.

When all of the works are performed on the same concert, they are programmed in the following order: I) “emerge” for piano and bowed piano (5') II) “of resonance” for string quartet (9') III) “opening” for solo cello (5') IV) “increscent” for violin and piano (11') V) “cadence” for piano, bowed piano, and string quartet (4') All of the works, except “Cadence” may be extracted and performed as individual works.

Glossary Piano

&

· # ···

= Depress silently. Silently hold these keys down while playing lower notes on the piano to cause these pitches to sympathetically vibrate.

harmonic

&

(

?

·)

˙ ◊

·

)

˙ pizz.

&

?

(

= Harmonics. Lightly touch string inside piano on the node while simultaneously playing that key on the keyboard to produce the designated harmonic (in parathesis).

œ

= Pluck strings inside piano.

felt mallets

≤≤

≤≤

≤≤

≤ ≤≤≤≤ ≤≤≤≤

= Hammer on the strings with felt mallets to produce cushioned sound. Pitches should sound as ambiguous as possible.

Strings

&

subharmonics

˙. (˙ .)

˙

= Subharmonics. Apply pressure to string (upper note) to obtain resulting tone that sounds one octave lower than the open string. The result will likely be incredibly unstable (which is acceptable).

˙

( )

harmonic glissando

&

nIV·

= Harmonic glissando. Move finger from designated harmonic along string toward the bridge to obtain as many natural harmonics as possible.

n· .

col legno battuto

&

.

. . . . ..... = Battuto. Let the bow bounce on the string. If "col legno battuto," with the wood; if "half col legno battuto," with half wood and half hair; if "battuto," only with the hair of the bow.

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~

I nœ

II nœ

( )

& n· n· nœ

= Harmonics color trill. Trill between designated harmonics. The resultant pitches are indicated by small noteheads should the performer choose to use alternative fingerings to achieve the same effect. When only a harmonic notehead is indicated, the harmonic notehead, is in fact, also the desired resultant pitch.

bow travel (to fingertip)

nœ

& n n ·œ

1

bœ

& b· bœ

= Bow travel. While executing bowing, move bow along the fingerboard or toward the bridge as indicated. Toward where the fingers are positioned on the fingerboard if indicated "fingertip" or "ft.," toward the bridge if indicated "toward the bridge."

2 = Increasing bow pressure. The level of bow pressure is indicated by numbers, 1 being very little bow pressure resulting in a mildly noise-like tone and 3 being moderate bow pressure to produce a moderate noise-like tone (should not be as dramatic or jarring as a scratch tone). When the number zero appears, the overpressure ends.

Both Piano and Strings

&

#œ œœ œ #œ œ œ œ #œ œ bœ

#œ œ #œ # œ &

&

o

(ppppp)

#œ

œ

= Grace note figures. Play as fast, lightly, delicately and swiftly as possible.

= Grace note figures with three ligatures. Play with the same delicacy and swiftness as grace notes with one ligature, only three times faster.

= Invisible barlines, dotted barlines, solid barlines. Invisible barlines indicate a lack of meter and extraordinary rhythmic freedom and rubato, dotted barlines are somewhat less rubato, solid barlines indicate a presence of meter and ordinary rubato (left to the discretion of the performer). = Niente (nothing, silence). = Sentiment of dyamic. Even when physically impossible (i.e., while achieving overpressure or subharmonics which are naturally loud) play as close to the dynamic indicated within the parenthesis (in this case, as close to quintuple piano as possible, or with the sentiment of quintuple piano). = Dovetailing. When a vertical dotted drawn between two instruments playing the same pitch in the same register, dovetail these enunciations to line up or overlap as if one instrument's gesture is being passed to the other. = Transformational arrow. One sound or idea located to the left of the arrow should gradually and seemlessly become the sound or idea located to the right of the arrow.

for the JACK quartet

Of Resonance natural harmonic gliss.

n·

IV

Violin I

&

pp scordatura, string IV: g tuned down to f in Violin II

Violin II

n·

IV

&

Kirsten Broberg

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IV III n· n·

col legno battuto

arco

Ÿ~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~ IV III III III III IV n · (n · ) nœ nœ nœ #œ n · æ æ # n· n· n· æ n· n œ n œ· n · æ · IV œ

( )

. .....

pp

n·

pp

IV œ

n III œ

n n ·œ

( )

Ÿ~~~~~~ III III III III III III III III n· n· nœ nœ · n· nœ n· nœ n· nœ æ n· æ n n ·œ æn n ·œ æ n n ·œ n n ·œ æ n n ·œ nœ

col legno battuto III nœ

n·

.

.

arco III III nœ

. . . . .....

III

Violoncello

III nœ

B

n·

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I nœ

&

II nœ

n·

(n n œ· )

pp

1

2

3

III

pp

Ÿ~~~~~~~~~~~~~~~ Viola

IV œ

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III nœ

IV œ

III #œ

#· n œ

Ÿ~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~ IV nœ

III nœ

IV

III

n· n œ ) (n n ·œ ) ( n· n· nœ

nœ

III nœ

III nœ

( )

n· n·

Ÿ~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II nœ

n· nœ

pp

4

© Kirsten Broberg, 2007. All Rights Reserved.

I nœ

( n· )

II #œ

I #œ

# · n # œ·

( )

2 Of Resonance

IV œ

Vln. I

IV

IV œ

IV œ

Ÿ~~~~~~ IV III n· (n· )

œ

& n· æ n· æ n· n·

Ÿ~~~~~~~~~~~~~~~~~~~ IV IV III n · (n · ) n· arco

Vln. II

& ·œ

III nœ

Vla.

(·

III

III

Ÿ~~~~~~~ III III III III n · n œ n œ (n · ) æ n · n n ·œ

)

( )

n· n·

Ÿ~~~~~~~~~~

III nœ

III nœ

n · n n ·œ

pp

( )

Ÿ~~~~~~~~~~ III III nœ

nœ

n · n n ·œ

( )

IV #œ

III

n·

II nœ

I nœ

& n · æ n· nœ 5

#œ

.....

III nœ

Ÿ~~~~~~~~~~~~~ Ÿ~~~~~~~~~

III nœ

III nœ

III nœ

( )

n · n n ·œ

III

( )

n · n n ·œ

( ) ( )

#œ

I nœ

I #œ

# · n # œ·

( )

III nœ

( )

n· n·

II nœ

8

IV III

( ) n · ( n n ·œ ) n · (n n ·œ )

#œ

nœ

nœ

II

I #œ

# · n # œ·

( )

pp

7

III nœ

IV nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~

n · n n œ· 6

IV #œ

n # ·œ # ·

pp

Ÿ~~~~~~~~~~~

II #œ

n·

III nœ

n· B n · æn # ·œ # · n # ·œ n · n œ #œ

æ n·

Ÿ~~~~~~~~~~~~~ Ÿ~~~~~~~ Ÿ~~~~~~~ Ÿ~~~~~~~~

III nœ

IV nœ

III nœ

arco

half col legno battuto III n œ . ..... nœ .

Ÿ~~~~~~~~ Ÿ~~~~~~~~~

Ÿ~~~~~~~~~~~

Vlc.

. . .....

pp

Ÿ~~~~~~~~~~~

III nœ

Ÿ~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~ Ÿ~~~~~~~ IV III III IV IV nIV· (nIII· ) n · (n · ) n · nœ nœ

col legno battuto arco

9

( ) 10

3

Of Resonance

Vln. I

Ÿ~~~~~~~~~~~~ III IV n · (n · )

&

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III nœ

Vln. II

n III œ

& n · n n ·œ

( )

pp

Vla.

n·

IV

n·

IV nœ

IV

æ n·

battuto (crine)

. . . . .....

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IV III n œ (n · ) arco

n·

Ÿ~~~~~~~~~~~~~~~~~~~~~~~

III nœ

n n ·œ

III

(n · )

( )

III nœ

( )

( )

pp

nœ

&

III nœ

æ n· n·

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~ nIII œ nIII œ nIII œ nIII œ nIV· (n III· ) IVœ æ n n ·œ n · n · n ·œ n·

B

11

Ÿ~~~~~~ n · nIIIœ n·

III nœ

I Vlc.

nIV· n· æ IV nœ

III œ

( n· )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II nœ

n · n n œ·

pp 12

13

( ) 14

15

4

Of Resonance natural harmonic gliss.

Vln. I

Vln. II

n ·II

&

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I II III II n · n · (o) n · n ·o

( )

&

pp

B

I nœ

II nœ

n· n · nœ pp

Vlc.

( )

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Vla.

Ÿ~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I IV II III IV n ·o (n ·o ) nœ nœ n · ( n ·o ) n· n· II

( )

battuto I nœ .

.

n·

. . . . .....

arco Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

n Iœ

II

III nœ

n· n· (n œ )

n·

(n · )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II #œ

&

II #œ

( )

#· n· pp

16

III nœ

17

18

19

20

21

5

Of Resonance

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IV

Vln. I

Vln. II

&

&

nœ

IV

nœ

( )

n· n·

n · (n ·o III

II

)

Vlc.

B

&

22

IV

nœ

nœ

( )

n· n·

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I II II II n · n · III o (o ) n · (n · ) nIII· (n ·o )

n · n ·o II

I

( )

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Vla.

IV

I nœ

n·

II

(n

n ·œ )

III nœ

III nœ

n· (n· )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I nœ

n· n· (n œ

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#· n·

#· n·

II #œ

( )

II #œ

II #œ

( )

#· n· 23

II #œ

24

IV

)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II #œ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ III n · (n · )

II

II #œ

( )

25

26

27

6 Of Resonance

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Vln. I

IV nœ

&

IV nœ

( )

n· n·

pp

n· n· nœ · III nœ

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Vln. II

Vla.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ III IV III III nœ nœ n · (n · ) B n· n·

( )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Vlc.

I œ

& n·

pp

28

( )

II

II œ

nœ

(n œ· )

I

( ) nœ

n n œ· n · 29

30

( )

n· n·

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III nœ

IV IV nœ nœ

IV

III nœ

n · n n ·œ

&

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

( )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II I n · (n ·o )

natural harmonic gliss.

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ III IV III III nœ nœ n· ( n· ) n· n·

nIIIœ

( )

n·

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I œ

II œ

( )

n · n œ· 31

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II

nœ

I

nœ

( )

n n œ· n · 32

7

Of Resonance

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Vln. I

III IV n œ nœ

( )

& n n œ· ·

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

n · ( n ·o ) III

bow travel (to ft.)

Vln. II

III II œ nœ

( ) ·

B b·

III nœ

n · n n ·œ

& n n ·œ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Vla.

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III nœ

III nœ

II

( )

IV nœ

( )

n· n·

bow travel (from ft.)

III nœ

n · (n · )

b·

Vlc.

I œ

II œ

& n· n · œ

( )

33

I nœ

n n ·œ 34

III nœ

( ) ·

IV bœ

b b ·œ

I œ

II œ

( )

n · n œ· 35

1 I nœ

n n ·œ 36

II nœ

( )

n · n n ·œ

b b œ· 37

( )

bow travel (to ft.)

IV

b b ·œ bow travel (from ft.)

2

0 II

II

bœ

III nœ

bœ

·

overpressure gradually increasing

bow travel (from ft.)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

b·

( )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

n · (n · )

III œ

IV nœ

n· n·

IV IV nœ nœ

bow travel (to ft.)

bow travel (to ft.)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

( )

n n œ· ·

( )

III II œ nœ

IV nœ

III IV n œ nœ

n · n n ·œ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III

)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ III nœ

n n ·œ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~ IV

III II n · (n ·o

IV nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

nœ

n n œ· 38

8

Of Resonance

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~ III

Vln. I

nœ

&

n· nœ

n · (n · III

nœ

(· )

IV

)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III II n · (n ·o

III nœ

Vln. II

IV

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

& n·

II III n · (n ·o )

)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ n · (n · III

Vla.

B

&

II

)

n· n· IV

III

( )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~ I n ·II ( n ·o )

bow travel (to ft.)

IV nœ

n n ·œ

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

III nœ

n III œ

n · n n ·œ

Vlc.

&

39

bœ

b b œ· 40

bow travel (to ft.)

III nœ

IV

III

III

2

overpressure

( )

0

&

42

1

II

B

2

IV bœ

b b ·œ

bow travel (from ft.)

n III œ

n · n n ·œ

41

n· nœ

n · (n · )

n· (n· )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

?

III nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1

III nœ

bow travel (to ft.)

n· nœ

( )

overpressure bow travel (from ft.)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~ n · (n IV· ) III

II nœ

b n œ· 43

n·

II

( )

44

9

Of Resonance bow travel (to ft.)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~ III IV n · (n · )

IV nœ

Vln. I

Vln. II

& n n ·œ

&

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~ II nIII· n ·o

( )

III nœ

n n ·œ

bow travel bow travel (from ft.) (to ft.)

III nœ

III nœ

III nœ

n · n n ·œ

n n ·œ

( )

Vla.

b n œ·

IV

n·

natural harmonic gliss. ft.

nœ

n n ·œ

n n ·œ

bow travel (to ft.)

1

Vlc.

II bœ

& b· bœ 45

2

bow travel (to ft.)

0 II

nœ

n· nœ 46

2

nœ

n n ·œ

b n œ· 47

?

IV nœ

( )

n · n n ·œ

48

III nœ

&

III nœ

( )

n· n·

bow travel (to ft.)

3

IV nœ

IV

natural harmonic gliss.

Ÿ~~~~~~~~~~~~~~~ on the bridge

n n ·œ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I

nœ

bow travel (from ft.)

III nœ

overpressure overpressure

n·

IV

( )

II nœ

n n ·œ

n n ·œ

n· n·

0

IV nœ

b n ·œ

B n· nœ

III

overpressure

nIII œ

IV nœ

n n ·œ

harmonic gliss.

nœ

2

n n ·œ

IV nœ

on the bridge

bow travel (from ft.)

1

IV nœ

IV nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ natural

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

bow travel (to ft.)

bow travel (from ft.)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IV III n · (n · )

on the bridge natural harmonic gliss.

bow travel (to fingertip)

natural harmonic gliss.

III nœ

n·

on the bridge

natural harmonic gliss.

0 IV nœ

n n ·œ 49

nœ

n n ·œ

I nœ

n· nœ 50

nœ

n· nœ

10 Of Resonance natural harmonic glissando

Vln. I

n n ·œ

&

IV

natural harmonic glissando nIV œ

n· & n· n · b œ nœ

( )

natural harmonic glissando

nIV œ

Vla.

B n·

I nœ

Vlc.

& n n ·œ 51

moltissimo sul ponticello

IV nœ

Ÿ~~~~~~

Vln. II

white noise

IV nœ

n·

n ·o

n·

natural harmonic glissando

white noise

nœ

moltissimo sul ponticello

(nœ )

( nœ)

œ)

(

(moltissimo sul ponticello) IV

white noise

nœ

( nœ )

(n œ )

?

œ)

(

moltissimo sul ponticello

bow travel (to ft.)

IV nœ

IV

nœ

(nœ )

( nœ)

(

œ)

( nœ)

(nœ )

(n œ )

n n ·œ

white moltissimo noise sul ponticello

I

I

nœ 52

53

54

55

56

11 Of Resonance

Vln. I

&

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ nIII· ( n IV· )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (from ft.)

III IV III IV III n · (n · ) nœ n œ nœ n n ·œ n n œ· ·

Vln. II

nœ

(ppppp) bow travel (to ft.)

IV nœ

Vla.

B n n ·œ

nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

& n· bœ 57

nœ

( )

( )

nœ

bow travel (from ft.)

II nœ

( )

n n ·œ 58

III nœ

n III œ

n · n n ·œ

( )

?

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~

n IV œ

n n ·œ

bow travel (to ft.)

II nœ

&

nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~ III II n· n·

bow travel (from ft.)

I nœ

III IV

( )

subharmonics

? nœ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ n · (n · ) nIII· (n IV· )

bow travel

IV nœ

n· ( n· )

subharmonics

nœ

( n œ)

nœ

nœ

bow travel (from ft.)

II nœ

bow travel (to ft.)

II nœ

n n ·œ

n n ·œ

overpressure 1

o

?

œ 59

≥ (œ )

1

2

(œ ) pp

60

(œ )

61

62

0

12 Of Resonance

bow travel (to ft.)

III nœ

Vln. I

& n n ·œ

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ nIII· (n IV· )

arco bow travel (from ft.)

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ nIII· (n IV· ) arco

III nœ

n n ·œ

arco bow travel (to ft.)

Vln. II

Vla.

? (nœ )

&

nœ

B

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ III II n· n·

( )

II nœ

n n ·œ

pp

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ nIII· ( n II· )

Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ III II n · (n · )

pp

pp

arco

overpressure

? ≤ (œ ) 63

1

≥ (œ ) 64

2

≤ ≥ nœ nœ 65

3

≤ (œ )

66

1

≥ ≤ nœ nœ p

67

≥ nœ

0

≤ (œ ) 68