Numerical Associations

8/12/2019 Numerical Associations

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Prelude & Fugue & Postlude

Numerical Associations

for

Solo Cello

Joseph Buchheit


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Prelude & Fugue & PostludeNumerical Associations

for Solo Cello

Numerical Associations is a collection of three pieces for solo cello. They are aPrelude: 5ths by 3rds, a Fugue: 1 Less, and a Postlude: Odds and Squares. Eachpiece uses a numerical association as the basis for its composition. The performer doesnot need to know about the following in order to perform the piece.

The Prelude, 5ths by 3rds, uses a collection of three notes a fifth apart. Threegroupings of these collections, transposed by a major third, are used in all. The threethree-note collections are A-E-B, D!-A!-E!, and F-C-G. The melody uses only thesenotes, and is in 11-measure phrases. After completion of the phrase, the whole melody istransposed by a major third. The only constant, non-transposed element of the melody isopen C. This is because C is zero. The third statement of the melody cuts off where A-E-

B would be played, this is because

A-E-B is a collection from the prelude that is used as the first half of the subject of theFugue, 1 Less. The second half of the subject is an inversion of the F-C-G collection. Afugue for solo cello can be somewhat limiting, as opposed to a keyboard instrument orensemble of instruments, because most counterpoint is impossible with a soloinstrument. The subject had to be deliberately chosen as a melody that is recognizable,yet adaptable and interesting in the context of where the fugue goes musically.Including a countersubject with a defined set of pitches would have been very difficult,and probably would have made the fugue very mechanical and predictable. The phrase1 Less refers to the relationship between the tonic key and the leading tone key. Theleading tone key is one half step less than the tonic. The recurrence of this 1 Less key

serves as the countersubject.

The Postlude, Odds and Squares, is based off the association of odd and squarenumbers. The sum of N sequential odd numbers will equal N2, which, also, is equal tothe sum of N sequential integers and the N-1 sequential integers. An integercorresponds to one half step of pitch. C2 is equal to 0 in this piece. The pitches rise fromC as N sequential odd numbers, and fall as pitches that are !(N2) apart. For example, ifN = 3, the first sequence of pitches is [(C+1), (C+1+3), (C+1+3+5)], which corresponds tothe pitches [C#, E, A]. The second sequence of pitches are [C+3, C+3+3, C+3+3+3],which correspond to the pitches [D#, F#, A].Each section lasts 12 quarter note beats, and is divided by the ration of N:(N-1). Thesequence of N odd numbers sustain for (N/12) quarter note beats, and the sequenceof !(N2) pitches sustain for ((N-1)/12) quarter note beats.


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Performance Notes

Prelude

A little bit of space can be put between the low grace notes (open C and G strings) andthe high notes. This may just be the natural space that occurs because of the stringcrossing.At the end of the piece, take a short pause before going into the fugue. While the preludeand fugue are different entities, it should not be longer than 3 seconds between the endof the prelude and the beginning of the fugue.

Fugue

All fermatas should be held for at least 3 seconds, as they provide a small break in themiddle of the piece. All bowings and slurs are intentional. However, if the performer

can get the same effect using a different bowing or slurring, then the performer shoulddo what is best for his or her own performance.

[Feathered Beaming] :: Increase speed of notes and reducespeed of notes, respectively. In this piece, all feather-beamed notes last the duration ofone half note (m. 26, 27, 65).

:: Arpeggio. All arpeggios should be played from lowest pitch to highest. Thehighest pitch (or pitches, when notated) should be sustained as written.

:: Hammer-on. Player should strike string with left hand to produce the notated pitch.

o above a note :: Open Harmonic

sfz :: sforzando with an accent. Dig deep into the string to get a harsh sound, but not soharsh that it would be considered overpressure. sfz only applies for the note it is markedon; the following notes go back to the original dynamic.

sf :: sforzando without an accent. Play forte, but pay special attention to bring it out as asudden forte. Unlike the above sforzando, play following notes forte until dynamicchanges.

Postlude

All lines of music should be played in standard, top-to-bottom order. The physicallength of each line is no indication of note duration.Performer can hold quarter note rest with fermata at the end of a line for however longhe or she sees fit. However, all sound from the previous staff line should end before

beginning a new staff line, whether it is natural dying off of sound or the performerdamping the strings.


4/9

? 8 Solemn q. = 40

P J J j B

. pB4 J J . . .?F . J jp?8 .

F

J B F

B11 > J

pizz.

arco

P J J? j .

15

B J J .

. .P . J j ?p?19 # . F

J F 22 > j ?

pizz.

arco

P fAgitated

J J jF?25 . P j j U

PreludeJoseph Buchheit

(2013)

5ths by 3rds

atta

ca.

Copyright Joseph Buchheit 2013

All Rights Reserved


5/9

? 4 Slow, Somber q = 52

p

pizz.arco

pizz.arco

? j j r . R . p r . J R . B

B r . R . ?P j R .

r .J> J> F?

r .R> . J>

# J> - j> j> BP F

B j> R j # ?f P J> J> f F j> ?f

j> ? j> ? j>

Fugue

6

9

12

15

17

1 Less

2


6/9

J> J> ?F J p

? r>+ B > r>+ r>+ > . . ?F? . fjfl

cresc.

. > . . . U ?P

r > > > >pizz. arco

f> P

pizz.

. UL.V.p? + w L.V.

arco

p + w L.V. w

L.V. ww# arcop

wwF

p? j j

pizz.

arco

pizz.

pj B

pizz.

arco

arco

F pj - U?F g

# .#

P

19

21

23

25

27

31

37

1 Less

increase speed

decrease speed


7/9


8/9

? r> r> R> p r>

r> J U J Uarco

F? r # R r r> P

pizz. arco

F r> > > R J ,pizz.

? r r r

r

Barco

col legno

ord.simile

> R> J ?pizz.

ord.

? r r > > > F f

arco

col legno col legno

ord. ord.

r> r> r>

? R> , J> p

pizz.

j j )arco

P ) (harmonic)

J ). ( ). ?a tempo

P jU .$ ) ) # .. >F wPlay open harmonic on G string

and stopped F on C String.

57

59

61

63

65

68

n

1 Less

decrease speed


9/9

? j Uq = ca.80L.V.pizz.

F? warcop w w U

?wp w .

U? . P w

U? . jp

j U? F

5f

U?

f ?

P ?

> > > >>>> >> >

> > > > U? J . pI ?P

rit. . JIII U

Postlude

Odds and Squares

0

1

2

3

4

5

6

7

6

Documents

Numerical Associations