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Thomas Nicholson

MOTTE (2017)

0

NOTES

Standard Tuning Required Tuning

Pitch Class

(written)

e.g. ET-12 Freq. (Hz)

Harmonic Ratio (from A)

Cent Deviation from ET-12

e.g. Resultant Freq. (Hz)

A 220.000 1:1 0 220.000

A#/Bb 233.082 16:15 +12 234.667

B 246.942 13:12 -61 238.333

C 261.626 7:6 -33 256.667

C#/Db 277.183 5:4 -14 275.000

D 293.665 4:3 -2 293.333

D#/Eb 311.127 11:8 -49 302.500

E 329.628 3:2 +2 330.000

F 349.228 8:5 +14 352.000

F#/Gb 369.994 13:8 -59 357.500

G 391.995 7:4 -31 385.000

G#/Ab 415.305 11:6 -51 403.334

An informal introduction to the Helmholtz-Ellis Accidentals

by Marc Sabat

Berlin, April 2009

In learning to read HE accidentals, without having to rely on an electronic tuning device, it is important to be familiar with three things:

First, to keep in mind the natural tuning of intervals in a harmonic series, which deviate from the tempered system.

Second, to get to know how the accidentals refer to these overtone

relationships.

Third, to observe that each written pitch may be related to many other pitches by natural intervals, and to tune it accordingly.

In most cases, this approach will allow the player to quickly and intuitively play just intonation (JI) pitches quite accurately. Any remaining adjustments can be

made by ear, based on the specific sound of JI intervals.

Just intervals are readily learned because they are built up from simple, tuneable harmonic relationships. These are generally based on eliminating

beating between common partials, finding common fundamentals and audible combination tones, and establishing a resonant, stable sonority which

maximizes clarity: both of consonance and of dissonance. A well-focussed JI sound is completely distinct from the irregular, fuzzy beating

of tempered sounds. Just consonances, when marginally out of tune, beat slowly and sweetly and may be corrected with the most subtle adjustments of

bowing or breath. Just dissonances produce a sharply pulsing regular rhythm and have very clear, distinct colors.

To become familiar with the notation and sounds of JI, the fundamental

building blocks are prime number overtones 3, 5, 7, 11 and 13, each of which is associated with a specific pair of accidentals and a basic musical interval.

3 is associated with the signs flat, natural, sharp and refers to the series of untempered perfect fifths (Pythagorean intonation). Generally, A is taken as the

tuning reference, and the central pitches C-G-D-A-E can be imagined as the normal tuning of the orchestral string instruments. The just C is rather lower

than tempered tuning because of the pure fifths. The further this series is extended, the greater the deviation from tempered tuning: the flats are lower,

the sharps higher.

5 is associated with arrows attached to the flat, natural, sharp signs and refers

to the pure major third. These arrows correct the Pythagorean intervals by a Syntonic Comma, which is approximately 1/9 of a wholetone or 22 cents. So,

for example, the note E-flat arrow-up is a just major third below G, and the note F-sharp arrow-down is a major third above D. In most music, flats are often

raised by a comma and sharps are lowered. Because of the open string tuning, it is common to sometimes raise F and C (to match A and E) and to sometimes

lower A and E (to match F and C). Corrections by one Syntonic Comma have been used throughout Western music history and are relatively familiar to the ear. However, traditionally these corrections have been hidden by players, for

example in Meantone Temperament where fifths are mistuned narrow by ! comma so that the third C-E ends up sounding pure. More recently, the

currently prevailing Equal Temperament has made us accustomed to beating thirds, so at first the pure intervals may seem unfamiliar. To play the arrows

accurately, one must carefully learn the sound of the consonant major and minor thirds and sixths, and learn to articulate comma differences clearly.

7 is associated with a Tartini sign resembling the numeral. It corrects the

Pythagorean intervals by a Septimal Comma, which is approximately 1/7 of a wholetone or 27 cents. When the Pythagorean minor third is lowered by this amount, it becomes a noticeably low third often heard in Blues music.

11 is associated with the quartertone signs (cross and backwards flat). The

accidental is used to raise the perfect fourth by 53 cents, producing the exact tuning of the 11th partial in a harmonic series. The sound is most easily

learned by playing one octave plus one fourth and raising it by a quartertone.

13 is associated with the thirdtone signs (cross and backwards flat, each with 2 verticals). The accidental is used to lower the Pythagorean major sixth by 65 cents, producing the exact tuning of the 13th partial in a harmonic series. The

sound is most easily learned as a neutral-sounding sixth, one-third of the way between the just minor and just major sixths (closer to minor than to major).

The following table presents the accidentals together with their associated

ratios and cents deviations. To calculate the cents deviation from Equal Temperament of a specific written pitch (if desired) the following shortcut may

be used: 1.) Find the cents deviation of the Pythagorean pitch, by calculating how many

fifths it is away from A, multiplying by 2, and using a plus sign if it is on the sharp side and a minus if it is on the flat side.

2.) For each microtonal accidental, add or subtract its approximate cents value

(as given above), keeping in mind whether the accidental is raising or lowering the pitch.

The resulting value should be a cents deviation within 1 or 2 cents accuracy,

which is an acceptable starting point for fine-tuning by ear.

A C C I D E N T A L S EXTENDED HELMHOLTZ-ELLIS JI PITCH NOTATION f o r J u s t I n t o n a t i o n d e s i g n e d b y M a r c S a b a t a n d W o l f g a n g v o n S c h w e i n i t z The exa ct intonatio n of each pit ch m ay b e writt en o ut b y means o f the fo llo wing ha rmonically- de fined signs:

E e n v V Pythagorean series of fifths – the open strings ( … c g d a e … )

dmuU Ffow lowers / raises by a syntonic comma 81 : 80 = ci rca 21.5 cent s

cltT Ggpx lowers / raises by two syntonic commas circa 43 cent s

< > lowers / raises by a septimal comma 64 : 63 = ci rca 27.3 cent s

• ¶ lowers / raises by two septimal commas circa 54 .5 cents

4 5 raises / lowers by an 11-limit undecimal quarter-tone 33 : 32 = ci rca 53.3 cent s

0 9 lowers / raises by a 13-limit tridecimal third-tone 27 : 26 = ci rca 65.3 cent s

: ; lowers / raises by a 17-limit schisma 256 : 255 = ci rca 6 .8 cent s

/ \ raises / lowerss by a 19-limit schisma 513 : 512 = ci rca 3 .4 cent s

! ±" raises / lowers by a 23-limit comma 736 : 729 = ci rca 16 .5 cents

In addition to the harmonic definition of a pitch by means of its accidentals, it is also possible to indicate its absolute pitch-height as a cents-deviation from the respectively indicated chromatic pitch in the 12-tone system of Equal Temperament. The attached arrows for alteration by a syntonic comma are transcriptions of the notation that Hermann von Helmholtz used in his book “Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik” (1863). The annotated English translation “On the Sensations of Tone as a Physiological Basis for the Theory of Music” (1875/1885) is by Alexander J. Ellis, who refined the definition of pitch within the 12-tone system of Equal Temperament by introducing a division of the octave into 1200 cents. The sign for a septimal comma was devised by Giuseppe Tartini (1692-1770) – the composer, violinist and researcher who first studied the production of difference tones by means of double stops.

V O R Z E I C H E N EXTENDED HELMHOLTZ-ELLIS JI PITCH NOTATION f ü r d i e n a t ü r l i c h e S t i m m u n g k o n z i p i e r t v o n M a r c S a b a t u n d W o l f g a n g v o n S c h w e i n i t z Die Stimmung jedes Tons is t m it fo lgenden ha rm onisch definier ten Vo rzei chen a usnoti er t :

E e n v V Pythagoreische Quintenreihe der leeren Streicher-Saiten ( … c g d a e … )

dmuU Ffow Erniedrigung / Erhöhung um ein Syntonisches Terzkomma 81 : 80 = ci rca 21.5 cent s

cltT Ggpx Erniedrigung / Erhöhung um zwei Syntonische Terzkommas circa 43 cent s

< > Erniedrigung / Erhöhung um ein Septimenkomma 64 : 63 = ci rca 27.3 cent s

• ¶ Erniedrigung / Erhöhung um zwei Septimenkommas circa 54 .5 cents

4 5 Erhöhung / Erniedrigung um den undezimalen Viertelton der 11er-Relation 33 : 32 = ci rca 53.3 cent s

0 9 Erniedrigung / Erhöhung um den tridezimalen Drittelton der 13er-Relation 27 : 26 = ci rca 65.3 cent s

: ; Erniedrigung / Erhöhung um ein Siebzehner-Schisma 256 : 255 = ci rca 6 .8 cent s

/ \ Erhöhung / Erniedrigung um ein Neunzehner-Schisma 513 : 512 = ci rca 3 .4 cent s

! ±" Erhöhung / Erniedrigung um ein Dreiundzwanziger-Komma 736 : 729 = ci rca 16 .5 cents

Zusätzlich zu der harmonischen Definition der Tonhöhe durch das Vorzeichen für jeden Ton ist auch der Cents-Wert der Abweichung der gewünschten Stimmung von der Tonhöhe des jeweils bezeichneten chromatischen Tons der gleichstufig temperierten Zwölfton-Skala angegeben. Die attachierten Pfeile für die Alteration um ein Syntonisches Terzkomma sind eine bloße Transkription der Notation, die Hermann von Helmholtz in seinem Buch “Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik” (1863) verwendet hat. Die kommentierte englische Übersetzung “On the Sensations of Tone as a Physiological Basis for the Theory of Music” (1875/1885) stammt von Alexander J. Ellis, der auch eine enorme Verfeinerung der Tonhöhendefinition innerhalb des Zwölftonsystems der gleichstufig temperierten Stimmung durch die Unterteilung der Oktave in 1200 Cents eingeführt hat. – Das Vorzeichen für die Alteration um ein Septimenkomma wurde von Giuseppe Tartini (1692-1770) erfunden, der als Komponist, Geiger und Wissenschaftler die durch Doppelgriffe erzeugten Differenztöne untersucht hat.

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-51

5

-2

-6

-18

m

3

-53

?

-2

3

+51

4m

-18

3

&

-4

sfppp

-37

<

sfppp

&∑ ∑ ∑ ∑

&

pp

3

°

°

?∑ ∑ ∑ ∑

&

-6

pizz. s.p.

mp

-4

sfppp

arco sempre s.p.

<

7°/IV

-35

5°/IV

-20

m

-18

-2

5°/III

3°/IV

m

5

B

-6

pizz. s.p.

mp

-4

sfppp

arco

s.p.

III

poco s.t.

-18

(II)

m

Ó

˙ œ

œ ™ œ ™ œn

j

˙ œB œn œ

Œ ‰

œ

j

œ œB ™œn

œn ™ œ

J

œn œ œB ™ Œ

Ó Œ

˙n ˙ œ œ œn w ˙ ™

Œ

wn w w

Œ ‰ œn

j

œ

˙n œ

j

œ# ™

Ó Ó œn

œn

Ó Œ ‰ œn

J

Ó ‰

œn ™ w œ

j ‚ ™ ‚

j

‚ ‚

n

Ó Œ ‰

œn

J‰

œn ™ ˙ w

Ó Œ

œ

23

ù

û

ù

û

{

103

™™

™™

™™

™™

™™

™™

™™

™™

™™

fl

sax

bsn

hn

tb

pno

vln

vla

&∑

+55

4f

pp

-2

o

+16

&

+12

f

pp

-16

<f

-4

+24

o

+55

4f

5

-17

<f

3

?

+12

f

sfpp

+24

o

&

?

+16

o

pp

3

&∑ ∑ ∑ ∑

&

ppp

5

3

°

.

?

pp

3

5

3

.

&

norm.

pp

II

III

5

+14

o o

B ∑

+18

o

pizz. (norm.)

p

+25

g

+14

o<f

-17

poco

0

-46

o

+16

o

-71

o

s.p.

5

œ ™j

œ œn œ

j

œ ™ w w

Œ ‰ œ

J

˙ œ œ œn œ œ œ ˙ ˙ w

Ó Œœ ˙ ™ œ ™

œ w w

œ

j‰ Œ Ó Ó ‰ œ œ w w

œ

j

œ#

‰Ó

Ó

˙

˙n

n

Œ œn œn œb œn œn œn œb œ œb

Œ

Ó Œœb œ

j œn œÓ Œ

œn œn œb œn œb œbœn œ œb Œ

Ó ˙n

Œ

w

‰œn ˙

wwn

œœ

j

œœn™™

˙˙

w

œ œ œ œ œ œ œB Œ

24

ù

û

ù

û

{

™™

™™

™™

™™

™™

™™

™™

™™

™™

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P

107

fl

sax

bsn

hn

tb

pno

vln

vla

&4

+67

o

ppp

+2

o

+14

5

+18

o

flutter. norm.

5

&∑

+16

o

ppp

flutter.

sf

?∑

+2

ppp

growl

sf

?∑ ∑ ∑

&

&∑ ∑ ∑

&

3 3

?3

°

&o

+16

(beating!)

ppp

III

s.p.

3

sf

[

+18

o

at the tip, s.t.

II

(III)

play second time only >

ppp sempre

-

poco marcato

o

-

/

-

+16

fœo

-o

-

5

B

-8

4°/IV

ppp

- -

5

[

+2

at the tip, s.t.

I

(II)

play second time only >

ppp sempre

-

poco marcato

-

3

-

<f

-17

-

Œœ œ

j

œn œÓ Œ ‰

œ

j

˙

ææææ˙ œ

Œ

œ

ææææœ

j

‰ Œ

Ó Œ ‰

œn

J

˙ œ

J7

œ ™

œn

œn

œn

Ó˙n œ

˙nn

œnœn

J

Œ œb

œn

Ó œ œ

J

‰ Œœœn œœn œn œœn œœn

Œ

On On

Œ

œœnn

œœnn

œœ

J

œœnn

œœn

J

25

ù

û

ù

û

{

110

fl

sax

bsn

hn

tb

pno

vln

vla

&∑ ∑ ∑

&

ppp -22

m

p poco sf

growl norm.

o

?∑

-6

ppp

-49

-

<

-39

5

&o

+14

ppp sempre

[

+18

o

poco marcato

play second time only >

-

-8

-

-49

-

-24

m

-

5

-20

m

- -

-4

-

5

&∑ ∑ ∑

&∑ ∑ ∑

?∑ ∑ ∑

&u

-16

-

-17

<f

-

u

(s.t.)

-

3

/fœ

+16

o

+18

o

+14

o-- - -

-/fœ

-22

m

(III)

-

3

-8

m

(III)

(IV )

-

-4

m

-

m

-

3

-49

-

-22

m

-

-6

-24

m

-

3

m

s.p.

m

-10

m m

m

- - - -

B

+16

/fœ

+18

o

-16

u

+14

o

- - -

u<f

-17 -2

- - - - -

-6

sfppp

IV

at the frog, s.p.

-4

-22

m

at the tip

-

-8

m

-

-6

-

-4

-

5

wn œ

J ‰ Œ ˙

7

˙ ˙

Ó Œ œn ˙ ™ œBœb

w œ œ œnœB

œ œ ˙n ™ œn

œœn

œœn

œœn

œœ œn œœn œ

œn œœn œn œœœ

n œœn œœ

n œœB

n œœ

œn

œ

œn

œ

œB

œ

œb

œ

œ

œœ

œn œœn œœn œ

œn œ

œnn

œœn œ

œn œ

œ

n

n Œ

˙n ™ œ

j

œ

œ

n œ

œ

n

J

œ

œ

J

œœnn

œ

œ

n

n

J

26

ù

û

ù

û

{

113

Q

Q

fl

sax

bsn

hn

tb

pno

vln

vla

& m

-22

ppp

4

+45

-6

4

+45

&∑

[

m

-18

ppp sempre

poco marcato

play second time only

-

3

<

-37

-

-8

/

-

-2

-

3

m

-20

- u

-14

-

-6

-

3

m

-18

-

u

-

-37

<

-

3

?∑ ∑

-2

poco marcato

B

ppp sempre

-

-4

3

-

&

-

-2

- -

/

-8

- - -

5

-14

u

-<

-37

-

u

-

/

- -

5

&∑ ∑ ∑

&∑

[

ppp sempre non legato

poco marcato

play second time only >

-

- - - - -

-

7

- - - -- - -

7

?∑

[

senza P

-

- -- -

&

- -

7

- -- -

-

-

-

7

&-8

-4

-

-22

m

-

-20

m

(s.p.)

sfppp

-

3

] m

(ppp)

s.t.

play both times >

-

B

-6

-

sfppp

at the frog (s.p.)

]

(ppp)

s.t.

play both times >

3°/III

-2

Ó Œ ‰ œ

j

œœ ˙ œ

œn ˙ ™œ

Ó œ œb

œb œn œœ œn œ œ œb

Œ˙n

˙n

œ

j

œn‰ Ó

œn œn œb œn œn œ œb œœb œn

œœbn

œ

œ

b

nœœn#

œœnn œ

œbb

œœnn

œ

œn

œœbb

œ

œ

n

n

œ

œ

n

#

œ

œ

b

n œœbn œœn# œœnb

œœn#

œ

œ

n

n

œœn#

œœnn

œœbb

œœ#

n œœnn œ

œb

b œœnnœœ#

n œ

œ#

n

œ

œ

b

n œœbnœœ#n

œ

œn

n œ

œn

œ

œ

n ˙

˙

w

w

w

w

n

œ

œ

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œn

n œn

j

˙ w wn

Ó Œ ‰ ‚n

j

27

ù

û

ù

û

{

116

fl

sax

bsn

hn

tb

pno

vln

vla

&

+12

f

-20

m

& - 4

+45

-

-20

m

-

3

-4

-

+22

f

- 4

-

3

-8

-m

-

-6

-

3

-m

-18

-

3

-

]

play both times >

(ppp)

-37

<

B4

+45-

-4

-

-65

0

&

-6

-

]

5

(ppp)

?

-4

play both times >

-6

&∑ ∑ ∑

&

- - - -

--

-

7

- -

- ]

7

&

-- - - -

--

7

- --

7

]

&

s.t.

+45

4

poco s.p.

s.t.

B

s.t.

poco s.p.

s.t.

w ˙ œ

J ‰œ œ ˙ ™

œnœ œ

œn œœ œn œ

œn

œn ˙ ˙ Œ ‰ œb

J

œ ™ œn

J

˙ w œ

J ‰ ‰

œ

J

˙

œn

‰ Œ

˙n w œ

Œ

˙n

œœnn œœn#

œ

œ

n

bœœn#

œ

œ

#

n

œœbn œ

œn#

œœn# œ

œ

b

n œœn#∑

œœn

nœœn

n œœb

b œœn

b œ

œn

#œœnb

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n œœn#œœ#

n

w

w

œ

œ

˙

˙

n ™

w

w

w

~

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˙n ™

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w

~

28

ù

û

ù

û

{

119

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™™

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™™

™™

™™

™™

™™

™™

5x

1: q = 45

2: q = 56.25

3: q = 67.5

4: q = 78.75

5: q = 90

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™™

™™

™™

™™

™™

™™

™™

™™

fl

sax

bsn

hn

tb

pno

vln

vla

&

f

&

f

B

f

?

f

mute out

&∑ ∑ ∑

&

mf (beating!)

play both times >

>

3

∑ ∑

&∑ ∑ ∑

&

(-4)

s.p.

f

B

s.p.

f

«

-8

sempre più s.t.

f

w ˙Ó

w ˙ Ó

w ˙

Ó

w ˙

Ó

Óœn œ

J‰ Œ

w

wn

n ˙

˙Ó

w

~n

n ˙

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j ‰ Œ Ó

29

ù

û

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û

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R

R

122

fl

sax

bsn

hn

tb

pno

vln

vla

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-8

u

m

ram

f

>

+2

>

>

&

+45

4

«

slap

f

>

-20

m

«

>

m

«

>

B

-35

<

«

f

>+45

4

«>

4

«>

?∑

&

-22

m

f

senza sord. >

cuivré

>

3

-49

-6

mp

-18

m

-2

sffp

>

&∑ ∑ ∑ ∑

&

(cluster)

nn‚

secco

f

bb‚

mf

5

°

&∑ ∑ ∑

3

&

«

-6

f

s.t.

-22

m

«

2°/IV

norm.

-4

p

5°/III

(2°/IV )

-18

m

sffp3

B

«4°/IV

ff

norm.

>

5

-

f

o

-

p

-

3

3°/III

-2

sffp

2°/IV

-6

3

3

Ó Œ ‰™œ

1

R

Ó Œœ

1

n

n

R

≈ ‰ ‰œ

1

n

n

R

≈ Œ Ó

Ó Œ ‰™œ

rÓ Œ

œ

r ≈ ‰ ‰

œ

r ≈ Œ Ó

Ó Œ ‰™œ

R Ó Œ

œ

R ≈ ‰ ‰

œ

R ≈ Œ Ó

‰ œ œ œB ˙ œ ˙n œ œ

J

‰ Œ ‰

œn ™

Ó Œ ‰™r

Ó Œr≈ ‰ Ó œb œn œb ˙ ™ Œ

œnœn œn œ

Œ

œn

J

‰ Œ

œ

J Ó ÓOn ‚ O

On ™

Œ Œ

œn

‚n

≈ Œ Œ

‚n ‚n

j

j

‚n ‚

‚n O

Ó

~ On

30

ù

û

ù

û

{

126

™™

™™

™™

™™

™™

™™

™™

™™

™™

S

S

q. = q = 60

q. = q = 60

fl

sax

bsn

hn

tb

pno

vln

vla

&

-6

mf

flutter. to piccolo

∑ ∑ ∑

&4

«

ff

>

to contrabass clarinet

∑ ∑ ∑

B

-65

?0

«

ff

> to contrabassoon

∑ ∑ ∑

&

-20

?m

sffppp

norm.

1st time: sempre ppp

2nd time: ppp, follow dynamics

m

-

&∑ ∑ ∑ ∑

&n#‚

ff

∑ ∑ ∑

&

n?

#‚

∑ ∑ ∑

&m

mf

∑ ∑ ∑

B

mf

nn

f

-37

<

port.

1st time: sempre ppp

2nd time: ppp, follow dynamics

<

-

<

s.t.

-

˙n

ææææ˙

Ó Œœ

r≈ ‰

Ó Œ

œ

R ≈ ‰

Ó Œ œ w w w

Ó Œr≈ ‰

Ó Œ R ≈ ‰

‚‚

OO

n ™™

OO ‚

j

Jœn ™

œn ™œb ™

w

w

œ

œ

j

œ

œb

n ™

˙

˙

˙

˙

œ

œ

j

œ

œb

n ™

31

ù

û

ù

û

{

130

T

T

fl

sax

bsn

hn

tb

pno

vln

vla

&∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑

?∑ ∑ ∑ ∑ ∑

?m

5

m

-m

pp

-

&∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑

?∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑

1st time: sempre ppp

2nd time: pp, follow dynamics

-2

s.t.

IV

3

B<

s.p.

-

s.t.

<

s.p.

pp

-

w ˙

7

˙ ™ ˙ ™ œ w œ ˙ ™

Ó

œn ˙

w

w

˙

˙

œ

œ

j

œ

œb

n ™

w

w

˙

˙

œ

œ

œ

œb

n w

w

32

ù

û

ù

û

{

135

fl

sax

bsn

hn

tb

pno

vln

vla

&∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑

?∑ ∑ ∑ ∑ ∑

?m m m

p

m m m m

&∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑

?∑ ∑ ∑ ∑ ∑

&

+45

4

3s.p.

-65

0

4

s.t.

p

-0

4

-0

4

-

3

0

4

s.p.

-

3

B

s.t.

<

s.p.

-

s.t.

<

s.p.

p

-

<

s.t.

s.p.

-

5

s.t.

˙

7

˙ ˙ ˙ œ ˙ œ œ œ ˙

7

œ ™ œ ™ œ

˙ ˙ œœ

n ww

œœ

˙

˙

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œ

œ

˙

˙

˙

˙

˙

˙

œ

œ

˙

˙

w

w

œ

œ

œ

œb

n

j

˙

˙

w

w

w

w

˙

˙b

n ˙

˙b

n ™

33

ù

û

ù

û

{

140

™™

™™

™™

™™

™™

™™

™™

™™

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U

U

fl

sax

bsn

hn

tb

pno

vln

vla

&∑ ∑ ∑ ∑ ∑

&∑

contrabass clarinet

1st time: pp

2nd time: mp

?

mf f

?∑ ∑ ∑ ∑ ∑

?

?m

mp

m m

mf

m

f

&∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑

?∑ ∑ ∑ ∑ ∑

&

norm.

0

4

mp

-

3

0

poco s.t.

4

-

3

0

4

mf

-

3

0

4

f

-

3

B<

mp

norm.

-

<

poco s.t.

-

5

mf

<

-

<

f

-

5

Ó ˙n wn w ˙ ˙n

w œ ˙ œ w ˙ ™

7

œ

7

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7

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˙

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w

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˙

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˙

w

wb

n w

w

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n w

w

˙

˙

˙

˙b

n œ

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n w

w

34

ù

û

ù

û

{

145

fl

cbcl

cbsn

hn

tb

pno

vln

vla

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8

5

8

5

8

5

8

5

8

5

8

5

8

5

8

5

8

&∑ ∑ ∑ ∑

&

?

ff

>

?

contrabassoon

f

> > >

ff

> >

?m m

ff

m m m

fff

<

-37

-2

4

+45

&

>>

>

>

&∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑

?∑ ∑ ∑ ∑

&

0

4

-0

4

-

3

0

4

-

3

0

4

0

4

- -0

4

ff

0

4

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0

4

>

0

4

fff

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0

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-2

4

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3

3

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fff

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n

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>

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5

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7

˙

7

˙

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J

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4

8

4

8

4

8

4

8

4

8

4

8

5

16

5

16

5

16

5

16

5

16

5

16

5

16

5

16

5

16

4

8

4

8

4

8

4

8

4

8

4

8

4

8

4

8

4

8

&∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

B∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

&∑ ∑ ∑ ∑ ∑

ppp

sempre con P >

&

pppp

similepp

?

pp

-

ø ø ø

&∑ ∑ ∑ ∑ ∑

molto s.p.

fo

B ∑ ∑ ∑ ∑ ∑ ∑

<

-31

pizz.

mf

˙b œn œ

r

œn ™œn œ ˙n ˙b œn ™ œn ™

˙

˙n

b œ

œn

b œ

œ

r

˙

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b

n

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˙˙

b

nb

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b

nb

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b

nb

œ

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b

nb ™

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b

nb ™

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˙

˙n

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n

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nœb

j

œ

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r

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n

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r

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69

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{

289

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12

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B∑ ∑ ∑ ∑ ∑ ∑

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pp

∑ ∑

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pp

mp

..

. . .

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3

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.

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3

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û

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295

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?

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. .

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°

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°

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ô

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ô

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repeat ca. 25 sec.

growing level of swell

to mf over duration

repeat ca. 25 sec.

growing level of swell

to mf over duration

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repeat ca. 20 sec.

varying duration of rest

independently of the

other players

repeat ca. 20 sec.

varying duration of rest

independently of the

other players

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repeat ca. 15 sec.

gradually returning in

phase with conductor,

dimin. over duration

repeat ca. 15 sec.

gradually returning in

phase with conductor,

dimin. over duration

poco rall.

poco rall.

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sax

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vln

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4

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4

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4

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&

+4

o omf

o omp

o o

&0

-59o o

0

decresc. independently

of the other players

over duration

mfo o

∑ ∑

?

contrabassoon

o o

decresc. independently

of the other players

over duration

mfo o

to bassoon

&

+2

?

con sord. >

o o

?

decresc. independently

of the other players

over duration

mfo o

∑ ∑

&

pppp disappearing

decresc. independently

of the other players

>P

lift pedal slowly

∑ ∑

&

pppp disappearing

decresc. independently

of the other players

∑ ∑ ∑

?∑

lift pedal slowly

∑ ∑

&

*

o

+51

4

con sord. >

o o

o4

mfo o

o

mpo o

B

* Note: this is not a typical “overtone chord”: the violinist must take extra care to tune the C-natural as a 6/5

with the viola’s A.

-31

<

con sord. >

o o

<

mfo o

mpo o

po o

œn œ

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?∑ ∑ ∑ ∑

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?

ppp lontano, al fine

sempre con P al fine >

∑ ∑ ∑

&

-2

p semplice al fine

-20

m

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m

-42

l

-28

m m

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o

+16

ppp lontano, al fine

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w w w œ

j ‰

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long...

long...

fl

sax

bsn

hn

tb

pno

vln

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o

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+51

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>o

(9/7 > 5/4)

-6

B

-4

+12

f

+45

>of

+8

f

3

-4

3

-2

Fredericton, 07.2016

— Victoria, 03.2017

(Berlin, 11.2017)

wn

∑ Œ

œn w w w w w

Ó

wn w w

Ó

˙n w w

œb

Œ Œ

œn

Ó Ó Œ

œn

w ™ œ˙ œ œ ˙ œn ˙ ˙n œ ˙nn ™

™ œœ

j ‰ Œ Ó

˙n ˙n ˙ ˙˙ w ˙ ˙ wn ˙ ™ œ

œn

n w

w

81