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Supplemental 1

Prepared 27 April 2005

Paul Coleman

1. AN INTRODUCTION TO THE MUSIC OF

SOFIA GUBAIDULINA

Fig. 1.1. Gubaidulina, Chaconnefor piano (1962), theme, mm. 1-8.

Fig. 1.2. Theme from BachsMusical Offering, with Gubaidulinas orchestration for theopening ofOffertorium.1

1 Sofia Gubaidulina, Offertorium(Deutsche Grammohon 427 336-2), 4.

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Supplemental 2

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2. DYNAMIC PROPORTION IN THE MUSIC OF

SOFIA GUBAIDULINA

Early Experiments in Dynamic Proport ion

Fig. 2.1. Gubaidulinas formal sketch of the twelfth movement ofPerception.2

(a) Gubaidulinas Sketch.3

(b) Categorized, showing horizontal and vertical consonantdissonant relationships.

Fig. 2.2. Additive-automorphological number sequences.

2 Vera Lukomsky, Hearing the Subconscious: Interview with Sofia Gubaidulina, Tempo 209 (July 1999), 29.3 Ibid., 28.

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Fig. 2.3. Gubaidulinas formal sketch of conflicting formal proportions 1:2 and 1:7.4

Fibonacciseries: 1 2 3 5 8 13 21 34 55 89 144 Lucasseries:+1 3 4 7 11 18 29 47 76 123 199

Evangelists series: 2 5 7 12 19 31 50 81 131 212 343

Fig. 2.4. The Evangelists series as result of summation of the Fibonacciand Lucasseries.

Fig. 2.5. Bachs Series, showing mirrored symmetry within digits.5

Fig. 2.6. Bach, Vor deinen Thron tret ich hiermit, Gubaidulinas sketch of formal proportions.6

4 Ibid., 28.5 Lukomsky, Sofia Gubaidulina: My Desire is always to Rebel, to Swim against the Stream! Perspectives of

New Music36/1 (winter 1998), 18.6 Ibid.

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Supplemental 4

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Light , Color , andAlleluja (1990)

(most intense) (least intense)

Yellow

[7:1]

Orange

[6:2]

Red

[5:3]

Green

[4:4]

Lt. Blue

[3:5]

Blue

[2:6]

Violet

[1:7]

Fig. 2.7a. Colors with light reflection-absorption ratios, arranged by descending intensity.7

Fig. 2.7b. Color schemes with ray absorption ratios and resulting linear proportions.

7 Data from Lukomsky, Sofia Gubaidulina: My Desire, 29.

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Supplemental 5

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StimmenVerstummen (1986)

I

Eternal

II

Earthly

III

Eternal

IV

Earthly

V

Eternal

VI

Earthly

VII

Eternal

VIII

Earthly Apocalypse

IXZeroCadenza for

conductor

X

Eternal

XI

Earthly

XII

Eternal

Fig. 2.8. StimmenVerstummen, Distribution of movements.8

I

1:38

II

2:06

III

0:56

IV

2:01

V

0:39

VI

4:25

VII

0:30

VIII

11:07

IX

0:56

X

1:39

XI

1:53

XII

6:11

Fig. 2.9. StimmenVerstummen, Lengths of movements from recorded performance.9

Fig. 2.10. StimmenVerstummen, first movement, tonal/register scheme.

8 Based on Vera Lukomskys table, Hearing the Subconscious, 31, ex. 5.9 Sofia Gubaidulina, StimmenVerstummen, Stufen(Chandos 9183).

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Fig. 2.11. StimmenVerstummen, movement IX, cadenza for conductor.

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Supplemental 7

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Fig. 2.11. (cont.)

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Supplemental 8

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Fig. 2.11. (cont.)

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Supplemental 9

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Fig. 2.12a. StimmenVerstummen, graphed using pulse-duration lengths.10

Fig. 2.12b. StimmenVerstummen, graphed using recorded performance lengths.11

10 Lower markings on graphs based on those found in Clive Pascoe, Golden Proportion in Musical Design,Ed.D. Diessertaition (University of Cincinnati, 1973).

11 Gubaidulina, StimmenVerstummen, Stufen(Chandos 9183).

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Supplemental 10

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Fig. 2.13. StimmenVerstummen, alternate graph (original marked tempo for XI).