208472288 shostakovich s string quartets their tonal structure3

8/17/2019 208472288 Shostakovich s String Quartets Their Tonal Structure3

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

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their tonal structure

Shostakovich's string quartets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

In the introduction I alluded to the possibility of the quartets being a whole tonalwork. Elizabeth Wilson supplies the evidence for this. She recalls that when askedhow many quartets he intended to write, Shostako vich replied, twenty- four:

“Haven't you noticed that I never repeat a key? I'll write twenty-four quartets, so asto have a complete cycle” (Shostakovich: A Life Remembered, p 389).

If he intended to write twenty-four and never repeat a key then it is pertinent toenquire in which order he intended to compose them. As we shall see this, in thephraseology of the m ath em ati cia n, i s a no n-t rivi al q ues tion .

The seminal work for a complete tonal cycle is Bach's 'Das Wohltemperierte Klavier'.This consists of two collections, BWV 846 to 869 and BWV 870 to 893, eachcomposed of twenty-four preludes and fugues. In each collection Bach used the

same simple system, based on s emitones, to progress from one scale to the nextthroughout the cycles. He started with C major then selected, as the tonic for thenext s cale, the next note to the right on the keyboard thus placing flats beforenaturals, and naturals before sharps. Before proceeding to the next major scale hecomposed a piece in the same minor scale. This arrangement is shown in Table 1where the right-hand column shows the number of flats o r sharps in each of thescales. This system produces an "alphabetic" arrangement rather one than based onan orderly progression of flats o r sharps.

Table 1:The tonality arrangement in Bach's 'Das Wohl-temperierte Klavier'

No. key no. of ♯ or ♭

1 C major 0

2 C minor 3 ♭

3 C sharp major 5 ♭

4 C sharp minor 5 ♯

5 D major 2 ♯

6 D minor 1 ♭

7 E flat major 3 ♭

Shostakovich and his st ring quartets

The string quartets: ways to listen

The quartets and symphonies compared

The tonal structure of the cycle of quartets

Related articles

Socialist Realism and music

The Lad y Macbeth Affair

The genealogy of the string quartet

Appendices

Bibliography

Feedback

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Between October 1950 and February 1951, Shos takovich 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 cont inued 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 t he 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 of sharps 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 t he previous pair. As can be seen Shostakovich's method of arranging the works is jus t as methodical as that us ed 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. Key no. 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 d ominant 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 Emajor

as in E major but leading note Araised 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 do minant of G flat major

as in G flat major but leadingnote lowered to C

16 B flatminor

5 ♭

17 A flatmajor

4 ♭ A flat being the do minant of D 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 of A flat major as in A flat major but leading notelowered to D

20 C minor 3 ♭

21 B flatmajor

2 ♭ B flat being the do minant of E flat major

as in E flat major but leadingnote lowered to A

22 G minor 2 ♭

23 F major 1 ♭ F being the do minant of Bflat major

as in B flat major but leadingnote lowered to E

24 D minor 1 ♭

For the quartets Shostakovich appears t o 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 of the 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 st ring 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 f lats) 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 firstcontain an increasing number of flats and then a decreasing number of sharps as isshown in Table 3.

Table 3: Tonality arrangement using submediant of previous scale

BasicTonality

Number of sharps /flats

Submediant of Scale

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 d isguises his plan for the tonality of the 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 of A 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 himself when 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 Stephe n Harris

quartet he returned to, and faithfully followed, his original scheme. Howeverbecause of the modifications started in 1960 the tonality of t hese 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 Strachan 1 has proposed that the insertion of F sharp minor and the rotation of E 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 Shost akovichwould 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; Cmajor: 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 detailednumerical records of football scores 2 , 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.
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208472288 shostakovich s string quartets their tonal structure3

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