Segmenting the Labyrinth:
Sketch Studies and the Scala Enigmatica in the Finale of Luigi Nono’s Quando stanno morendo Diario Polacco N. 2 (1982)
I can’t utter too many warnings against overrating these
analyses, since after all they only lead to what I have
always been dead against: seeing how it is done;
whereas I have always helped people to see: what it is!
Patricia Hall once observed that musical sketches are most helpful for “highly defined theoretical systems.” She then went on to state that sketch material pertaining to music created within transitional (i.e. poorly defined) systems is likely to be ambiguous, telling us little more than what we may already have discovered in the finished score. With respect, I submit that the very idea of stable, “highly defined theoretical systems” somehow standing outside of the historical flux of musical thought is at once a figment of my colleague’s imagination and one of enduring myths of modern music theory. Be that as it may, Gianmario Borio has since turned Hall’s observation on its head. Referring to the study of new music composed during the latter half of the twentieth century, he wrote that philological research (i.e. sketch studies) should not be used to confirm analytical hypotheses formulated in advance, but rather it becomes the conditio sine qua non for the formulation of these hypotheses. In other words, when studying music for which appropriate analytical hypotheses have not yet been developed or remain underdeveloped, the careful examination of the composer’s surviving sketch material often provides the requisite criteria with which a plausible analytical hypothesis can be established.
To exemplify this point, the last 36 bars of the third and final movement (labelled Part III) of Luigi Nono’s Quando stanno morendo, Diario Polacco N. 2 for two sopranos, mezzo soprano, contralto, bass flute, violoncello and live electronics will be examined in some detail. The goal is to show how a study of the composer’s working documents can provide a framework, within which basic units of Nono’s compositional technique can be identified. By combining data obtained from a close reading of the published score and surviving sketch material with the information gained from what we know of the work’s context, the student of this music can more efficiently circumscribe what Allen Forte once called the “analytical object.” To accomplish this task we will scrutinize working documents Nono used to produce Quando stanno morendo, as well as the related work ¿Donde estas, hermano? Per ‘los Desaparecidos en Argentina’ for two sopranos, mezzo soprano and contralto (1982), and we will also examine aspects of the context within which these two works were written.
The Archivio Luigi Nono conserves a substantial collection of diverse documents pertaining to the composition of Quando stanno morendo. At present that collection contains 827 leaves of manuscript material. Of these, 420 leaves have been classified as sketches and drafts in the narrow sense of the term (i.e. documents containing work directly related to the compositional process). The rest of the collection is made up of a fair copy (47 leaves) and 360 leaves of various documents pertaining to pre-compositional stages and documents related to the first performance of the work. The size of the collection is typical of compositions written in the early 1980s and is representative of Nono’s compositional practice.
The four-voice a cappella Finale of Quando stanno morendo constitutes not only the chorale-like concluding section of Part III, but also functions as a coda for the entire work. This is not the first time Nono has turned to the unadorned human voice to complete a composition. His Epitaffio No. 3 Memento, Romance de la Guardia civil española (1952-53) for choir and orchestra ends in a similar manner. This early work sets a poem by Federico García Lorca in which the author presents a stunning confrontation between order and chaos, law and magic, power and lyricism, and authority and liberty. The work ends with unaccompanied choir singing the last four lines of García Lorca’s allusive text (bars 411- 442). The last 31 bars are the only section in which the vocal ensemble is presented a cappella and in which it actually sings (in the preceding sections the ensemble functions as a speaking choir), setting it off from the rest of the composition. The text is clearly meant to be understood as a concluding statement. Similar concluding sections for unaccompanied voices or voice can also be found in works such as Intolleranza (1960-61) and La fabbrica illuminata (1964).
Jeannie Guerrero has examined this aspect of Nono’s work and noted that the concluding function of these finales is not only a matter of content but also of form. She contrasts the multidimensional counterpoint and complex textures of Sarà dolce tacere (1960) with the retrograde canon at the end in which these dense structural procedures are clarified.
The multidimensional counterpoint thus reaches utter silence at the conclusion of Sarà dolce tacere. The ending serves as a structural cadence for the entire song and aptly reflects the work’s title, “It will be sweet silence.” Further the gradually aligning generator paths throughout the middle of the song indicate a large-scale progression toward the final cadence. The increasing contrapuntal alignment across four dimensions binds the entire work into an organic whole.
Compared to the ‘noisy’, agitated textures of the beginning and middle of Sarà dolce tacere, the retrograde canon at the end of the composition “performs the act of falling silent.” In Cori di Didone (1958), Guerrero notes that the duration-dynamics palindrome of the Finale brings the complex, chaotic textures of the work to rest. At the same time, this place of structural repose resonates strongly with the text’s emphasis on the “silence of dead seas.” In the following, we shall see that the homophonic textures of the a cappella Finale of Quando stanno morendo bring into focus certain structural aspects of the music of preceding sections, while at the same time presenting a concluding commentary on the work as a whole. For reasons that will become apparent in the course of the text, this article will focus on Parts II and III of Quando stanno morendo. In any case, an exhaustive analysis of the entire work would not be possible within the space provided here. 
Work and Context
Completed on 3 September 1982, Quando stanno morendo is the third of a series of four works conceived and written at the Experimental Studio of the Heinrich Strobel Foundation of the Südwestfunk at Freiburg im Breisgau between 1981 and 1983. It is one of the first in which Nono successfully integrated the real-time manipulation of sound using information technology developed specifically for this purpose at the Foundation. The innovative concepts, procedures and technologies developed at the Foundation would strongly mark Nono’s compositions written during his last decade from both a technical and an aesthetic point of view and constitutes one of the primary factors providing coherence to what has come to be known as the composer’s late work (1980-90). This being said, the music produced during this period is not merely about applying new technology to old compositional problems. Quando stanno morendo, first performed in Venice on 3 October 1982, has a rich history that is recounted in the composer’s dedication.
In October 1981 the organizers of the Warsaw Music Festival invited me to compose
Diario polacco No.2 which should have taken place this year.
Then came the 13th of December.I have had no news of the friends who invited me.
The organizers were dismissed, the Festival did not take place.
My desire to write this Diary became even stronger.
I dedicate it to my Polish friends and companions, who - in exile, in hiding, in prison, at
work - resist and hope even if they despair, believe even if they are incredulous.
The suppression of Solidarno by General Jaruzelski with the tacit support of the Soviet Union in December 1981 had a devastating impact on Nono. This can be clearly felt in the work’s libretto: a collage of fragments taken from poems by Czes_aw Mi_osz, Endre Ady, Aleksandr Blok, Velemir Khlebnikov and Boris Pasternak, selected and edited by Massimo Cacciari, who became one of Nono’s principal advisers during the last decade of his career. Part II (the second movement) is entirely based on a text by the Russian futurist poet, Velemir Khlebnikov (1885-1922). In their ‘Notes’ concerning the elocution of this text, the editors of the published score state: “The text requires enunciation that is free, not measured, serious and decisively articulated: an apostrophe sculpted to produce dramatic introspection rather than declamation.” The text is thus not only to be heard for its musical value but also for its semantic content. Its central section, translated in Italian, reads:
Mosca chi sei? Moscow – who are you?
Io so che voi siete I know that you are
lupi ortodossi. orthodox wolves.
Ma come mai, come mai non udite But how, how on earth don’t you hear
Il fruscìo dell’ago della sorte? the rustling of the needle of fate?
Figure 1: Transcription and English translation of lines 7 to 11 of the text of Part II
Khlebnikov’s words resonate well with the context in which they were written, i.e. the disintegrating regime of Tsar Nicolas II. That Nono and Cacciari should have chosen to use the work of this particular poet to make a statement on the repression of Solidarno__ speaks volumes on their attitude toward the Soviet regime under Leonid Brejnev.
Compositional History of the Finale
The compositional history of the Finale (Part III, bars 59-94) is complex and in some respects remains unclear to this day. In the following Plate we see an early typescript of the text fragments which established the ternary framework of Part III.
The word “ALBA” scrawled graffiti-like near the top of the page means “dawn” and can also refer to the age-old vocal genre otherwise known as ‘aube’ or ‘aubade’. Carola Nielinger-Vakil has pointed out that the term appears on numerous sketches from the late 1950s onwards and almost invariably refers to the poetry of Cesare Pavese, in which the unspoilt beginning of the day - dawn - stands for hope. The lines of Pasternak’s text that begin Part III refer to a period when we will return to light (“noi verremo alla luce”). Commenting on Quando stanno morendo shortly after the work had been composed, Nono wrote:
And if each thing were to be seen in this way - as unheard, individual, indivisible - then each thing
would escape the fate of death to which it would be consigned by the winter of the “orthodox wolves”.
If we are able to sustain this expectation, then we might be able to shine the “light of day” and thus
defeat the death that today hangs over us. 
The musical tone of Part III is also far less agitated and more lyrical than that of Part II, conforming to the general idea of a ‘chant d’aube’.
Marco Mazzolini has identified cuts which were made in both the text and the music of Part III (see Figure 2 below). Mazzolini’s observations are based on two scores of the work, which he labelled “Stesura originaria” [Original draft] and “Stesura con taglio”[Draft with cuts] (see Example 2 below). Initially Nono had intended to divide the first text fragment(marked ‘a’ in Plate 1) into three subsections. In the end he cut the last part of Pasternak’s text following the word ‘chiamerà’ and in so doing eliminated the last 18 bars of what would have been the third subsection of a fifty-four-bar ternary form. He also cut the first three lines of the third text fragment, leaving only the last line of Khlebnikov’s text and in so doing eliminated half of the music that had been composed for this final section of the work.
Plate 1: Luigi Nono, Typescript of the Original Text of the Third Movement.
Reproduced with the kind permission of the Archivio Luigi Nono. © Eredi Luigi Nono.
“Stesura originaria” [Original Draft] “Stesura con taglio” [Draft with cuts]
(Original structure of Part III) (Definitive structure of Part III)
a) 1. bars 1-21 a) bars 1-36 (subsection 3 was cut. In the published
2. bars 22-36 score, double bar separates bars 21 and 22,
3. bars 37-54 identifying the dividing line between subsections1 and 2.)
b) bars 1-22 b) bars 37-58
c) bars 1-70 c) bars 59-94 (bars 1-34 of the earlier version were cut)
Figure 2: Comparison of the original and definitive structures of Part III presented by Marco Mazzolini in 1993
These cuts were made late in the compositional process. The Archivio Luigi Nono conserves an autograph fair copy (catalogue no. 47.12.02, no doubt the document Mazzolini labelled the “stesura originaria” in his 1993 conference). This fair copy is dated 3 September 1982. The publication of this date at the double bar in the published score (which presents the “stesura con taglio”, or definitive version of Part III) is misleading because the cuts must have been made after 3 September 1982. Erika Schaller observes that during the last phase of his career, Nono would often make cuts during rehearsals leading up to the first performance.
As can be seen in Plate 1 above, the Finale of Part III was originally supposed to have set four lines of another text fragment by Khlebnikov.
Quando stanno morendo, le erbe intristiscono When they are dying, [blades of] grass wither
Quando stanno morendo, i cavalli respirano When they are dying, horses breathe
Quando stanno morendo, i soli si spengono When they are dying, suns fade away
Quando stanno morendo, gli uomini cantano When they are dying, men sing
Figure 3: Transcription and English translation of the last four lines of text presented in Plate 1
The music composed to set this text, exists in three distinct versions, which for the purposes of this paper will be labelled 1, 2 and 3. The numbers refer to the chronological order in which Nono composed the three versions.
Example 1: Quando stanno morendo, Part III, Original Draft of the Finale, bars 1-70, Pitch Content of Versions 2 and 1 of the Finale
1 Version 1 is the last thirty-six bars as they appear in the published score, which set only the last line of Khlebnikov’s text (see Example 1).
2 Following the completion of version 1, a new version of the same music was composed by permuting the order of the compositional units. Version 2 was to have set the first three lines of Khlebnikov’s text, and, together the two versions would have constituted a Finale seventy bars in length, twice as long as it actually is. As noted above, Nono cut version 2. In the following example the dyads, trichords and tetrachords of versions 2 and 1 are presented as they appear in the “stesura originaria” (duration values have been eliminated). The intervals and chords of version 1 are numbered and a cursory comparison of the two versions reveals that except for chords 23 and 24, which are missing in version 2, the pitch content of version 2 is identical to that of version 1.
3 On 28 September 1982, three and a half weeks after having completed Quando stanno morendo, Nono used version 1 to create a new work entitled ¿Donde estas, hermano? Per ‘los Desaparecidos en Argentina’ for two sopranos, mezzo soprano and contralto. He did this by replacing Khlebnikov’s text with the Spanish words “¿Donde estas hermano?” With regard to the music, though minor changes do occur in dynamics, phrasing and note doublings, the pitch and duration structures of versions 1 and 3 are identical.¿Donde estas hermano? was first performed on 24 November 1982 in Cologne as part of a solidarity concert organized by the German section of the ‘Association Internationale de Défense des Artistes victimes de la répression dans le monde’ (AIDA). The concert’s goal, clearly reflected in Nono’s subtitle, was to reinforce public awareness of those who had disappeared during the years of state sponsored terror and specifically of the approximately one hundred Argentinean artists who remained unaccounted for at that time. The event’s motto was ¿Donde estas, hermano?, which Nono appropriated for both the title and the text of this new vocal work. ¿Donde estas hermano? has since been published and recorded. This last version is mentioned here in passing for two reasons: first, it clearly demonstrates that though the texts of Nono’s works are always important and should never be ignored, they do not necessarily constitute the determining factor for the organization of the music; second, this version shows that the Finale of Quando stanno morendo can be understood as a musical entity in its own right and can thus be analyzed as a self-standing piece, without taking into account the live electronics that are minimally present in version 1 (see footnote 10 above).
How do we know that version 2 was derived from version 1 and not the other way around? The study of sketch material pertaining to Quando stanno morendo provides an answer. Plate 2 below presents a sketch used by Nono as he began to compose the Finale. It shows how vocal parts of the previously composed Part II and the first two sections of Part III were used to create the pitch structures of version 1.
The Roman numerals in the left margin refer to Parts II and III and the lower case letters refer to the sections of each movement. The pitch content of this page is almost completely derived from the vocal parts in the five sections of Parts II and III that precede the Finale. For example, the pitches notated on the uppermost staves of the page present the melodic material sung by the second soprano and mezzo-soprano in sections ‘a’ (bars 10-37) ‘b’ (bars 56-81) and ‘c’ (bars 82-105) of Part II. Except for one note the correspondence between the sketch and the vocal lines in Part II is exact both in terms of pitch and register. The pitches notated on the following staves present the melodic material of Part III sung by the first soprano in section ‘a’ (bars 1-27) and by the contralto in section ‘b’ (bars 37-53).
Plate 2: Quando stanno morendo, Part III, bars 59-94, Sketch.
Reproduced with the kind permission of the Archivio Luigi Nono. © Eredi Luigi Nono.
Plate 3: Quando stanno morendo, Part III, bars 59-94, sketch.
Reproduced with the kind permission of the Archivio Luigi Nono. © Eredi Luigi Nono
This sketch presents the compositional units with which Nono composed the four-voice chorale of the Finale. The units are made up of single pitches, dyads, trichords and tetrachords. The column of numbers written in the upper right corner (1=6; 2=9; 3=16; 4=5) indicates the sum of one-, two-, three-, and four-note units Nono intended to use at one point in the compositional process. The octava bassa signs in the left margin show Nono modifying register. The pitch content of the entire upper staff is sung an octave lower in the Finale than where the same material was sung in the second movement. Nono also eliminated units (the encircled tritone e''' b''flat on the first staff, the same interval on the third staff, as well as the following tritone) and changed their order (the b'' became the fourth unit on the second staff). At some point he appears to have envisioned the Finale being made up of 35 units (see the encircled figure on the right side of the page). In the published score, the Finale contains 31 units: the sum of the squared and circled figures to the right of the compositional units.
Some time after he had completed the page presented in Plate 2, Nono set his compositional pitch units in a metric structure and added duration to the pitch structure of the Finale. This can be seen on the bifolium presented in Plate 3. In both sketches presented in Plates 2 and 3, Nono used different coloured ink (blue, red and black) to distinguish between first ideas and corrections. Despite the sketch-like quality of the writing in Plate 3, the pitch and durational aspects of the Finale are now firmly in place. Though the text, phrasing, dynamics and the live electronic manipulation are still missing, the document presented above can be seen as a first rough draft of what would become the music of the Finale of Quando stanno morendo and of ¿Donde estas hermano?
From the information gleaned from these two pages, we are able to draw the following conclusion. The sketches in Plates 2 and 3 present the compositional units in the order that corresponds with version 1 of the Finale. This confirms that version 2 is derived from version 1 and not the other way around, because the structures of version 1 are directly related to previously composed vocal material of Parts II and III.
Segmenting Pitch Structure in the Finale
What are we to make of this seemingly chaotic collection of mainly 3-5 and 3-8 trichords in the Finale of Quando stanno morendo? How are these compositional units related to one another and how did Nono recompose this material for version 2? In a broader context, how should we understand these harmonic structures which are so characteristic of Nono’s late work as a whole? The phrase structure of vocal music (following text/music relationships) often constitutes a good point of departure for an examination of the above questions. However, as we have seen, the same compositional units were used to set three completely different texts, and, in the case of ¿Donde estas hermano? (version 3 of the Finale), a new text was simply superposed on a pre-existing musical structure (version 1). As a result, though the text/music relationship is significant, it can not be the sole reference for a coherent explanation of Nono’s phrase structures.
One promising line of endeavour in this particular case is to examine how the so-called scala enigmatica is related to the pitch structure in the Finale of Quando stanno morendo. Commentators and analysts have noticed the presence of this scale in Nono’s late work, beginning with the string quartet Fragmente - Stille, An Diotima (1980). According to Laurent Feneyrou, it is so pervasive in the compositions of the 1980s that it parallels Nono’s use of the all interval row in works of the late 1950s. The scala enigmatica was invented by Adolfo Crescentini, a Bolognese music professor who, in a letter published in the Gazetta Musicale di Milano on 3 August 1888, challenged readers to harmonize a seven-note scale made up of an eight-note pitch collection organized in a succession of major, minor and augmented seconds, the eighth pitch being the lowered fourth degree in the descending version (see Example 2). The following year, Giuseppe Verdi used the scale as a cantus firmus in his "Ave Maria" (subtitled Scala enigmatica armonizzata a 4 voci miste), which became the first of the Quattro Pezzi Sacri (1898).
Example 2: The Scala Enigmatica as used by Giuseppe Verdi in “Ave Maria,” bars 1-16
In Nono’s compositions, the scala enigmatica never appears as such. This fact has led some, notably Heinz-Klaus Metzger, Luigi Pestalozza and Jürg Stenzl, to suggest that Nono used it as a kind of generalized background matrix with only vague relationships to the structure of a particular work. Paraphrasing Nono, Metzger stated that the scale should be seen as a “generative constellation” [generativer Konstellation] from which the composer derived his diastematic material, and went on to suggest that the beginning of the string quartet Fragmente - Stille can be related to the scala enigmatica transposed to A. He did not explain how he came to this conclusion and indeed dismissed such explanations as pedantic. More recent studies of Nono’s late work have attempted to provide a more precise definition of the term “generative constellation.” Taking Metzger’s remarks as his point of departure, Hermann Spree noted that in Fragmente-Stille, An Diotima the scala enigmatica has neither a determinant function (like that of a series) nor can it be dismissed as mere neutral background material. He observed that the pitches A, E-flat, D and A-flat are clearly present at the very beginning of the string quartet and that this pair of interlocking tritones presents the four transposition levels of the scala enigmatica that play a framing role throughout the work. He also stated that the pitch structure of the string quartet should not be understood as a succession of transpositions, moving from one level to another, but rather as intervals and chords derived from specific transposition levels which appear to be freely mixed, leaving the impression that the music seems to hover between two or more forms of the scale.
Contradicting Spree’s findings somewhat, the first fifteen units of version 1 of the Finale of Quando stanno morendo can be grouped into a succession of segments derived from specific transposition levels of the scala enigmatica. The first three compositional units contain seven of the eight pitches of the scale transposed to B flat. As is often the case in Nono’s late work, tritones, perfect fourths and fifths, major sevenths and minor seconds dominate the diastematic structures of the compositional units 1 through 3 and continue to do so throughout the Finale. The first trichord presents two characteristic intervals of the scale transposed to B flat: with the minor second between the first and second scale degrees and the tritone between the first and fourth scale degrees.
The minor second is spelled enharmonically as B natural rather than as C flat. Numerous analysts have noted the idiosyncratic manner with which Nono notated music derived from the scale. Spree spoke of Nono’s “insensitivity” to questions concerning enharmonic spelling. Though this aspect of Nono’s writing does not provide an unequivocal key to the composer’s pitch structures, notation can be an indication of how closely various transposition levels of the scale are related to specific sections of his music. For example, in an undated sketch produced for Prometeo, some time between 1981 and 1985 (the period during which he composed Quando stanno morendo), Nono copied out all twelve transpositions of the scala enigmatica, starting on C at the top of the page and descending by half-step to B at the bottom of the page (as though he were deploying a serial table). Nono’s notation of the scale in this table is not rigorously systematic (it contains numerous inconsistencies), but neither is it incoherent. The guiding principle seems to be the facilitation of reading and writing. Throughout the sketch he avoids all infrequent accidentals: B sharp, F flat, all double sharps and flats, etc. Though on occasion, the spelling of a degree in the ascending form of the scale will differ from that of the descending form, this does not occur frequently. In Example 3 below, the first six compositional units (setting the word “Quando”) are placed above the transposition levels from which they can be derived. The scales are spelled exactly as Nono wrote them in his sketch for Prometeo.
Example 3: Quando stanno morendo, Part III, Finale, Compositional Units 1-6 Placed Over Transpositions of the Scala Enigmatica, Transcribed from a Sketch for Prometeo
The spelling of all pitches conforms to that used in the sketch for Prometeo. For example in compositional unit 1, the B natural conforms to the manner in which Nono notated the second degree of the scale in both ascending and descending forms. In cases where a discrepancy arises between the spellings of the same degree on ascending and descending forms of the scale (G sharp ascending and A flat descending in the B flat transposition for example), Nono tends to choose spellings used in the ascending form. Of the first 22 enigmatica, only one pitch (A flat of unit 9, see Example 4 below) does not conform to Nono’s idiosyncratic notation of the scale found in his sketch for Prometeo.
Example 4: Quando stanno morendo, Part III, Finale, Compositional Units 7-15 Placed Over
Transposition of the Scala Enigmatica, Transcribed from a Sketch for Prometeo.
The next compositional unit (4) breaks with the previous group of three because it contains F and C sharp, neither of which are found in the B flat transposition of the scale. These two pitches are contained in the scale transposed to F. In fact they are the only two notes of the scale on F which do not occur in the scale on B flat. Furthermore, D and G sharp, the only two notes of the B-flat transposition that do not occur in the F transposition, form the tritone of the preceding compositional unit (3). Thus units 3 and 4 display the strongest possible contrast that can be obtained between these two overlapping pitch collections. Units 4 through 6 are made up of five of the eight pitch classes of the scale transposed to F. These five scale degrees are also characteristic of the scale on F: the lowest note, the fourth in both ascending and descending forms, the augmented fifth and the major seventh. Note should also be taken of the fact that unit 4 also contains the tritone made up of the first degree and the ascending fourth degree of the scale, analogous to the tritone found in unit 1. The transposition levels from which these compositional units can be derived, divide the setting of the word in two equal halves.
The transposition identity of compositional units 7 through 9, which set the second word of the text (“stanno”), is not quite as certain as the first two groups (see Example 4 below). The six pitches of these units all belong to the scale transposed to E flat and all are in normal spelling. Only one pitch (G) distinguishes the pitch collection of the E-flat transposition from those of the B -flat or F transpositions and it is absent. Consequently all of the pitches used in compositional units 7-9 could be derived from the B-flat and F transpositions. This reading of the pitch content of units 7 through 9 is however unsatisfactory because unit 7 contains a C sharp and a D. The former is present in the B-flat transposition and the latter in the F transposition, making the trichord impossible to classify. Moreover, the six pitches of units 7 through 9, like those of units 4 through 6, correspond to characteristic scale degrees of the E-flat transposition: the lowest note, the fourth degree in both ascending and descending forms, the augmented fifth, the augmented sixth and the major seventh.
The units 10 through 12, which set the word “morendo”, can be derived either from the B-flat or the F transpositions of the scale. Their spelling conforms to both transpositions. However, when combined with compositional unit 13, which contains pitches that can only be derived from the scale on F, the set (units 10 -13) constitutes a convincing whole. Here again, the pitch material of these units is made of six characteristic pitches of the scale on F: the lowest note, the major third, the fourth degree in both ascending and descending forms, the augmented fifth, and the major seventh.
The last three units of this first section of the Finale are in a mirror relationship with units at the beginning, which corresponds to the fact that the vocal line of the third section of Part II is the retrograde of the vocal line of the first section (see the sketch presented in Plate 2: the pitch material of the third staff marked “c” is in a retrograde relationship with the pitch material of the first staff marked ‘a’). However, this relationship is not exact: units 1 - 3 - 4 correspond to units 15 -14 - 13. Unit 2, which should have been placed between units 15 and 14, is missing. As noted above, when Nono constituted the compositional units of the Finale, he deliberately eliminated the interval e''-flat – a'', which would have been placed between units 14 and 15 (see Plate 2, third staff from the top of the page). If we examine the register displacement of pitches making up these units, it is clear that Nono was constructing a tight symmetric relationship between the compositional units at opposite ends of this first section of the Finale. In all three pairs of trichords, at least one note retains its initial register. The tritone of units 1 and 15 is inverted (the augmented fourth equals the diminished fifth); the tritone of units 3 and 14 is transposed two octaves higher, and the tritone of units 4 and 13 is inverted in the opposite direction to that of units 1 and 15. Clearly, these complementary melodic patterns (the first curving down, the second curving up) were consciously composed, reinforcing the notion that the units of the B-flat sections at opposite ends of the first fifteen compositional units belong together and do have a shared identity (see Example 5).
Example 5: Quando stanno morendo, Part III, Finale, Compositional Units 1-4 (bars 59 - 62) and 13 – 15 (bars 73 - 75)
Units 16 through 21 can be derived from the scala enigmatica on B flat (see Example 6). Though the group contains twice as many compositional units, its pitch material is exactly the same as that deployed in units 1 through 3. In both cases, seven of the eight pitch classes of the B-flat transposition are deployed and in both cases the missing pitch is F sharp.
Example 6: Quando stanno morendo, Part III, Finale, Compositional Units 16-21 Placed Over the B-flat
Transposition of the Scala Enigmatica, Transcribed from a Sketch for Prometeo.
Unit 22 contains an F and thus breaks with the preceding group derived from the B-flat transposition (see Example 7 below). This suggests the beginning of a new group of units derived from the F transposition, notably because it contains the characteristic tritone formed by the lowest tone and the ascending fourth degree of that scale. Unit 22 could be grouped with units 23 and 24, because the pitches of the latter two units can also be derived from the F transposition of the scale. This interpretation is however problematic. As shall be shown below, units 23 and 24 appear to belong to the last section of the Finale. However, this segmentation leaves unit 22 in an orphaned situation, a lone dyad derived from the F transposition, isolated between two larger groups; the only such occurrence in the Finale. This interpretation is nevertheless plausible when unit 22 is placed together with the two units that would have surrounded it, had the composer not eliminated them late in the compositional process. The reader will remember that Nono cut the last 18 bars of section ‘a’ of Part III. In these bars the soprano solo was to have sung the text fragment “faremo luce al giorno” [we will shed light on the day]. The pitches Nono used to set the soprano’s text can be seen in the following plate, (see Plate 4) which presents a close-up shot of a portion of the sketch: E flat, A, C sharp; B, F; E, B, B flat. All of these pitches can be derived from the scale on F. They constitute seven of the eight pitch classes of the scale and the E flat corresponds with Nono’s idiosyncratic manner of writing the sixth degree of the scale: E flat instead of D sharp.
Example 7: Quando stanno morendo, Part III, Finale, Compositional Unit 22 Plus Two Compositional Units Eliminated by Nono, Placed Over the F Transposition of the
Scala Enigmatica, Transcribed From a Sketch for Prometeo. All eliminated pitches are shown in parenthesis.
Plate 4: Quando stanno morendo, Part III, Finale, Detail From the Sketch Presented in Plate 2.
Reproduced with the kind permission of the Archivio Luigi Nono. © Eredi Luigi Nono
The point is not to criticize or even question Nono’s decision to cut this section of the Finale (any discussion of that lies outside the framework of this paper). However it is interesting to note that the compositional units that were eliminated reproduce the patterns of selection and organization that clearly dominate the pitch structures of the first twenty-two compositional units of the Finale.
Units 23 through 25 set the last word of the text (“cantano”) and are different from the previous compositional units in two ways. First, as tetrachords they thicken and enrich the harmonic texture by allowing all four voices to sing simultaneously for the first time. Second from unit 25 onwards, the pitch content differs significantly from that which dominated the first fifteen compositional units. This can be seen by comparing the pitch content of units 1 through 22 to that of units 23 through 31. As noted above, all pitch classes in units 1-22 are derived from the transposition levels of the scala enigmatica on B flat and F. Together these two transpositions form a collection of 10 pitches: the absent notes are C and G. Nono also systematically avoided using F sharp (present both in the B-flat and F transpositions of the scale) throughout the first section of the Finale (units 1-22). All three pitch classes are deployed in the compositional units of the last section of the Finale (units 23-31). Of the nine compositional units, five contain one of the three pitch classes absent in the first 22 compositional units. If we include the two compositional units Nono eliminated (see Plate 2), the proportion remains approximately the same: six of eleven units contain those three pitch classes.
The last nine compositional units are difficult to classify in terms of transposition levels. On the one hand, these units contain all twelve pitch classes of the chromatic scale. The units can of course be derived from various transposition levels: notably on F (units 23, 24, 30); C (26, 30), C sharp (26, 27), F sharp (27, 31), and G sharp (25, 28, 29). However, no coherent grouping similar to that found among units 1-22 can be achieved. An examination of the spelling of this pitch class material reveals that it tends to correspond with Nono’s idiosyncratic habit of writing the C transposition of the scale. (In his sketch for Prometeo he uses C sharp instead of D flat and B flat instead of A sharp.) Also C is prominently deployed as the highest pitch and as one of the last two pitches. However, only two units (26 and 30) can actually be derived from this transposition level and so though the idea that Nono was working with a chromatically enriched C transposition of the scale seems tempting, such an interpretation is inconclusive (see Example 8).
Example 8: Quando stanno morendo, Part III, Finale, Compositional Units 23-31 Placed over the Chromatic
Scale Based on the C Transposition of the Scala Enigmatica as Spelled in a Sketch for Prometeo.
In order to reinforce the proposed segmentation of the Finale’s pitch structures, we shall now turn to version 2. As noted above Nono reordered the compositional units of version 1, creating a new version intended to set the opening lines of Khlebnikov’s text. In version 2, two compositional units (23 and 24) are missing. Otherwise the pitch content and register deployment of the compositional units in version 2 is identical with that of version 1. These two versions also present a number of striking similarities in the manner in which the compositional units are combined (see Example 1 above).
1 The division established in version 1 between compositional units 1-22 (derived primarily from B-flat and F transposition levels) on the one hand and units 23-31 (which show no grouping according to transposition levels) is clearly maintained in version 2. Nono used compositional units 25-31 to complete the Finale. Indeed, the contrast between compositional units 1-22 and 25-31 is heightened in version 2. The compositional units 23 and 24, which begin the last section of version 1, can also be derived from the F transposition of the scala enigmatica. In version 1 they could thus be related to compositional unit 22, creating a transitional or pivotal group between the two sections of this version. No such transition exists in version 2. With its prominent C, compositional unit 27 makes a clear break with the preceding units.
2 More often than not, words and musical phrasing coincide with groups of compositional units derived from a specific transposition level. In version 1 only the first word of the text (“Quando”) does not. To set this word, Nono used six compositional units, divided equally into two groups of three: the first clearly derived from the B-flat transposition and the second from F. This occurs twice in version two (see the words “intristiscono” and “i cavalli”). Nevertheless, throughout these two sections convergence of text, musical phrasing and compositional groups constitutes the rule rather than the exception.
3 The patterns of grouping identified in version 1 tend to be replicated in version 2. For example the first fifteen compositional units of version 1 form a subsection by virtue of the fact that they are encased in mirror relationship (see Example 1 above). No such mirror relationship obtains in version 2. However the first fourteen compositional units can be seen as forming a subsection bounded by groups derived from the B-flat transposition level. Within this subsection similarity also prevails. Certain groups from version 1 are maintained intact in version 2. Compositional units 7 through 9, which were said to derive from the E flat in version 1, remain together in version 2, reinforcing the argument that they do indeed constitute a group.
Notwithstanding the inconclusive analytical results concerning units 23-31 of version 1, Nono clearly reserved a different configuration of his pitch material and a different end. The structure of the Finale reminds us of comments Guerrero made on those of Sarà dolce tacere and Cori di Didone (see above). Here too, the clear, calm, homophonic structures of the a cappella chorale provide fitting closure, both in terms of form and of content.
Furthermore, by singling out the vocal material of Parts II and III to compose the Finale, Nono is not simply constructing a logical end to a closed form; he also appears to be using musical means to make an indirect commentary on the work’s content. “Cantano” means ‘they (the men who are dying) sing’ and suggests that Nono set the songs of dying men on another musical plane, creating an uncanny allusion to the last twenty bars of Arnold Schoenberg’s A Survivor from Warsaw in which the chorus of condemned men break out in song. Rather than continuing to circulate along the well-trodden paths of previously composed material, this last song breaks out into new uncharted territory. It is here that Schoenberg’s two categories of knowledge about music (how it was made and what it is) meet and interact in Quando stanno morendo.
Among the sketch material conserved at the Archivio, I have not come across any documents explicitly confirming that Nono consciously used transposition levels of the scala enigmatica to organize the pitch structures of the Finale of Quando stanno morendo. But then one rarely finds smoking guns in archives and libraries because sketches are by their very nature incomplete. Pascal Decroupet has astutely observed:
They are the result of a process and not just evidence of a journey. In and of themselves, sketches are incapable of revealing all of the stages linking the material and the work. However through careful observation one can extrapolate, generalize and even invent fundamentally important criteria, which may have left no trace in the composer’s working documents. The analyst must therefore fill in the blanks and engender coherence¼ If the archaeological reconstruction of the composer’s thinking is by its very nature an illusion, careful study of sketch material can endow the analyst’s hypothesis with a certain degree of probability.
The above citation brings us back to the point made by Borio at the outset of this article. The information concerning palindromes, the symmetric relationships in terms of register among compositional units and even the use of specific transposition levels of the scala enigmatica to structure pitch content is of course all in the score to be uncovered. But these relationships have to be identified among the multitude of all possible relationships that can be produced from the data at hand, and more importantly, the analyst has to be alerted to the significance these structures can have for his or her object of study. The fact that Nono composed the vocal material of the second movement in the form of a palindrome and then partially obscured this structure in the Finale through the elimination of certain units and the modification of pitch and register in others is important and can be best apprehended from the study of his sketches. It is in this regard that the study of the composer’s working documents is useful. As well as providing quantitative information, which may not be otherwise available (i.e. information gleaned from a comparison of versions 1 and 2 of the Finale), they also enable the scholar to construct a qualitative environment within which he or she can better validate the interpretation of analytical data.
Albèra, Philippe ed. Luigi Nono, Programme for Prometeo Tragedia dell’ascolto
(Paris: Contrechamps/Festival d’automne, 1987).
Arnold, Denis. [Preface], in Giuseppe Verdi, Quattro Pezzi Sacri (London: Eulenburg,1973)
Borio, Gianmario. “Sull’interazione fra lo studio degli schizzi e l’analisi dell’opera,” La nuova
ricerca sull’opera di Luigi Nono, Gianmario Borio, Giovanni Morelli and Veniero Rizzardi eds.
(Venice: Leo S. Olschki, 1999).
Breuning, Franziska. Luigi Nonos Vertonungen von Texten Paveses (M_nster: LIT, 1999).
Cacciari, Massimo ed. Luigi Nono: Verso Prometeo (Milan: Ricordi 1984).
Campbell, Roy. Lorca: An Appreciation of His Poetry (New Haven: Yale University Press, 1959).
De Benedictis, Angela Ida and Veniero Rizzardi eds. Luigi Nono Scritti e colloqui, Volumes
1&2 (Lucca: Ricordi, 2001).
Decroupet, Pascal. “Floating hierarchies: organization and composition in works by Pierre
Boulez and Karlheinz Stockhausen during the 1950s,” A Handbook to Twentieth-Century
Musical Sketches, Patricia Hall and Friedemann Sallis eds. (Cambridge:Cambridge
University Press, 2004), 146-160.
Dress, Stefan. Architektur und Fragment: zu späten Kompositionen Luigi Nonos
(Saarbrücken: Pfau, 1998).
Feneyrou, Laurent ed. Luigi Nono Écrits (Paris: Christian Bourgois, 1993).
Forte, Allen. The Structure of Atonal Music (New Haven: Yale University Press, 1973).
Guerrero, Jeannie. “Multidimensional Counterpoint and Social Subversion in Luigi Nono’s
Choral Works,” Theory and Practice 28 (2003): 53-77.
______________. “Tintoretto, Nono and Expanses of Silence” unpublished paper presented at
the Dublin International Conference on Music Analysis, University College Dublin, 2005.
Hall, Patricia. A View of Berg’s Lulu Through the Autograph Sources (Berkeley:
University of California Press, 1996).
Haller, Hans Peter. Das Experimentalstudio der Heinrich-Strobel-Stiftung des Südwestfunks
Freiburg 1971-1989. Die Erforschung der elektronischen Klangumformung und ihre
Geschichte, Vol. 2 (Baden-Baden: Nomos, 1995).
Mazzolini, Marco. “Problematiche editoriali in Quando stanno morendo. Diario polacco N. 2,”
unpublished paper presented at a conference entitled “Problemi critico-testuali nelle edizioni
dell’ultimo Nono” organised by the Biennale di Venezia (June 1993).
Metzger, Heinz-Klaus. “Wendepunkt Quartett?” Musik-Konzepte Luigi Nono 20 (1981): 93-112.
Nielinger-Vakil, Carola. "Quiet Revolutions: H_lderlin, Fragments by Luigi Nono and Wolfgang Rihm."
Music & Letters 81/2 (May 2000): 245-274.
Nono, Luigi. Quando stanno morendo Diario polacco no 2, André Richard and Marco Mazzolini
eds. (Milan: Ricordi, 1999).
Ogburn, David, “‘When they are dying, men sing ...”“ Nono’s Diario Polacco n.2,” Ems:Electro-
acoustic Music Studies Network - Montréal, 2005, http:/www.emsnetwork.org/article,php3?id_article+175 .
Pestalozza, Luigi. “Nono, parole e suono”, Luigi Nono Scritti e colloqui, Vol. 2, Angela Ida De
Benedictis and Veniero Rizzardi eds. (Milan: Ricordi, 2001), 603-630.
Sallis, Friedemann. “Le paradoxe postmoderne et l’œuvre tardive de Luigi Nono,” Circuit
musiques contemporaines, Analyses 11/1 (2000): 69-86.
Schoenberg, Arnold. Letters, Erwin Stein ed., Eithne Wilkins and Ernst Kaiser trans. (New
York: St. Martins Press, 1965).
Solare, Juan Maria. “¿Donde estas hermano?: Die ewige Utopie. Die politische Haltung Nonos
nach dem Streichquartett und seine Auseinandersetzung mit Lateinamerika,” Klang und
Wahrnehmung. Komponist – Interpret – Hörer, Darmstädter Beiträge 41 (Mainz:Schott, 2001), 215-248.
Spree, Hermann. “Fragmente – Stille, An Diotima” Ein analytischer Versuch zu Luigi Nonos
Streichquartett (Saarbrücken: Pfau,1992).
Stenzl, Jurg. “Gli anni Ottanta,” Nono, Enzo Restagno ed. (Turin: EDT, 1987), 206-226.
Umbral, Francisco. Lorca, poeta maldito (Barcelona: Editorial Planeta, 1998).
 This article is an amalgamation of two conference papers: 1. “Sketch material and the study of late twentieth-century music: the case of Luigi Nono’s ¿Donde estas, hermano? (1982)” presented at a meeting of the American Musicological Society (New England branch) held at Harvard University on February 5, 2005; 2. “Segmenting the Labyrinth; Sketch Studies and the scala enigmatica in Luigi Nono Quando stanno morendo. Diario Polacco N. 2 (1982)” presented at the annual meeting of the Society for Music Theory held at Cambridge (Mass.) on November 13, 2005. I would like to thank the Social Sciences and Humanities Research Council of Canada and the Faculté des études supérieures et de la recherche of the Université de Moncton for funding the costs involved in this project. I am deeply grateful to Erika Schaller and the Archivio Luigi Nono for providing timely support and assistanceand to Carola Nielinger-Vakil for her honest and helpful comments on this text. I am indebted to Marco Mazzolini (BMG Italy) and Jeannie Guerrero (Eastman School of Music, University of Rochester) for sharing unpublished papers on their research with me. I also heartily thank my numerous student assistants (Renée Fontaine, Rémy Fortin, Frederic Hétu, Sylvie LeBlanc and Nicholas Smith) who worked with me in the course of this project. Finally I warmly thank my colleague, Edward Jurkowski (University of Lethbridge) for his thoughtful help and advice.
 Arnold Schoenberg, Letters, Erwin Stein ed., Eithne Wilkins and Ernst Kaiser trans. (New York: St. Martins Press, 1965), 164. (Schoenberg’s emphasis).
 Hall’s example of music written in a “highly defined theoretical system,” is of course Alban Berg’s Lulu. As a counter example she presents Hugo Wolf’s “Der Glücksritter” from the Eichendorff Lieder (1888), which alas finds itself consigned to the purgatory of music written in an “ambiguous, less well defined system.” Patricia Hall, A View of Berg’s Lulu Through the Autograph Sources (Berkeley: University of California Press, 1996), 7-12.
 Gianmario Borio, “Sull’interazione fra lo studio degli schizzi e l’analisi dell’opera”, La nuova ricerca sull’opera di Luigi Nono, Gianmario Borio, Giovanni Morelli and Veniero Rizzardi eds. (Venice: Leo S. Olschki, 1999), 5-6.
 The composition’s three movements are labelled Part I, Part II and Part III in the published score. This convention has been adopted for this article.
 Allen Forte, The Structure of Atonal Music (New Haven: Yale University Press, 1973), 83.
 According to Erika Schaller, chief musicologist at the Archivio Luigi Nono the quantity of working documents pertaining to Quando stanno morendo (manuscript material, recordings, heliographic material [photographs, photocopies, engraver’s score, etc.]) is relatively large, but nevertheless typical of similar-sized works produced during the early 1980s. Email received from Erika Schaller on 19 January 2005.
 Francisco Umbral, Lorca, poeta maldito (Barcelona: Editorial Planeta, 1998), 138. Umbral’s summing up of the poem’s content also resonates remarkably well with the intertwined strands of thematic content running through both the Epitaffio cycle and Quando stanno morendo. Indeed they are characteristic of Nono’s entire oeuvre, making the composer’s decision to set this text at the beginning of his career particularly significant.
 Federico García Lorca, Romance de la Guardia civil española (1926) (last four lines of the poem)
¡Oh, ciudad de los gitanos! O city of the gipsies, who
¿Quién te vió y no te recuerda? That saw you could forget you soon?
Que te busquen en mi frente. Let them seek you in my forehead.
Juego de luna y arena. The playground of the sands and moon.
Roy Campbell, Lorca: An Appreciation of His Poetry (New Haven: Yale University Press, 1959), 78.
 Nono’s handling of the vocal textures in the final sections of Epitaffio No. 3 and Quando stanno morendo enables the establishment of another interesting parallel between these two works at opposite ends of his career. In the former, Nono sets solo voices against the choir singing the same music bocca chiusa (bars 411-426 and 436-442). In the latter, the score calls for a reverberation of 2 to 3 seconds and the displacement of the singers’ sounds in circular patterns through loud speakers placed around the hall. This is achieved by using a digital spatializer (the so-called Halaphon). From bars 59 to 88 the singers’ sounds are simultaneously displaced in a clockwise direction (10 seconds per cycle) and a counterclockwise direction (7 seconds per cycle). Throughout the Finale the dynamic level of sounds transmitted via the loud speakers must remain slightly lower than that of the singers, shadowing the sound production of the singers and creating a soft, vocal background texture, not unlike a choir singing bocca chiusa. For a detailed description of the digitalized sound direction of Quando stanno morendo, see André Richard and Marco Mazzolini, “Notes”, in Luigi Nono, Quando stanno morendo Diario polacco no 2 (Milan: Ricordi, 1999), XXV-XXIX.
Jeanne Guerrero, “Multidimensional Counterpoint and Social Subversion in Luigi Nono’s Choral Works,” Theory and Practice 28 (2003): 69.
 Ibid., 68.
 Jeannie Guerrero, “Tintoretto, Nono and Expanses of Silence” unpublished paper presented at the Dublin International Conference on Music Analysis, University College Dublin, 2005.
14 For a discussion of certain aspects of the first movement involing an examination of sketch material, see David Ogborn, “‘When they are dying, men sing...’: Nono’s Diario Polacco n.2, “ EMS: Electro-acoustic Music Studies Network - Montréal , 2005, http://www.ems-network.org/article.php3?id_article=175.
 The other three works are Das atmende Klarsein for bass flute, chamber choir and live electronics (1981); Io, frammento dal Prometeo for three sopranos, chamber choir, bass flute, contrebass clarinet and live electronics (1981); Guai al gelidi mostri for two contraltos, flute, clarinet, viola, violoncello, double bass and live electronics (1983). According to Hans Peter Haller (the inventor of the Halaphone and one of Nono’s principal collaborators at the Strobel Foundation) the group of four works should be seen as steps toward Prometeo. Tragedia dell’ascolto for soloists, chamber choir, chamber orchestra and live electronics (1983-86), the major work of Nono’s last decade. Hans Peter Haller, Das Experimentalstudio der Heinrich-Strobel-Stiftung des Südwestfunks Freiburg 1971-1989. Die Erforschung der elektronischen Klangumformung und ihre Geschichte, Vol. 2 (Baden-Baden: Nomos, 1995), 127-128. To the above list one should also add Omaggio a György Kurtág for alto, flute, clarinet, tuba and live electronics (1983-86).
 Luigi Nono, [Dedication], Quando stanno morendo Diario polacco no 2, unpaginated.
 Together with Vladimir Mayakovsky (1893-1930), Khelbnikov founded the Futurist literary movement in Russia. Following his premature death, Khlebnikov’s reputation declined, though his work did continue to exert a considerable influence on Mayakovsky, Pasternak and Osip Mandelstam. After World War II, Soviet critics attacked Khlebnikov’s work for being formalist and decadent. The poet’s rehabilitation began with the death of Stalin in 1953, but Khlebnikov remained a marginal figure in the Soviet literary scene. By the early 1980s no new edition of his complete work had yet appeared.
 André Richard and Marco Mazzolini, “Notes”, in Nono, Quando stanno morendo, XXI.
 “Texts selected and edited by Massimo Cacciari”, in Nono, Quando stanno morendo, LIII.
 E se ogni cosa può essere cosi vista - come inaudita, singola, indivisibile – ogni cosa potrà ancora sottrarsi a quel destino di morte cui vuole consegnarla l’inverno dei «lupi ortodossi». Se sapremo custodire quest’attesta, potremo ancor far «luce al giorno» rifiutare la morte che ora ci viene. (Nono’s emphasis) Luigi Nono, Scritti e colloqui, Vol. 1, Angela Ida De Benedictis and Veniero Rizzardi eds. (Lucca: Ricordi, 2001), 490. I am very grateful to David Ogborn for providing me with the above translation.
 Marco Mazzolini, “Problematiche editoriali in Quando stanno morendo. Diario polacco N. 2,” 6-7. This unpublished paper was presented at a conference entitled “Problemi critico-testuali nelle edizioni dell’ultimo Nono” organised by the Biennale di Venezia (June 1993).
 Nono’s reasons for making these cuts are unknown, though his motivation may have involved formal considerations. By cutting 18 bars from section ‘a’ and 34 bars from section ‘c’ Nono endowed Part III with a balanced ternary form (‘a’ 36 bars; ‘b’ 22 bars; ‘c’ 36 bars). Furthermore, the length of these sections in terms of bar numbers establishes a set of proportionally symmetric relationships based on the golden mean. The total length of Part III is 94 bars: 94 x .618 = 58.09 (the length of sections ‘a’ + ‘b’). The relationship can also be established between sections ‘a’ and ‘b’. Thus the relationship obtaining between the length (measured in bar numbers) of section ‘a’ and the whole of Part III is the same as that obtaining between the length of sections ‘a’ and ‘b’. Of course these relationships only exist ‘on paper’. The tempo marks of the three sections of Part III (‘a’: quarter note = 45; ‘b’: quarter note = 35; ‘c’: quarter note = 45) indicate that the proportional relationships in terms of bar numbers were not meant to be perceived audibly. This does not however preclude the possibility that these proportionally symmetric relationships were part of the formal concept of this work. For more on the significance of proportionally symmetric relationships and specifically the golden mean in Nono’s late work, see Friedemann Sallis, “Le paradoxe postmoderne et l’œuvre tardive de Luigi Nono,” Circuit musiques contemporaines, Analyses 11/1 (2000): 69-86.
 Email received from Erika Schaller on 23 February 2006. The Archivio conserves an undated heliograph of the original version, in which cuts were made. For the moment though, we do not know whether these cuts occurred before or after the first performance of Quando stanno morendo.
 Throughout versions 1 and 2 all pitches have only one duration value: the whole note. The duration of silences separating these whole notes varies constantly. The silences have been eliminated from Example 1 in order to focus on pitch structure.
 For more information on ¿Donde estas hermano? as well as Nono’s long-standing interest in the culture and the political situation in Latin America, see Juan Maria Solare, “¿Donde estas hermano?: Die ewige Utopie. Die politische Haltung Nonos nach dem Streichquartett und seine Auseinandersetzung mit Lateinamerika”, Klang und Wahrnehmung. Komponist - Interpret - Hörer, Darnstädter Beiträge 41 (Mainz: Schott, 2001), 215-248.
 From here on, bar numbers refer to the published score unless otherwise indicated.
 The only discrepancy is the third note of the first trichord: the e'''. The corresponding note of the vocal line of section ‘a’ in Part II is an a'', an exception which in this case proves the rule.
 The first three tetrachords of the staff marked ‘III b’ on the sketch contain three pitches (E flat of the first tetrachord, e' flat of the second tetrachord and b' of the third tetrachord) that are not part of the contralto line. These pitches are however present in the violoncello part in bars 37, 39 and 41 respectively.
 Plate 2 presents a black and white reproduction of the page on which Nono used three different colours of ink: blue, red and black. The colours appear to indicate two or perhaps three chronologically distinct stages of composition. The same is true of Plate 3 below. The difference between black ink on the one hand and blue and red ink on the other hand can be distinguished in the lighter shades of grey and textural qualities of the pen and marker strokes on Plates 2 and 3. To be able to use this information to identify the layers of compositional activity presented, we would need to take a close look at colour reproductions.
 Heinz-Klaus Metzger (1981) was the first to make a substantial commentary on the impact of the scala enigmatica on Nono’s compositional technique in his study of the string quartet Fragmente-Stille, An Diotima (1980). Heinz-Klaus Metzger, “Wendepunkt Quartett?”, Musik-Konzepte Luigi Nono 20 (1981): 93-112. Since then, the publication of sketch material pertaining to the composition of Prometeo, Tragedia dell ascolto has demonstrated the extent to which Nono used the scala enigmatica in the composition of his last major achievement. See Massimo Cacciari ed. Luigi Nono: Verso Prometeo (Milan: Ricordi 1984); Philippe Albèra ed., Luigi Nono (Programme for Prometeo Tragedia dell’ascolto) (Paris: Contrechamps/Festival d’automne, 1987); Sallis, 75.
 Laurent Feneyrou, “Introduction”, Luigi Nono, Écrits (Paris: Christian Bourgois, 1993), 18.
 Denis Arnold, [Preface], Giuseppe Verdi, Quattro Pezzi Sacri (London: Eulenburg, 1973), III. Nielinger-Vakil suggests that Hermann Scherchen may have introduced Nono to this work in the late 1940s. See Carola Nielinger-Vakil, "Quiet Revolutions: H_lderlin, Fragments by Luigi Nono and Wolfgang Rihm," /Music & Letters/ 81/2 (May 2000): 250.
 The source of Metzger’s paraphrase was a workshop given by Nono in Bonn, presumably at the time Fragmente Stille, An Diotima was first performed in 1980. Metzger, 106-107. This view of the scala enigmatica in Fragmente Stille, An Diotima is shared by Jürg Stenzl, who states that in the string quartet the scale constitutes an underlying, inaudible structure, another secret world of the work [“¼una struttura profunda, inudibile direttamente, un altro “mondo segreto” dell’opera.”]. J. Stenzl, “Gli anni Ottanta”. Nono, Enzo Restagno ed. (Turin: EDT, 1987), 215. For his part Luigi Pestalozza has described the scale as basic material for the string quartet. L. Pestalozza, “Nono, parole e suono”, Luigi Nono, Scritti e colloqui, Vol. 2, Angela Ida de Benedictis and Veniero Rizzardi eds. (Milan: Ricordi, 2001), 610.
 Hermann Spree, “Fragmente Stille, An Diotima” Ein analytischer Versuch zu Luigi Nonos Streichquartett (Saarbrücken: Pfau, 1992), 28-29.
 Spree, 35. Indeed, Stefan Drees has noted that even in cases such as “Hay que caminar” sognando for two vioins (1989), where Nono specifically identified the scala enigmatica transposed to C as the source of the intervals performed quasi senza vibrato in the introduction to the published score, certain intervals in the third section (Leggio 3) do not belong to the C transposition of the scale. Drees suggested that these pitches were derived from the scale transposed to F. Stefan Drees, Architektur und Fragment. Zu späten Kompositionen Luigi Nonos (Saarbrücken: Pfau, 1998), 176.
 These intervals are prevalent in the scala enigmatica and sketches pertaining to the composition of Prometeo show Nono listing the number of such intervals that can be derived from the a scala enigmatica transposed to C. Sallis, 75.
 Given that the scala enigmatica is a seven-note diatonic scale, normal spelling presumes a different note name for each scale degree, implying note names such as B sharp, F flat, E double flat and C double sharp. For an example of normal spelling, see Example 2 above.
 Spree, 30.
 This sketch is published in Albèra ed., Luigi Nono, 1987, inside front cover.
 In the sketch for Prometeo, mentioned above, Nono spells the second and sixth degrees of the scale on F idiosyncratically in both ascending and descending forms of the scale (F sharp instead of G flat and E flat instead of D sharp). Neither of these degrees is present in compositional units 4 through 6.
 The second degree, which Nono spells idiosyncratically in his sketch (E natural instead of F flat) is not used in units 7 through 9.
 Mazzolini also identified this relationship in his 1993 conference. Mazzolini, 9.
 Interestingly units 23 and 24 constitute two transpositions of the same tetrachord, pc 4-16. This set happens to be the complement of pc 8-16, the set corresponding to the scala enigmatica. At present there is no evidence to suggest that this is nothing other than a curious coincidence.
 With regard to Nono’s string quartet, Spree has noted that broad sections of this work can be seen as constituting a grand, complex ‘Spiegelkabinett’, and goes on to point out that exact palindromes are in fact hardly ever found. Spree, “Fragmente - Stille, An Diotima” Ein analytischer Versuch, 35-36. I prefer to describe this aspect of Nono’s late work as mosaics made up of fragments of broken mirrors.
 Pascal Decroupet, “Floating hierarchies: organization and composition in works by Pierre Boulez and Karlheinz Stockhausen during the 1950s,” A Handbook to Twentieth-Century Musical Sketches, Patricia Hall and Friedemann Sallis eds. (Cambridge: Cambridge University Press, 2004), 146-7.