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7/23/13 Shostakovich's String Quartets: Their Tonal Structure

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Between October 1950 and February 1951, Shostakovich composed his opus 87 asa tribute to Bach. Like Bach this work is a cycle of twenty-four preludes and fuguesfor piano, each piece being written in a different key. But he chose not to followBach's method for progressing from one key to the next, deciding instead on aslightly different arrangement. Shostakovitch also arranged the pieces in pairs but

now each couple consisted of a major and its relative minor (that minor scale withexactly the same notes as the major). The first two pieces were in C major and Aminor respectively; both of these scales have neither sharps nor flats. The third andfourth pieces were in G major and E minor, each of which has one sharp in its scale(it is actually C sharp). The two scales with two sharps were then employed for thefollowing two pieces and this system, of adding one sharp, was continued until thethirteenth piece in F sharp major; a scale with six sharps. The next prelude andfugue was in E flat minor which has six flats. From then on scales were employedwith flats but the number of flats was progressively decreased by one until the finaltwo pieces were reached. These, written in F major and D minor, have only one flat(it being B flat).

This arrangement is generated not by raising each tonic by a semitone, as Bach did,but by using the dominant (the fifth note in the rising scale) as the tonic for thenext scale. Doing this will generate a major scale with one sharp more than those inthe previous major scale, and then, after G flat major (which is equivalent to Fsharp major) has been reached it, will decrease by one the number of flats

incrementally. Finally Shostakovich, like Bach, placed the major scale before theminor.

This arrangement, is shown in Table 2. In this table the first column shows theorder of the piece Prelude and Fugues as it appears in the opus 87. Column 2 showsthe scale in which the work is written whilst the next column shows the number ofsharps or flats in that scale. Next comes an explanation how the next major scale isderived from its predecessor (remember the following minor scale is just the relativeone of the major) , whilst the final column explains the change that has occurred inthe scale from that of the previous pair. As can be seen Shostakovich's method ofarranging the works is jus t as methodical as that used by Bach, and although itmight at first sight appear rather miraculous it is based on elementary musicaltheory. The reason for giving such a detailed explanation of the tonal arrangementof the opus 87 will be understood when the scheme used in the fifteen stringquartets is analysed.

9 E major 4

10 E minor 1

11 F major 1

12 F minor 4

13 F sharp major 6

14 F sharp minor 3

15 G major 1

16 G minor 2

17 A flat major 4

18 G sharp minor 5

19 A major 3

20 A minor 0

21 B flat major 2

22 B flat minor 5

23 B major 5

24 B minor 2


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Table 2:Tonality Arrangement in Shostakovich's 24 Preludes and Fugues Op.87

No. Keyno. of

or Reason for choice of scale Notes in scale

1 C major 0 notes are all naturals

2 A minor 0

3 G major 1 G being the dominant of Cmajor

as in C major but leading note Fraised to F

4 E minor 1

5 D major 2 D being the dominant of Gmajor

as in G major but leading note Craised to C

6 B minor 2

7 A major 3 A being the dominant of Dmajor

as in D major but leading note Graised to G

8 F sharpminor

3

9 E major 4 E being the dominant of Amajor

as in A major but leading note Draised to D

10 C sharpminor

4

11 B major 5 B being the dominant of E

major

as in E major but leading note A

raised to A

12 G sharpminor

5

13 F sharpmajor

6 F sharp being the dominantof B major

as in B major but leading note Eraised to E

D sharpminor

6 notes identical to E flat minor(no.14)

C sharpmajor

7 notes identical to D flat major(no.15)

A sharpminor

7 notes identical to B flat minor(no.16)

C flatmajor

7 notes identical to B major(no.11)

A flatminor

7 notes identical to G sharp minor(no.12)

G flatmajor

6 notes identical to F sharp major(no.13)

14 E flatminor

6

15 D flatmajor

5 D flat being the dominant ofG flat major

as in G flat major but leadingnote lowered to C

16 B flatminor

5

17 A flatmajor

4 A flat being the dominant ofD flat major

as in D flat major but leading notelowered to G

18 F minor 4

19 E flatmajor 3

E flat being the dominant ofA flat major as in A flat major but leading notelowered to D

20 C minor 3

21 B flatmajor

2 B flat being the dominant ofE flat major

as in E flat major but leadingnote lowered to A

22 G minor 2

23 F major 1 F being the dominant of Bflat major

as in B flat major but leadingnote lowered to E

24 D minor 1

For the quartets Shostakovich appears to have selected a system similar to that


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used in the opus 87. As we have seen, in the cycle for piano the dominant note ofthe major scale was used to generate scales with an increasing number of sharpsand then a decreasing number of flats, each of which he then selected for acomposition. For the string quartets he used the submediant note in the scaleinstead of the dominant note for this purpose. The submediant is the sixth note inthe rising scale, and in any major scale the submediant note defines the tonic of themajor scale's relative minor, that is the minor scale which uses exactly the samenotes (naturals, sharps and flats) that the major uses. For example the scale of Cmajor has no flats or sharps and thus uses only the white notes on the pianokeyboard. The sixth note in this scale is A, and the scale of A minor (the relativeminor to C major) has exactly the same notes in its scale as C major (the differencebeing, of course, that the scale starts on A and is played as a minor!) Bygenerating scales using the submediant a cycle would contain pieces which first

contain an increasing number of flats and then a decreasing number of sharps as isshown in Table 3.

Table 3: Tonality arrangement using submediant ofprevious scale

BasicTonality

Number of sharps /flats

Submediant ofScale

C major 0 A

A minor 0 F

F major 1 D

D minor 1 B flat

B flat major 2 G

G minor 2 E flat

E flat major 3 C

C minor 3 A flat

A flat major 4 F

F minor 4 D flat

D flat major 5 B flat

B flat minor 5 G flat

G flat major 6 E flat

E flat minor 6 B

B major 5 G sharp

G sharpminor

5 E

E major 4 C sharp

C sharpminor

4 A

A major 3 F sharp

F sharpminor

3 D

D major 2 B

B minor 2 G

G major 1 E

E minor 1 C


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However Shostakovich then added cryptic complications into this scheme. Whetheror not this was his aim, the first complication disguises his plan for the tonality ofthe quartets. What he did was that instead of using the submediant note togenerate the next scale in an alternating succession of major and minor as is shownin Table 3, he first chose to use only major scales and only when they had beenused did he start to compose in the minor scale. This first modification is shown inTable 4. In that table the first three columns reproduce the scheme already shown intable 3, whilst the fifth shows his scheme of using the key of column 3 first as thetonic of a major scale before it is employed in the minor.

Table 4: Submediant tonality arrangement and Shostakovich's scheme for the Quartets

BasicTonality

Number ofsharps/ flats

Submediantof Scale

QuartetNumber

Shostakovich's basic tonalityscheme for the quartets

Q1 C major

C major 0 A Q2 A major

A minor 0 F Q3 F major

F major 1 D Q4 D major

D minor 1 B flat Q5 B flat major

B flatmajor

2 G Q6 G major

G minor 2 E flat Q7 E flat major

E flatmajor

3 C Q8 C minor (C major already used)

C minor 3 A flat Q9 A flat major

A flatmajor

4 F Q10 F minor (F major already used)

F minor 4 D flat Q11 D flat major (C sharp major)

D flatmajor

5 B flat Q12 B flat minor

B flatminor

5 G flat Q13 G flat major (F sharp major)

G flatmajor

6 E flat Q14 E flat minor (E flat major alreadyused)

E flatminor

6 B Q15 B major

B major 5 G sharp Q16 G sharp minor (A flat major alreadyused)

G sharpminor

5 E Q17 E major

E major 4 C sharp Q18 C sharp minor (C sharp majoralready used)

C sharpminor

4 A Q19 A minor

A major 3 F sharp Q20 F sharp minor

F sharpminor

3 D Q21 D minor

D major 2 B Q22 B minor

B minor 2 G Q23 G minor

G major 1 E Q24 E minor

E minor 1 C C major

But in 1960 he introduced a second complication when he wrote his seventh


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quartet. Table 5 compares the tonality scheme derived in the previous table withthose that he actually employed. As can be seen there is complete agreement up to,and including, quartet number six, but then two further modifications occur. Thetonality of F sharp minor instead of E flat major is suddenly used for quartet numberseven and then after correctly proceeding to C minor, E flat major follows instead ofA flat major.

Why this divergence? Both these alterations occur in the quartets dedicated to hiswives. As can be seen in Table 5 these modifications however cause only a transientdisturbance to the guiding scheme which Shostakovich seemed to have set himselfwhen he composed his first quartet in 1938. From the tenth to his final fifteenth

Table 5: Shostakovich's scheme for the Quartetsand the actual tonality used

Quartet Shostakovich'splanned tonalities

(Table 4, Column 5)Actual tonalities

Q1 C major C major

Q2 A major A major

Q3 F major F major

Q4 D major D major

Q5 B flat major B flat major

Q6 G major G major

Q7 E flat major F sharp minor

Q8 C minor C minor

Q9 A flat major E flat major

Q10 F minor A flat major

Q11 D flat major F minor

Q12 B flat minor D flat major

Q13 F sharp major B flat minor

Q14 E flat minor F sharp major

Q15 B major E flat minor

Q16 G sharp minor

Q17 E major

Q18 C sharp minor

Q19 A minor

Q20 F sharp minor

Q21 D minor

Q22 B minor

Q23 G minor

Q24 E minor

C major


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2004 - 2013 Stephen Harris

quartet he returned to, and faithfully followed, his original scheme. Howeverbecause of the modifications started in 1960 the tonality of these last six quartetswould, due to the insertion of the F sharp minor in quartet seven, always be onequartet in arrears compared to his original scheme. Can his deviation from his firstconcept be explained by certain tonalities associations with his first and third wives,or could it be more prosaic?

Ian Strachan1has proposed that the insertion of F sharp minor and the rotation ofE flat major and C minor were done so that quartet number nine would be written inE flat major and quartet number sixteen in B major. (By doing so Shostakovichwould ensure that his initials (DSCH) were used as the keys in quartets whosenumber are a perfect square (D major: quartet number four or 2 squared; S, in theGerman notation or E flat major in the English: quartet number nine or 3 squared; C

major: quartet number one or 1 squared; and H or B major in the English notationas quartet number sixteen, or 4 squared).

So it seems that Shostakovich, a tonal composer who delighted in keeping detailed

numerical records of football scores2, indulged in numerical as well as musicalciphers.

Footnotes:

[1]. Ian Strachan, 'Shostakovich's DSCH Signature in the String Quartets' DSCH Journal, 10, (Winter1998), 48-49.

[2]. Laurel E. Fay, Shostakovich: A Life(Oxford University Press, 2000), p.111.
http://www.quartets.de/articles/structure.html#twohttp://www.quartets.de/articles/structure.html#one

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