A Tribute To György Ligeti In His Native Transylvania

A Tribute to György Ligeti in His Native Transylvania 35

While Atmosphères is undoubtedly unusual and distinctive compared with
works from the classical concert canon, it is in some respects not so unusual.
The playing with sound masses and timbres is nothing new per se and has
been heard before, for example, in the music of Richard Wagner (the
Prelude to Das Rheingold from 1869) or Arnold Schönberg (Colors from his
Five Orchestral Pieces, Op. 16 from 1909). Moreover, and considering its use
as film music, it is very easy to fade it in and out at almost any point.

Rule 4 | Have the right position in the list of works

Note: ‘The type of devotion inspired amongst pubescent teenage girls for a
certain singer or band takes effect on the second or third single.’18 In the
same way, the devotion for Atmosphères took effect only after Apparitions
gained some attention a year earlier.

This leads on to ‘The Golden Rules of Chart Pop’ formulated in
Drummond and Cauty’s Manual which can – by the simple exchange or
removal of a few words – be turned into ‘Four Golden Rules of Successful
New Music’. The following quotations come from The Manual, with
removals (strikethrough) and inserts (italics) marked.

was a phonograph and an enormous collection of records, practically all of them
contemporary music. Kubrick told me that he thought he had listened to almost every
modern composition available on records in an effort to decide what style of music would fit
the film. Here, again, the problem was to find something that sounded unusual and
distinctive but not so unusual as to be distracting. In the office collection were records by the
practitioners of musique concrète and electronic music in general, and records of works by
the contemporary German composer Carl Orff. In most cases, Kubrick said, film music tends
to lack originality and a film about the future might be the ideal place for a really striking
score by a major composer.’ Cited in: Kate McQuiston, ‘“An effort to decide”: More Research
into Kubrick’s Music Choices for 2001: A Space Odyssey’, Journal of Film Music 3, no. 2 (2011):
146.

18 Drummond and Cauty, The Manual, xxi.

36 Heimerdinger: How György Ligeti had His Number One

(Golden) Rule 5 | Have an irresistible draw
Firstly, it has to have a dance groove sound that will run all
the way through the record piece and that the current 7″
buying generation concert-going public will find irresistible.

(Golden) Rule 6 | Be of reasonable duration
Secondly, it must be no longer than three minutes and thirty
seconds 10 minutes (just under 3’20 10 is preferable). If they
are any longer, Radio One daytime DJs orchestras will start
fading early or talking over the end, when the chorus is
finally being hammered home not be able to place it before a
symphony or a concerto in the first half of a concert programme –
the most important part of any record.

(Golden) Rule 7 | Have a characteristic structure
Thirdly, it must consist of an intro, a verse, a chorus, second
verse, a second chorus, a breakdown section, back into a
double length chorus and outro.

Even though Atmosphères is one slowly changing sound mass, it contains a
most dramatic breakdown section at the shift from section F to G with its
four high piccolos and the following double bass drone – not to mention the
smoothly brushed diminuendo at the end of the piece.

A Tribute to György Ligeti in His Native Transylvania 37

(Golden) Rule 8 | Have some extramusical content

Fourthly, lyrics extramusical content. You will need some, but
not many much.19

Extramusical associations for Atmosphères are not only suggested by the
piece’s French title but also by Ligeti’s commentary: ‘It is dedicated in
memoriam to Mátyás Seiber and contains moments of a requiem in
symbolic form.’20 What more can you do?

Rule 9 | Deal with emotions

The lyrics for the chorus must never deal with anything but
the most basic of human emotions. This is not us trying to be
cynical in a clever sort of way when we say ‘stick to the
clichés’. The clichés are the clichés because they deal with the
emotional topics we all feel. No records are bought in vast
quantities because the lyrics are intellectually clever or deal
in strange and new ideas. In fact, the lyrics can be quite
meaningless in a literal sense but still have a great emotional
pull.21

Clearly, one reason why Atmosphères is liked is its emotional charisma,
which is partly owed to its continuous flow of different states and its
specific dynamics – wide, narrow, shrill, grumbling, strong, tender, and so
on. In an interview with Monika Meynert in 1971, Ligeti talks about the role
of the emotional:

19 All quotations modified from Drummond and Cauty, The Manual, 50.
20 György Ligeti, Über Atmosphères (1963), in György Ligeti: Gesammelte Schriften, edited by
Monika Lichtenfeld, 2 vols. (Mainz, 2007), (= Publications of the Paul Sacher Foundation, 10),
2:181. ‘Es ist dem Andenken an Mátyás Seiber gewidmet und enthält in symbolischer Form
Momente eines Requiems.’
21 Drummond and Cauty, The Manual, xii–xvii.

38 Heimerdinger: How György Ligeti had His Number One

Monika Meynert: The avant-garde partly presented itself in a
way that one could believe they don’t have any feelings, they
work only mechanically. The process and the artificial are
given priority. But this is not the case with you.

György Ligeti: Yes. And I believe it is not the case with the
others. In the ’50s it was fashionable to emphasise the
speculative. So it was among my colleagues, whose music I
do like a lot, especially Stockhausen and Boulez. I believe
they also work emotionally.

Meynert: But you were one of the first to bring the emotional
into play again, and to set a precedent with it. Is this perhaps
because of your Hungarian origin?

Ligeti: No, No. Well, emotions are international.22

So much for clichés.

Rule 10 | Appear in another’s books

One main indicator for a canonical work is ‘[t]he number of books and
articles written about [it]. This indicates a certain level of interest and

22 Monika Meynert: Die Avantgarde hat sich teilweise so gezeigt, dass man glaubte, die
haben gar kein Gefühl, die arbeiten nur mechanisch. Das Machen, das Artifizielle steht doch
sehr im Vordergrund. Das ist bei Ihnen aber nicht der Fall.
György Ligeti: Nicht der Fall. Und ich glaub bei anderen auch nicht. Es war Mode in den
50er Jahren zu betonen das Spekulative. Es war bei meinen Kollegen, [...] deren Musik ich
sehr gern habe – also in den 50er Jahren waren vor allem Stockhausen und Boulez. Man sagte
sie arbeiten sehr spekulativ. Sie arbeiten genauso emotionell glaube ich.
Meynert: Das hängt nicht mit Ihrem... Sie waren ja einer der ersten, der das Emotionelle
eigentlich mehr ins Spiel brachte und betont hat und darin eigentlich auch Schule gemacht
hat. Liegt das vielleicht auch ein bisschen an Ihrer ungarischen Abstammung?
Ligeti: Nein. Nein. Also Gefühle sind international.
In: György Ligeti: Ein Komponist gibt Auskunft. Ein Portrait von Monika Meynert, television
broadcast, ZDF, first broadcast: 4 January 1970, 22:10, transcript by the author.

A Tribute to György Ligeti in His Native Transylvania 39

engagement, and implies at least the expectation of longevity.’ 23 Atmosphères
has been the subject of more than a dozen in-depth analyses and dozens of
other texts. Moreover, it is mentioned in almost every book on the history of
western music since the 1980s. As for the analyses and introductions from
the decade following the piece’s premiere, Ligeti actually took an active part
in the writing of many. First of all in the writing of musicologist Harald
Kaufmann, with whom Ligeti communicated extensively. Kaufmann’s
analysis was published in 1964 as the first comprehensive text on
Atmosphères. In this much-quoted text, Kaufmann picked up many
corrective suggestions from Ligeti who thereby influenced how his work
was received – not least including a change of the article’s title from
Klangfarbentextur unter dem Mikroskop to Strukturen im Strukturlosen.24

Rule 11 | Be complex, but hide it.

Now for Atmosphères’ place in a separate ‘new music’ canon. As Shreffler
describes it:

A separate canon of contemporary music esteemed by
composers, academics, and educated musicians has arisen; its
contents can be roughly deduced from university curricula
and (to a lesser extent) from the continuing segregation of
new music in record stores. This canon is based on a
historiography of twentieth century music as a series of
technical and formal accomplishments, starting with
atonality and ranging from the twelve-tone technique to
serialism to indeterminacy, polystylism, New Complexity,
and beyond. In this canon, which is a kind of mirror image of

23 Shreffler, ‘Musical Canonization’, 9.
24 See Harald Kaufmann, Strukturen im Strukturlosen: Über György Ligetis ‚Atmosphères’, in:
Spurlinien: Analytische Aufsätze über Sprache und Musik (Wien 1969), 107–17.

40 Heimerdinger: How György Ligeti had His Number One

the concert canon, Webern is ranked higher than Richard
Strauss; Boulez higher than Henze, and Ferneyhough higher
than Menotti.25

I might add: Ligeti is ranked higher than Penderecki, according to the often-
heard statement that Ligeti worked with ‘careful compositional calculation’,
instead of drawing blocks.26

And to quote Shreffler again, ‘although the new musical canon
shares many values with the mainstream one (such as a preference for a
“Werkekanon”, with works valued for their innovation, uniqueness, and
multifacetedness), it distinguishes itself by privileging intellectual qualities
and complexity over popularity.’ 27 The fact that Atmosphères is popular
though it is complex, and regarded as complex by academics even though it
is popular – in other words, that its complexity is not imposed upon the
audience but is there for anyone who wants to explore it, makes it an
extraordinary case in the new music business.

Congratulations!
☆ 12 October 1968: MGM’s soundtrack album of Stanley Kubrick’s 2001: A Space

Odyssey hits #1 in the Billboard charts’ Best-selling Classical LPs

☆2001: The 50th text on Atmosphères is published
☆2002: The 10th recording of Atmosphères is released
☆8 August 2014: The 500th (countable) performance of Atmosphères takes place

‘You are now at Number One. This is forever. It is now totally out of your hands.’28

25 Shreffler, ‘Musical Canonization’, 11.
26 ‘Was bei Penderecki als ein nur selten über den wirkungsästhetischen Zweck hinaus
reflektiertes Mittel eingesetzt ist, nahm im Œuvre György Ligetis als eine höchst
differenzierte Kunstidee Gestalt an. [...] Der Eindruck eines amorphen, in den Konturen
verwischten, zerfließenden Klanggebildes ergibt sich indessen durch ein sehr sorgfältiges
kompositorisches Kalkül.’ Hermann Danuser, Die Musik des 20. Jahrhunderts (Laaber, 1992), (=
Neues Handbuch der Musikwissenschaft 7), 388.
27 Shreffler, ‘Musical Canonization’, 11–12.
28 Drummond and Cauty, The Manual, 129.

A Tribute to György Ligeti in His Native Transylvania 41

BIBLIOGRAPHY

Danuser, Hermann. Die Musik des 20. Jahrhunderts. Laaber: Laaber Verlag, 1992.

Drummond, Bill, and Jimmy Cauty. The Manual (How to Have a Number One the Easy
Way). London: KLF Publications, 1988. Published in German as Das
Handbuch – der schnelle Weg zum Nr. 1-Hit (Berlin, 1998).

Heimerdinger, Julia. Sprechen über Neue Musik. Eine Analyse der Sekundärliteratur und
Komponistenkommentare zu Pierre Boulez’ Le Marteau sans maître (1954),
Karlheinz Stockhausens Gesang der Jünglinge (1956) und György Ligetis
Atmosphères (1961). Dissertation, Halle University, 2013.
http://digital.bibliothek.uni-halle.de/id/1801704.

Iverson, Jennifer. ‘Historical Memory and György Ligeti’s Sound -Mass Music 1958–
1968’. PhD diss., University of Texas at Austin, 2009.

Kaufmann, Harald. ‘Strukturen im Strukturlosen: Über György Ligetis Atmosphères.’
In Spurlinien: Analytische Aufsätze über Sprache und Musik, 107–17. Wien:
Lafite, 1969.

Ligeti, György. György Ligeti: Gesammelte Schriften, edited by Monika Lichtenfeld. 2
vols. Mainz: Schott, 2007.

Ligeti, György. Sketches of Atmosphères. György Ligeti Collection, Paul Sacher
Foundation Basel.

McQuiston, Kate. ‘“An effort to decide”: More Research into Kubrick’s Music
Choices for 2001: A Space Odyssey’. Journal of Film Music 3, no. 2 (2011): 145–
54.

Meynert, Monika. ‘György Ligeti: Ein Komponist gibt Auskunft. Ein Portrait von
Monika Meynert’. Television broadcast, ZDF, first broadcast: 4 January
1970, 22:10.

Michels, Ulrich. dtv-Atlas zur Musik: Tafeln und Texte. Bd. 2. Munich: Deutscher
Taschenbuch, 1994.

Nordwall, Ove. György Ligeti: Eine Monographie. Mainz: Schott, 1971.

Shreffler, Anne C. ‘Musical Canonization and Decanonization in the Twentieth
Century’. Published in German translation as: ‘Musikalische Kanonisierung
und Dekanonisierung im 20. Jahrhundert’, in Der Kanon der Musik: Theorie
und Geschichte. Ein Handbuch, edited by Klaus Pietschmann and Melanie
Wald-Fuhrmann, 606–25. Munich: Richard Boorberg, 2013.



The Significance of Timbre as a Structural
Component in Works by György Ligeti

MICHAEL SEARBY

The Hungarian composer György Ligeti is best known for his music which
primarily explores texture – especially in the works of the 1960s like
Atmosphères, Lux Aeterna, and Lontano. Even in his much later works such as
the Piano and Violin Concerti, Ligeti’s distinctive use of texture has a
prominent position in the structures of these works. In what follows, I will
explore the contention that Ligeti’s use of timbre is just as significant as his
use of texture, and that timbre can equally be seen to have a structural role
in many of his works. It is the way that the composite mixture of timbres
evolve within a piece that is as important as the resulting textures
themselves. Micropolyphony is one of Ligeti’s best-known compositional
techniques; it consists of multiple layers of arhythmic canons which create a
complex polyphonic texture. However it is actually a very simple process
and this process itself is not especially significant in shaping the overall
sound of a work – rather it is the timbres and dynamics that are more
significant. Even the specific pitches of these micropolyphonic works could
be changed without great detriment to the result so long as the generating
linear patterns were similar in terms of interval. Harrison Birtwistle said
that you could change all the pitches of his work but not fundamentally
change the resulting music for exactly those reasons – it is the specific

44 Searby: The Significance of Timbre

timbres and textures being used that is important for the effect and impact
of the work.

One significant question this raises is how we can analyse the use of
timbre in a work, and particularly how timbre can be used to generate
structure? One possibility would be to create a spectral graph of a work to
show what frequencies are being used at each given point and how they
evolve. But the ones I have seen are difficult to use, because they only show
general shifts in frequency at the macro level. They cannot reflect the
complexity of the music’s sound: how we actually hear the music.
Alternatively, the analyst could describe how the timbres and different
timbral combinations actually sound – exploring their qualities and
characteristics; however the danger with this approach is that it can become
quite subjective and overly descriptive. Any relevant analytical method for
musical timbre needs to relate to how the music is experienced by the
listener but avoid simple description.

I want to explore how we can write about timbre in musical analysis
through examining two of Ligeti’s works. In the late 1950s, Ligeti was
highly influenced by the use of total serialism – in spite of his controversial
public rejection of the approach – so he was aware of the idea of separating
various parameters of music and treating them individually. The idea of
using timbre as one of the serialised parameters along with pitch, dynamics
and articulation, was current at the time, and this is directly related to
Webern’s concept of Klangfarbenmelodie – the creation of a melody simply
from contrasts in tone colour. The world of Webern’s pointillist music has
quite clearly influenced Ligeti’s approach to timbre: for example, the end of
the first movement of his second String Quartet (1968) from bar 84 sounds
almost like a Webern quotation in that it is as much a melody of timbres as
it is one made up of pitches.

A Tribute to György Ligeti in His Native Transylvania 45

Jennifer Iverson (2010) has made some useful observations about
how Ligeti’s music in the early 1960s is directly related to his earlier
experiences in the Cologne Electronic Music Studio. To create sound with a
specific timbre in the studio at that time, you had to add sine waves
together through additive synthesis – building up each sound from the most
basic sonic building blocks. Ligeti ultimately abandoned the studio because
of the time and effort it took to create each sound, but Iverson suggests that
the way that clusters are generated in works such as Atmosphères can be
directly related to the structure of his electronic piece Pièce Électronique No. 3
which he was not able to realize during his lifetime due to its complexity
(subsequently it has been realized). This suggests that Ligeti was thinking
about timbre in quite a controlled and structural fashion even in his non-
electronic works.

In an article entitled ‘Timbre and composition – timbre and
language’, Pierre Boulez suggests that timbral complexity can destroy the
unity of the musical line. He states that ‘beyond a certain speed, a
succession of chords will be perceived as a mixture of timbres rather than as
a superimposition of pitches’ (1987, 168). In other words, Boulez is claiming
that a fast succession of chords will not be heard as a harmonic progression,
but rather as a series of evolving and contrasting timbres. This is certainly
the case with Messiaen’s chains of harmonies, for example in the second
movement of his Quartet for the End of Time, which are primarily colouristic
or timbral rather than harmonically functional – they are essentially static.
Boulez states that ‘to me the functional possibilities of timbre only seem
valid if they are linked to language and to the articulation of a discourse
through structural relationships; timbre both explains and masks at the
same time’ (1987, 170). What he is suggesting here is that timbre can only be
used functionally if it is linked to the musical language and narrative, but if
it is not in alignment with these aspects it can mask musical structures. He
points out that in Webern’s Symphony, Op. 21, the use of Klangfarbenmelodie

46 Searby: The Significance of Timbre

in the second canon of the first movement disrupts the identity of the line,
and thus the structural coherence. Therefore in this case the use of timbre
does not align with the basic structure of the work and has an undermining
effect. In this case it is likely that Webern was not so interested in whether
or not the serial structure could be heard, but rather he was more interested
in the timbral interplay.

Ligeti, in an interview with Josef Häusler in 1968, states that his
‘Atmosphères is a composition in tone-colours par excellence and is closely
connected with Schoenberg’s third orchestral piece from his opus 16
[Farben]’ (Ligeti 1983, 86). He also suggests that in his later works, such as
the ‘Cello Concerto, Lontano, and Lux Aeterna, the ‘tone-colours no longer
have predominance in articulating the form’ (86). A pertinent question is:
does Ligeti really no longer make use of ‘tone-colours’ or timbre in these
later 1960s works in the articulation of their form? Or are there still times in
his music when the timbre has a major role in the structure?

To examine this question I am now going to analyse the first part of
the seventh movement from Ligeti’s Ten Pieces for Wind Quintet (1966). This
virtuosic chamber work explores many different ways of developing and
shaping material, and deals with the problem of how to make use of
micropolyphony when there are only five instrumental lines. The seventh
movement is in two halves: the first half up to bar 38 deals with five note
chromatic clusters (pitch class set 5-1) mostly in very short note durations.
The process that Ligeti uses here is one in which the pitches of the chord are
rotated around the ensemble having the effect of transforming its overall
sound because each time the timbral mix is different. Each different iteration
of the chord sounds like a new one because of the transformation of the
resulting timbral mix. It is a form of additive synthesis with each instrument
functioning like one oscillator – although of course their individual timbre is
much more complex than that of a sine wave. With five different

A Tribute to György Ligeti in His Native Transylvania 47

instruments there are 120 different variants possible for a five-note chord
(5!) but Ligeti only uses ten versions of the first chord. The chord at bar 30 is
the same pitch class set but transposed and opened out in terms of register.
One underlying pattern is a tendency for instrumental parts to move
gradually upwards in semitones until they reach the top note B at which
point they jump down to the bottom note G. This pattern breaks up after a
while and becomes less uniform although the B to G downward leap is still
a feature of the movement – this is indicated in Figure 1.

Figure 1. Ten Pieces for Wind Quintet, mvt. 7, bb. 1–23; reduction and timbral
structure

Each timbral version of the opening cluster is indicated by A1, A2,
and so on. What appears to break up this pattern is when an instrument’s
pitch seems to stick and doesn’t move as expected – thus impacting on the
movement of the other instruments. For example, at bars 5-6 the clarinet’s
B♭ repeats for the A1 and A2 chords, which has an impact on the horn’s
pattern; it then repeats A♭ for A3 and A4, while the horn remains ‘stuck’ on

48 Searby: The Significance of Timbre

G. On chords A4 to A5, the bassoon’s Bs are also ‘stuck’, after which point
all the instruments’ parts become more mobile with no consistent pattern
other that the shift from B to G. The structure of how this section evolves
seems to be like a game in which there are five squares for each pitch, and
each player has to move from square to square after each chord. If a player
stays on their square (pitch) then this disrupts the process.

These observations show that Ligeti seems to be playing with the
idea of using the evolution of timbre as a main structural feature for this
section. When listening to this movement, the chords sound as if they are
actually changing in terms of pitch, but this is an illusion created purely
through evolving timbral mixtures and not changes of the harmony. This
may be partly caused by the way that the ear tends to focus on the upper
pitch of a chord, which here changes most frequently. Boulez points out that
Schoenberg creates a similar effect in ‘Eine Blasse Wäscherin’ from Pierrot
Lunaire in which the top notes of the chords keep switching between
instruments ‘to form a melody of timbres which emerges from the harmony’
(Boulez 1987, 169).

Ligeti’s Hamburg Concerto completed in 2002 is his last major work,
and is most notable for his use of natural horns which add untempered
‘dirtiness’ (a term Ligeti liked to use to described untempered harmony) to
the harmonic sound world. The fifth movement ‘Spectra’ uses elements of
Ligeti’s past music through the way it uses timbre as its main structural
feature and thus harks back to works such as Atmosphères. The harmony is
cloudy and rich through the combination of the non-tempered upper
partials of the natural horns’ harmonic series and also untempered notes in
the orchestra. In this movement, the natural horns are all pitched in E in
contrast to the solo valved horn, which provides dissonant counterpoint
against the natural horn quartet’s harmony. Each resulting chord seems to
be independent and the progression sounds quite unpredictable – it is

A Tribute to György Ligeti in His Native Transylvania 49

therefore the particular mix of timbres generated that are significant rather
than the resulting harmony. The movement is structured by chorale -like
horn passages interspersed with echo-like responses from the rest of the
orchestra, the nature of which also focuses on timbres rather than functional
harmony. The two chorale groups, horns and the rest, overlap with each
other ensuring continuity in the movement. The climax is created by the
horns canonically accelerating at bar 16 through their two contrasting
harmonic series of E and B♭ into a high dissonant chord (F, E +flattened D)
in the horns supplemented by (G♭, G, A, B♭) in the orchestra at bar 17. The
movement ends on a defiant orchestral D♭ in octaves that creates a
cadential-like resolution to the dissonance – a throwback gesture from
Ligeti’s works of the 1960s which often make use of such devices. The
concerto as a whole seems to reflect back on Ligeti’s preceding output in
terms of textural and stylistic foci. However, in ‘Spectra’ there is also an
experiment with complex microtonal harmony, but this creates a series of
rich complex timbres rather than functional harmonic progressions.

This is an exploratory examination of how Ligeti uses timbre as a
structural element in music beyond his early textural works such as
Atmosphères and his electronic music. I have shown that even in the later
music of Ten Pieces for Wind Quintet and the Hamburg Concerto, timbre plays
a very significant role in determining structural aspects of the music and are
not simply a subordinate surface feature. They are in fact, in Boulez’s words,
part of the work’s musical language and discourse. The two examples of
music by Ligeti I have explored are movements in which the timbral
dimension is both the most significant aspect of these movements’
structures and also the element the listener is most likely to focus on. In both
cases, Ligeti appears to be treating the instruments almost as if they were
electronic sources in the way he builds up timbral mixtures, and this
produces timbrally complex and aurally fascinating music. Ligeti’s
statement that after Atmosphères tone colours no longer has predominance in

50 Searby: The Significance of Timbre

structuring his works does not seem to be true for the works examined, but
rather it seems more accurate to say that in his later music the use of tone
colours to structure his music becomes more integrated into an increasingly
varied musical language.

BIBLIOGRAPHY

Boulez, Pierre. 1987. ‘Timbre and Composition – Timbre and Language’.
Contemporary Music Review 2(1): 161–71.

Iverson, Jennifer. 2010. ‘The Emergence of Timbre: Ligeti’s Synthesis of Electronics
and Acoustic Music in Atmosphères’. Twentieth-Century Music 7, no. 1
(March): 61–89.

Ligeti, György. 1961. Atmosphères for Large Orchestra, Vienna: Universal.
Ligeti, György. 1957 –1958. Pièce Électronique No. 3. Kees Tazelaar and Johan van

Kreij, 1995–1996, His Master’s Noise: The Institute of Sonology: BVHAAST
CD06/0701.
Ligeti, György. 1968. Ten Pieces for Wind Quintet. Mainz: Schott.
Ligeti, György. 1968. Second String Quartet. Mainz: Schott.
Ligeti, György. 1983. Ligeti in Conversation. London: Eulenberg.
Messiaen, Olivier. 1942. Quartet for the End of Time. Paris: Durand.
Schoenberg, Arnold. 1912. Pierrot Lunaire. Vienna: Universal.
Webern, Anton. 1929. Symphonie, op. 21. Vienna: Universal.

György Ligeti et l’image sonore de quelques
intuitions mathématiques

AMALIA SZŰCS-BLĂNARU

1 Introduction
György Ligeti est l’un des plus intéressants représentants de la musique
d’avant -garde de l’après-guerre, en particulier sous l’angle de la relation
entre musique aux mathématiques. Il a réussi à transfigurer des concepts
mathématiques sans recourir à des calculs rigoureux mais, comme il l’avoue
lui-même, en pensant intuitivement d’une manière mathématique. Les
œuvres auxquelles nous nous référons ci-dessous représentent, peut-être,
l’étape décisive qui distinguera le compositeur de ses contemporains. Sa
nécessité d’indépendance de tout groupe et de toute orientation esthétique,
associée à un esprit de rébellion et à une subtile ironie fut en permanence la
toile de fond de son évolution musicale.

2 Des pas dans la genèse de micropolyphonie
Peu avant 1956, Ligeti prend conscience que la pensée issue de ce que l’on
pourrait appeler le « système post-bartokien » et l’atmosphère politique de
l’après-guerre en Hongrie ne lui laissent pas assez de liberté créative. La

52 Szűcs-Blănaru: György Ligeti et l’image sonore

révolution hongroise déclenchera du même coup la « révolution » du
créateur lui-même.

Les premières expériences musicales faites dans la société
occidentale le plongent dans l’extrême avant-garde, néo-sérielle d’une part
et de la musique électronique d’autre part. Ce fut une étape décisive. Dans
la décennie à venir, il posera les bases de la micropolyphonie. Il fait d’abord
une expérience dans le Poème symphonique pour 100 métronomes : celle de ne
retenir strictement que les aspects rythmiques en éliminant tout autre
paramètre du son musical. Et ensuite seulement il réintroduira les autres
paramètres et envisagera aussi la question du timbre. C’est alors
qu’apparaissent successivement la première étude pour orgue Harmonie
(1967), Continuum pour clavecin (1968) et Coulée – la deuxième étude pour
orgue (1969). L’idée est d’obtenir des sons séparés dans le cadre d’une
structure de si dense texture que le son musical individuel perd les
caractéristiques qui l'individualisent pour devenir un atome dans un tissu
épais.

La formation intellectuelle de Ligeti est fondamentalement
cartésienne, mathématique. Même quand il affirme qu’il n’utilise pas les
mathématiques dans la pensée créatrice, elle est présente dans les couches
les plus profondes de l’idée première. L’utilisation des concepts
mathématiques intuitifs, parfois avant leur apparition, rend plus fascinante
la création de Ligeti. En outre, cela permet l’analyse mathématisée des
œuvres. Le calcul de la dimension fractale illustre d’une manière pertinente
l’exception constituée par ces œuvres.

À propos du Poème symphonique, l’auteur dit: « J’ai donc imaginé de
créer une grille rythmique si dense d’abord qu’elle en paraîtrait presque
continue : ce qui implique brouillage et désordre. Pour ce faire, il me fallait
un nombre suffisamment important de métronomes, le chiffre de cent ne
représentant qu’une estimation. » (Ligeti, 2013, 191) En exploitant les

A Tribute to György Ligeti in His Native Transylvania 53

possibilités techniques du clavecin dans Continuum, le compositeur conclut :
«Bien que l’on puisse nettement entendre le pincement des cordes, qui ont
un effet plus ponctuel que la frappe des marteaux au piano, ces points
fusionnent en des lignes. La tension entre les attaques ponctuelles et la
fusion en un continuum est fondamentale pour la forme musicale.» (Ligeti,
2013, 249) Il en résulte que dans les deux cas, la haute densité d’évènements
sonores est cruciale pour atteindre l’effet d’espace sonore continu. La
différence est que, par les métronomes elle est construite verticalement –
plusieurs sons avec des vitesses différentes, tandis que pour le clavecin la
densité résulte de la vitesse d’écoulement de la séquence sonore. La pensée
musicale de Ligeti était indissociable de l’esprit et de la rigueur des
mathématiques, lorsqu’il a utilisé des ensembles de sons ponctuels, comme
le compositeur les appelle, pour atteindre la texture micropolyphonique
continue.

3 Similitudes
3.1 La rythmique de l’isochronie aux rythmes illusoires

Une autre caractéristique que l’on retrouve dans les deux œuvres est celle
qui consiste à opérer avec des pulsations isorythmiques. Le Poème
symphonique est une simultanéité de différentes impulsions égales. En fait les
pulsations métronomiques sont regroupées en 10 sous-ensembles disjoints
basés sur des critères de la divisibilité. (Dans la première ligne du tableau 1
les groupes sont numérotés de 1 à 10 et chaque colonne contient les valeurs
de battement des métronomes.)

54 Szűcs-Blănaru: György Ligeti et l’image sonore
Tableau 1. Les pulsations métronomiques groupées par des critères de

divisibilité.

Chaque groupe produit un rythme non-rétrogradable avec une période qui
se répète tout au long de l’œuvre. La période appropriée de chaque groupe
est indiquée au tableau 2.

Tableau 2. Les périodes des groupes de métronomes

Dans les graphiques des figures 1-7 nous avons représenté le
nombre de pulsations pour chaque groupe sur une durée de 6 secondes qui
corresponde à la période plus longue – celle du premier groupe. Sur l’axe
horizontal est représenté le temps mesuré en secondes et sur l’axe vertical le
nombre de battements du métronome. L’image met en évidence le moment
initial (le premier battement des métronomes) puis la fin de la période
quand le nombre des battements est maximal, mais aussi un moment
intermédiaire de maximum local. La perception auditive sera concentrée sur
les trois moments d’accents contre le frottement quasi permanent (continu)
des autres métronomes. Chaque graphique (groupes 1 – 6) est précédé d’un

A Tribute to György Ligeti in His Native Transylvania 55

tableau avec l’intervalle de temps entre deux battements successifs et le
nombre des battements dans une période.

Tableau 3. Les intervalles de temps et le nombre des battements – groupe 1

Figure 1. Les battements des métronomes – groupe 1

Nous avons procédé de la même manière avec les calculs et les graphiques
pour les sous-ensembles suivants.

Tableau 4. Les intervalles de temps et le nombre des battements – groupe 2

56 Szűcs-Blănaru: György Ligeti et l’image sonore
Figure 2. Les battements des métronomes – groupe 2
Tableau 5. Les intervalles de temps et le nombre des battements – groupe 3

Figure 3. Les battements des métronomes – groupe 3
Tableau 6. Les intervalles de temps et le nombre des battements – groupe 4

A Tribute to György Ligeti in His Native Transylvania 57
Figure 4. Les battements des métronomes – groupe 4

Tableau 7. Les intervalles de temps et le nombre des battements – groupe 5

Figure 5. Les battements des métronomes – groupe 5
Tableau 8. Les intervalles de temps et le nombre des battements – groupe 6

58 Szűcs-Blănaru: György Ligeti et l’image sonore
Figure 6. Les battements des métronomes – groupe 6

Les quatre derniers groupes ont un comportement identique qui s’explique
par la similitude de relation entre les éléments. (Figure 7)

Figure 7. Les battements des métronomes – groupe 7 – 10

Continuum a une trame : c’est une texture de simples croches (selon
la notation de la partition). Ligeti utilise deux procédés différents pour
obtenir des résultats comparables. La similitude avec le Poème symphonique
se reflète dans les rythmes illusoires que nous percevons. Dans Continuum
l’illusion continue avec la « mélodie additionnelle » qui n’est pas notée dans
la partition. En fait, les premiers sons de chaque formule de main droite et
de main gauche ressortent particulièrement. Également, à chaque
changement de formule, le son nouveau venu se distingue. La simultanéité
et le décalage de ces sons accentués réalisent les rythmes illusoires
mentionnés précédemment. Dans les exemples suivants, chaque graphique
représente les sons initiaux des formules, et on peut observer comment ils
sont d’abord positionnés d’une façon relativement stable les uns par rapport
aux autres, puis comment cet écart se modifie. Sur l’axe horizontal la croche

A Tribute to György Ligeti in His Native Transylvania 59

est la durée étalon, sur l’axe vertical sont représentées les hauteurs des sons.
(Figures 8, 9)

Figure 8. Continuum – mesures 13–16, partition et les sons initiaux des formules

Figure 9. Continuum – mesures 17–20, partition et les sons initiaux des formules

3.2 La génération algorithmique de la forme musicale

Il y a une somme de traits communs aux deux œuvres. Un aspect important
est la genèse algorithmique (stricte) de la forme dans Poème symphonique et
quasi algorithmique dans Continuum. Dans les deux cas, il existe une
relation entre ordre et désordre d’une part et entre discret (ponctuel) et
continu d’autre part.

La rigueur de la façon de développer le Poème symphonique consiste
en une réitération de la même impulsion, théoriquement à l’infini.

60 Szűcs-Blănaru: György Ligeti et l’image sonore

Pratiquement, seule la limitation temporelle de fonctionnement des
mécanismes modèle la forme qui commence comme une explosion,
continue d’une manière perçue comme chaotique et se termine avec un
relâchement dans un decrescendo jusqu’à l’arrêt du dernier métronome.

Dans un modèle mathématique, limité à 39 métronomes, et utilisant
tous les coups de métronomes possibles, les six premières secondes se
passent comme dans l’image ci-dessous (Figure 10), où nous retrouvons la
réunion des ensemble représentés dans les figures 1-8. Il est facile de
remarquer le fait que les pulsations sont bien ordonnées mais que la densité
est trop élevée pour nos oreilles et qu’il y a trop peu de temps entre les
battements. Cela crée une illusoire impression de chaos.

Figure 10. Poème symphonique pour 100 métronomes - les coups de métronomes
pour les six premières secondes

Dans Continuum, Ligeti applique à la fois plusieurs algorithmes
indépendants, tant pour la synchronie que pour la succession des deux voix.
Partant d’un trémolo de tierce mineure et lui appliquant des algorithmes, il

A Tribute to György Ligeti in His Native Transylvania 61

transforme l’oscillation entre les deux sons en des formules allant jusqu’à
cinq sons différents dans une métamorphose continue. Les modalités de
transformation sont :

- ajout ou suppression d’un son dans l’extrémité supérieure ou
inférieure de la formule

- modification d’un intervalle externe ou interne à la formule
- chromatisations par l’insertion dans l’intervalle, et à l’inverse – par

l’élision d’un son interne à la formule.

Et voilà donc comment se présentent les formules en succession simple
(sans répétition) pour la main droite. (Figure 11) Dans l’images suivante
nous avons représenté sur l’axe vertical la hauteur des sons (de La2 = 1
jusqu’à do5 = 88) et sur l’axe horizontal les formules (numérotées) dans la
succession réelle sans répétitions.

Figure 11. Continuum - les formules en succession simple (sans répétition) pour la
main droite

De la même manière on peut obtenir l’image des formules pour la main
gauche.

62 Szűcs-Blănaru: György Ligeti et l’image sonore

3.3 La dimension fractale

Le graphique présenté pour le Poème symphonique a été associé à l’image de
« poussière de Cantor » obtenue en coupant un segment en trois et en
gardant les deux côtés extrêmes. À leur tour, les segments obtenus sont
soumis aux mêmes opérations et on peut continuer, en théorie, à l’infini. Le
chevauchement des tempi avec diviseur commun (voir figure 1) place d’une
manière similaire les points correspondants du graphique. La répétition des
périodes complètes est aussi une itération théoriquement infinie, qui prend
néanmoins fin en raison de la durée limitée de l’exécution. En outre, dans le
Poème symphonique pour 100 métronomes nous avons une superposition de
groupes quasi indépendants.

On peut imaginer le plan (la surface) du graphique comme un
rectangle contenant les points associés à chacun des 39 tempi des
métronomes (axe vertical) et aligné à un intervalle de 0,001 seconde sur une
durée de 6 secondes (l’axe horizontal) soit un total de 234 039 points. Parmi
eux, seuls sont conservés les points correspondant aux battements des
métronomes, en particulier les 422 points représentés dans le graphique.
Nous appliquons la formule et effectuons les calculs. Il en résulte:

Autrement dit, le Poème symphonique pour 100 métronomes a, dans sa
représentation graphique, une dimension fractale de 0.49
approximativement (quelque chose entre le point et la droite).

Le calcul de la dimension fractale pour Continuum permet des
approches multiples. L’une d’elles met en évidence les sons initiaux des
formules mélodiques qui se dégagent de l’ensemble. Par souci de cohérence,
nous choisissons le même calcul en tenant compte de l’inclusion des deux
œuvres dans la même catégorie de composition. Parmi la totalité du son et
parmi tous les points, nous considérons les sons d’attaque pour chaque

A Tribute to György Ligeti in His Native Transylvania 63

motif qui deviennent pour nous les points conservés. Avec la même formule
on obtient la dimension fractale suivante :

La dimension fractale calculée pour Continuum est aussi plus petite que 1,
mais plus proche de 1, ce qui signale que l’illusion de la continuité est plus
forte que dans le cas du Poème symphonique.

4 Particularités
4.1 Poème symphonique – l’abstraction du son musical

Même s’il a été conçu en plein essor de l’avant-garde d’après-guerre, le
Poème symphonique pour 100 métronomes parvient à nous surprendre encore
aujourd’hui. Le concept de son musical a été élargi avec l’électro-acoustique,
le piano préparé et d’autres aspects qui ont apporté de nouvelles
dimensions au timbre. Mais le métronome, ordonnateur et coercitif qui n’est
qu’un outil lorsqu’il est utilisé strictement pour l’étude de la musique,
devient le moteur du désordre. Obsédé par les romans de Gyula Krúdy,
Ligeti substitue des métronomes aux horloges, et réussit à travers le tic-tac
monotone à donner vie à un espace dynamique dont nous ne percevons
qu’une infime partie… Et à travers cette percussion subtile il remet en
question le son musical avec ses quatre qualités enracinées dans la
conscience des musiciens.

4.2 Continuum – allusions à l’architecture de la musique
classique

De la combinaison des deux successions, en répétant les cellules mélodiques
dont le nombre de répétitions est différent aux deux mains du musicien,
Ligeti obtient l'architecture suivante. (Figure 12) (Sur l’axe horizontal se

64 Szűcs-Blănaru: György Ligeti et l’image sonore

trouve l’unité de mesure (la croche), sur l’axe vertical apparaissent les
hauteurs des sons.)

Figure 12. Continuum - l'architecture

La représentation ne contient que les lignes de contour extérieur,
mais il est suffisamment suggestif pour voir la tripartition de la forme. Les
trois sections sont générées de la même manière, bien qu'elles aient des
comportements différents et conduisent à la forme ternaire. Un tel type
d’évolution peut être perçu aussi dans Atmosphères, c’est une constante
stylistique. À y regarder de plus près, nous pouvons l’associer à la forme
qui donne la mesure du classicisme musical. Si cette référence est
intentionnelle, ironique voire caricaturale ou seulement un simple réflexe
provenant des couches profondes de l’inconscient, nous ne le savons pas.
Mais l’allusion à la forme sonate est tout à fait évidente. Les trois sections
correspondent à l’exposition, au développement et à la reprise, dans la
mesure où l’on trouve des caractéristiques qui sont similaires à celles qu’on

A Tribute to György Ligeti in His Native Transylvania 65

peut voir dans le schéma suivant (tableau 9).

Tableau 9. Les sections de la forme sonate et la correspondance avec Continuum

Ci-après, nous nous permettons de nommer mesure un segment de
16 croches compris entre deux lignes en pointillé dans la partition, l’objectif
étant de faciliter l’orientation du lecteur.

La première section, jusqu’à la mesure 91, commence par une tierce
mineure sur laquelle le compositeur insiste pendant plus de 9 mesures. Il
continue avec des transformations, chaque formule ayant un certain nombre
de répétitions, probablement aléatoires. Par l’effet des transformations, la
tierce devient quinte juste qui à son tour devient seconde ; ensuite apparaît
la sixte mineure avant que ne survienne une stabilisation sur une quinte
juste qui, avec la pédale de la main gauche, donne un accord majeur. Cette
quinte comme résultat des transformations successives nous rappelle la
modulation à la dominante de la fin de l’exposition d’une forme sonate.

La section médiane, qui commence à la mesure 92 et se termine à la
mesure 153, est caractérisée par l’éloignement des deux plans mélodiques
dans les registres extrêmes du clavecin et la prédominance de l’attaque
simultanée. En outre, l’ambitus des formules va jusqu’à l’octave. L’image
d’ensemble diffère de la première section, elle peut être rapprochée du
développement qui apporte ses propres thèmes, outre qu’elle est instable du

66 Szűcs-Blănaru: György Ligeti et l’image sonore

point de vue tonal (nombreuses modulations). Cette section se termine
d’une manière ambiguë par une pédale sur do# qui a un rôle de sensible.

À la mesure 154 la succession des intervalles présentée au début de
l’œuvre est reprise sans insister (quantitativement) sur les répétitions, mais
en suivant le même chemin de développement vers la quinte. Pour
compléter l’image associée à la reprise, le retour à la tonalité de base est
associé à une sorte d’implosion : l’unisson (mesures 185 – 204).

5 Conclusions

Il semble que György Ligeti a bénéficié d’une forme de synesthésie (relation
son–couleur) plus complexe que d’ordinaire chez d’autres compositeurs.
Chez lui, même les mathématiques sont associées à la musique et ce, non de
manière « naïve », selon lui, mais dans une sorte de consubstantialité. Cela
nous autorise à penser que le Poème symphonique pour 100 métronomes (1962)
anticipe sur la fondation de la théorie du chaos. Edward Lorenz publie en
1963 l’article Deterministic Nonperiodic Flow –; c’est la naissance de cette
théorie fascinante. Et si les deux évènements sont relativement proches,
nous avons l’exemple de la structure quasi fractale de Continuum composé
sept ans avant que Benoît Mandelbrot définisse le terme, soit en 1975.

Le Poème symphonique pour 100 métronomes et Continuum représente la
première étape expérimentale de la solution musicale d’un problème unique.
La micropolyphonie et la texture sont quelques caractéristiques de la
musique de Ligeti de cette période. Nous avons vu lors de l’analyse que cela
résulte de différentes combinaisons de rythmes élémentaires. La
superposition durable de deux simples rythmes non proportionnels,
conduit à la transformation progressive de la résultante. Pour les deux
œuvres, l’association avec des créations visuelles appartenant à l’op’art
(optical art) est presque instantanée. L’illusion acoustique est aussi
fascinante que l’illusion visuelle.

A Tribute to György Ligeti in His Native Transylvania 67

Comme le roi Midas, dans la mythologie grecque antique,
transforme en or tout ce qu’il touche, Ligeti transforme en musique tout
qu’il a imaginé. Les deux œuvres présentées ont des caractéristiques
individuelles qui les distinguent, mais constituent ensemble l’image sonore
d’idées mathématiques magnifiques.

Revision of French text by Pierre Michel and Jean-François Antonioli

BIBLIOGRAPHIE

Chemilier, Marc. 2001. «György Ligeti et la logique des textures.» Analyse musicale,
nr. 38/2001, p. 75–85.

Duchesneau, Louise, and Wolfgang Marx, dir. 2011. György Ligeti: Of Foreign Lands
and Strange Sounds. Woodbridge: The Boydell Press.

Harley, James. 1994. “Algorithm Adapted From Chaos Theory: Compositional
Consideration.” Proceedings of the International Computer Music Association
(1994): 209–12. http://hdl.handle.net/2027/spo.bbp2372.1994.054 (consulté
29.12.2015).

Ligeti, György. 1970. Continuum. Mainz, Edition Schott.

Ligeti, György. 2013. L’atelier du compositeur. Genève, Edition Contrechamps.

Salter, Jonathan. 2009. “Chaos in Music: Historical Developments and Application
to Music Theory and Composition.” DMA diss. UNC Greensboro.
https://libres.uncg.edu/ir/uncg/f/Salter_uncg_0154D_10135.pdf (consulté
05.01.2016).

Shafer, Jennifer. 2010. “The Two-Part and Three-Part Invention of Bach: A
Mathematical Analysis.” Honors Project, East Texas Baptist University.
https://www.etbu.edu/files/2113/8608/9827/Jennifer_Shafer.pdf (consulté
08.01.2016)

Szűcs-Blănaru, Amalia. 2016. « Poème symphonique pentru 100 de metronoame sau
un principiu generator de formă. » Studii de muzicologie vol. XI. Iași, Editura
PIM, p. 213–22.



György Ligeti and Harry Partch:
Microtonal Adventures in the
Hamburg Composition Class

MANFRED STAHNKE

From the 1960s on, György Ligeti was, as we all know, extremely interested
in new ways of musical thinking which could lead away from the
mainstream avant-garde related to the Darmstadt School around
Stockhausen or Boulez. Entering his class in Hamburg, in October 1974, I
was confronted with the music of an American outsider, whom Ligeti had
discovered: Harry Partch. Partch had re-invented just intonation, a way of
harmonic thinking with intervals and chords using integer number relations
or ‘ratios’ (the term Partch preferred); for example, 4:5:6 for a just major
chord in Gioseffo Zarlino’s numerical terms. 1 This clashed with the old
European avant-garde ideology that forbade major or minor triads
(beginning with Schoenberg), and prohibited accompanied melodies, a
structural principle Partch focused on in his concept of ‘speechmusic’.

Figure 1 shows Partch’s ‘Tonality Diamond’, which includes the just
intonation intervals 9:8, 5:4, 11:8, 3:2, 7:4, and their inversions. All these
numbers are pitches, and most of them are easily linked to ancient Greek
thinking. Partch’s ‘Otonality’, on the right side of his Tonality Diamond,
starts with 1:1 on the bottom, his ‘Identity’: in this case, we can think of this

1 Gioseffo Zarlino, Le istitutioni harmoniche (Venice, 1558/1573).

70 Stahnke: György Ligeti and Harry Partch

as the classical pitch G. It continues with 9:8, a Pythagorean major second
above G or the justly tuned A, then 5:4, with indicates a just ‘major third’
between G and B – not Pythagorean of course, but Archytas knew it, and
later Ptolemy. Then comes 11:8 (unknown in any classical tuning), a kind of
‘just tritone’ G to low-C#. The Ancient Greeks never used it. Then follows
3:2, a Pythagorean fifth between G and D. Then 7:4 (again, unknown in any
classical tuning), commonly named as a ‘natural seventh’ between G and
low-F.

Figure 1. Harry Partch, ‘Tonality Diamond’

A Tribute to György Ligeti in His Native Transylvania 71

Again, Archytas knew the septimal intervals. The pitch classes of the
basic Partch Otonality on G are shown in Figure 2. We will soon see that
Ligeti is quite close to this pitch structure in his Viola Sonata, but to hint
briefly at the other features of Partch's Tonality Diamond: Partch’s
‘Utonality’ is the inversion of ‘Otonality’ and the additional pitches are
transpositions of O- and Utonalities built on their included ratios.

Figure 2. Pitch classes of Partch’s ‘Otonality’ on G

To understand these interval relations better, we can refer to the
overtone series with its partials. For example, the horn can overblow the
fundamental tone 1 up to the 16th partial. Ligeti uses this in his
Hamburgisches Konzert, which we will come to later on. String instruments
can also extend high up in the overtone series by playing flageolet tones,
also called harmonics. Ligeti notates this in his Konzert für Violoncello und
Orchester. In Figure 3, I calculate the rounded cent deviations from our
familiar equal temperament up to the 27th partial. 2 The deviations are
marked by accidentals with an arrow where the deviations are bigger than
25 cents.

2 Cent’ is a term developed by Alexander J. Ellis to denote a logarithmic hundredth of a
tempered semitone. It is first mentioned in the appendix of Ellis’s translation of Helmholtz’s
Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik
(Braunschweig, 1863). English translation by Alexander J. Ellis, On the Sensations of Tone as the
Physiological Basis for the Theory of Music, 2nd edn. (London: Longmans, Green, 1885).

72 Stahnke: György Ligeti and Harry Partch
Figure 3. Partials with cent deviations on C

Ligeti uses ‘Otonality’ in his Viola Sonata at the very beginning.
Below I notate the partials of the hypothetical ‘fundamental F’ on which
Ligeti apparently bases the work. In other words, his pitch relations, which
Ligeti painstakingly notates with different self-invented arrows for different
cent deviations from equal temperament, stem from transposed harmonics
of a non-existent F-string below the viola C-string. It is possible that this is a
reference to Mike Rutledge, a composition student of Ligeti's in the 1980s
and a jazz viola player who had an instrument with five strings, including
the low F-string.

The beginning pitches of the Viola Sonata are shown in Figure 4.
Influences from Partch and from rural Romania (Transylvania: Maramureş)
are somehow combined here, since Ligeti uses the beginning of one song in
the style of Hora lungă. We should also consider that Partch had sung and
played on his adapted viola for Ligeti as his guest. This unusual instrument
has coloured marks on its fingerboard that indicate just intonation.

A Tribute to György Ligeti in His Native Transylvania 73
Figure 4. Partials on F and opening pitches of the Viola Sonata

The thinking in integer numbers according to just intonation looks
quite mathematical, but it is very much linked to how our ear works. This
was a key insight that stemmed from Partch’s tuning of his instruments
himself. Apparently, the ear counts the relations of frequencies. So an
interval tuned to the ratio of 5:4 will be a beatless, ‘just’ major third, which
gives a certain simple interval impression that is linked to a simple
waveform combining 5 and 4. This is the major third in the mean-tone
temperament of the Renaissance and early Baroque era, predominant up to J.
S. Bach’s time. Ligeti refers to this 5:4 ‘just third’ in his cembalo piece
Passacaglia ungherese.

Even if we hear more complex relations of two pitches like 9:8, from
these numbers our ear forms a simple overall Klanggestalt (sound picture),
a waveform linkable to a ‘difference tone’ 9-8=1, which I overlay in the
following Figure 5. This resulting ‘quadratic difference tone’ is not apparent
in the sound signal, but the inner ear seems to pick out the peaks of the
basic waveform and produces it as a ‘virtual pitch’.3

3 Stanley A. Gelfand, ed., Hearing: An Introduction to Psychological and Physiological Acoustics
2nd edn. (New York: Marcel Dekker, 1990), 406

74 Stahnke: György Ligeti and Harry Partch

Figure 5. 9:8 (faster) and its quadratic difference tone 1 (slower)

If we listen to a tempered interval, the ear adjusts these intervals
mentally to conform to the simpler forms, and will accept a tempered third
as a third with some added noisy features. A ‘beating’ occurs in the sound,
but the overall aural image of the interval seems to remain, so long as the
beating is not too heavy. In my composition Partch Harp – to which we will
return later – the 5:4 ‘just third’ or the 7:4 ‘just minor seventh’ are actually
just intonations on the harp, while on the synthesizer they have such small
deviations from just intonation that we do not experience any ‘beating’ in
the sound.

I came into contact with Partch’s thinking through the LPs Ligeti had
brought from his stay in the United States in 1972. On his trip, Ligeti had
mainly been interested in the newest developments in computer music,
especially those taking place around his friend John Chowning in Palo Alto,
California, who had invited him. Ligeti was also in contact with Charles
Amirkhanian, a kind of all-round music manager and musicologist; through
Amirkhanian, Ligeti found out the whereabouts of the instrument builder,
musical philosopher, and composer Harry Partch. In an interview I
conducted with Ligeti in 2001, he said:

I stayed overnight in Venice [California], then Peter Hanser-
Strecker [from Schott-Verlag] picked me up, and we drove to
Encinitas – I got the address from Amirkhanian. [We drove]
through Orange County, everything was sweet with oranges,

A Tribute to György Ligeti in His Native Transylvania 75

wonderful. The journey took less than two hours. We could
not inform Partch, he had no telephone. He lived in a very
nice house close to the ocean. There he also had some of his
instruments, including the ‘Marimba Eroica’, his biggest
instrument. It did not fit into the house, so he had it in his
garage. A huge thing, consisting of one bar only [plus
resonator …] As a composer he was not really interesting,
but as very special American maverick […]

He was quite amiable […] maybe he had a good day.
Anyway, he had not the slightest idea who I was, or Peter
Hanser-Strecker. There was also a girl, a viola player, at that
time my girlfriend, I had stayed overnight with her, named
Barbara. She came with us because she wanted to get to
know Partch. Harry Partch went to the fridge, took some
milk, put it into four glasses, then vanished with his glass to
pour some whiskey into it secretly, maybe because of his
frugality, he was extremely poor […] I interrupt my story
and fill in another: Nancarrow told the story that Partch had
visited him in Mexico City once. Nancarrow was happy
about this. He then was asked, ‘Did you play a piece for him?’
– ‘No.’ – ‘Why not?’ – ‘He did not ask me.’ This is typical
Nancarrow. I think Partch was not interested in what others
did. But why did he visit Nancarrow?4

4 Ligeti: In Venice hab ich übernachtet, da hat mich der Peter Hanser -Strecker abgeholt und
wir sind nach Encinitas gefahren, die Adresse hab ich von Amirkhanian bekommen – über
Orange County, da roch alles nach Orangen, wunderschön. Die Fahrt dauerte nichtmal 2
Stunden. Partch konnte man nicht verständigen, er hatte kein Telefon. Er wohnte in einem
sehr schönen Haus nahe dem Meer, dort hatte er auch einen Teil seiner Instrumente, auch die
Marimba Eroica, sein größtes Instrument, das ging nicht ins Haus hinein. Er hatte es in der
Garage, ein Riesending. Eine Platte nur.

[…]

76 Stahnke: György Ligeti and Harry Partch

As I mentioned above, Ligeti had brought Partch LPs from his 1972
visit into his Hamburg class. He had started his professorship there in 1973.
Later I found out that Ligeti had proposed a Partch concert as early as 1972
for the ‘Berliner Festwochen 1973’ in a talk at the Akademie der Künste in
Berlin, where he stayed in that year as a guest artist.5 Yet, it was only in 1980,
some six years after Partch’s death in 1974, that a Partch concert came to
pass in Berlin. It staged Partch’s ‘The Bewitched’ with his original
instruments, really a major achievement considering the weight of the
enormous Marimba Eroica or the Kithara and the many other self-built
instruments which had to be transported from California.

Als Komponist war er nicht interessant, aber als spezieller amerikanischer Kauz […]
Er war sehr liebenswürdig […]
Vielleicht hatte er einen guten Tag, jedenfalls hatte er nicht die geringste Ah nung, wer ich bin,
wer Peter Hanser-Strecker ist, es war noch ein Mädchen, eine Bratschistin da, die war im
Augenblick meine Freundin und bei ihr habe ich übernachtet, Barbara. Sie ist auch
mitgekommen, war interessiert, Harry Partch kennenzulernen. Harry Partch ist zum
Eisschrank gegangen, hat Milch herausgeholt, in vier Gläser gefüllt und ist dann mit seinem
Glas verschwunden, um heimlich Whiskey nur in sein Glas zu füllen, vielleicht aus
Sparsamkeit, denn er war bitterarm. Harry Partch war nicht sehr freundlich … Ich
unterbreche die Geschichte und füge eine andere ein: Nancarrow hat erzählt, Partch habe ihn
in Mexico City einmal besucht. Nancarrow hat sich gefreut. Nancarrow wurde dann gefragt:
Haben Sie ein Stück vorgespielt? ‘Nein’. Warum nicht? ‘Er hat mich nicht gefragt!’ Das ist
typisch Nancarrow. Ich glaube, Partch war nicht interessiert, was die Anderen machten.
Aber warum hat er dann Nancarrow besucht?
Manfred Stahnke, ‘Den Ton finden’, Schriften zur Musik, privately published (Hamburg,
1996–), 2:70. To order, contact Stahnke Verlag [email protected].
Note that Partch occasionally drove his old Studebaker to visit purchasers of his LPs, of
whom Conlon Nancarrow was one. Ligeti discovered LPs containing Nancarrow’s Piano
Studies in Paris in 1980. Even more than Partch, Nancarrow was strongly promoted by Ligeti
in Germany from the 1980s on. He has a strong influence on Ligeti’s piano etudes and the
piano concerto; Ligeti considered him the most important composer of the 20th century.
5 Amy C. Beal, New Music, New Allies: American Experimental Music in West Germany from the
Zero Hour to Reunification (Berkeley, 2006), 179.

A Tribute to György Ligeti in His Native Transylvania 77

The orchestration for this ‘dance-oratorio’ includes some classical
instruments as well as all of the self-built Partch instruments that were
ready to play when Partch composed ‘The Bewitched’ in Urbana-
Champaign, Illinois, in the mid-fifties (see Table 1).

Table 1. The Bewitched, dance-satire for voices and large ensemble

Classical instruments Partch instruments Singers and dancers

Piccolo, Clarinet, Bass Kithara, two Harmonic Solo soprano (the witch)
Clarinet, Violoncello, a Canons, Surrogate
Japanese Koto Kithara, Chromelodeon, Chorus of musicians
Cloud Chamber Bowls,
Spoils of War, Diamond Approximately ten
Marimba, Boo, Bass dancers
Marimba, Marimba Eroica

Note that in keeping with Partch’s ‘corporeality’ concept, the music and the bodies
of both the instruments and the players come together as close as possible, so that
the players also sing as the chorus.

My American teacher Ben Johnston, who was deeply involved in just
intonation and had been one of the very first musicians who played in the
Partch ensemble in the late 1940s in California, had commissioned this work.
He gave Partch the opportunity to stage it in Urbana-Champaign, Illinois,
where Johnston was a composition professor at the University of Illinois.

The piece’s programmatic titles also reveal Partch’s ambivalence
towards ‘contemporary music’, as highlighted in Table 2:

78 Stahnke: György Ligeti and Harry Partch

Table 2. Scenes of The Bewitched, dance-satire for voices and large ensemble

Prologue. The Lost Musicians Mix Magic
Scene 1. Three Undergraduates Become Transfigured in a Hong Kong

Music Hall
Scene 2. Exercises in Harmony and Counterpoint are Tried in a Court of

Ancient Ritual
Scene 3. The Romancing of a Pathological Liar Comes to an Inspired End
Scene 4. A Soul Tormented by Contemporary Music Finds a Humanizing

Alchemy
Scene 5. Visions Fill the Eyes of a Defeated Basketball Team in the Shower

Room
Scene 6. Euphoria Descends a Sausalito Stairway
Scene 7. Two Detectives on the Trail of a Tricky Culprit Turn in Their

Badges
Scene 8. A Court in its own Contempt Rises to a Motherly Apotheosis
Scene 9. A Lost Political Soul Finds Himself among the Voteless Women of

Paradise
Scene 10. The Cognoscenti are Plunged into a Demonic Descent while at

Cocktails
Epilogue

Ligeti puts his own ironical distance from the avant-garde this way:

As to the avant-garde, I have this image in mind: I sit in an
airplane, the sky is blue, I see a landscape. Suddenly the
plane flies into a cloud: everything is white-grey. At first, this
grey seems to be interesting, in contrast to the earlier
landscape, but soon it becomes monotonous. Then I fly out of
the cloud, and again I see the landscape, but in the meantime
a completely different one. I think that we flew into such a
cloud of high entropy in this century, beca use of Schönberg,

A Tribute to György Ligeti in His Native Transylvania 79

the [2nd] Viennese School and then the post-war generation in
Darmstadt and Köln. More or less I belonged to it. In this
moment when I dive out of the cloud, I recognise – I am
very critical now – that we actually wrote ugly music. We,
and me too, my generation. This ugly music came from
twelve-tone music, from total chromaticism […] I constantly
search for a tonality which is not the modulatory, functional
tonality. Functional tonality needs the well -tempered piano,
at least since Bach. I search for alternative tunings, in an
insecure field. I try different, heterogeneous things.6

Ligeti must have instinctively understood the quality of Partch
whom he described in his composition class as a ‘One-Man-Tribe’. Re-
reading the preface of Partch’s epochal book Genesis of a Music, I very
strongly feel the similarity of the longing for freedom in Partch as well as in
Ligeti.7 Looking at the photograph of the two of them standing in front of

6 Ligeti: Ich sehe bezüglich der Avantgarde dieses Bild: Ich sitze im Flugzeug, der Himmel ist
blau, ich sehe eine Landschaft. Und dann fliegt das Flugzeug in eine Wolke: Alles ist
weißgrau. Zu Beginn scheint dieses Grau interessant zu sein, im Kontrast zur früheren
Landschaft, doch wirkt es bald monoton. Dann fliege ich heraus aus der Wolke, und ich sehe
wieder die Landschaft, aber eine inzwischen ganz andere. Ich meine, in diesem Jahrhundert,
und ganz besonders durch Schönberg und die Wiener Schule und dann durch die
Nachkriegsgeneration in Darmstadt und Köln - mehr oder weniger habe ich dazugehört -
sind wir hineingeflogen in solch eine Wolke von hoher Entropie. In dem Augenblick, wo ich
aus der Wolke heraustauche, sehe ich - ich bin jetzt sehr kritisch - , daß wir eigentlich
häßliche Musik geschrieben haben. Wir, also ich auch, meine Generation. Diese häßliche
Musik war eine Folge der Zwölftonmusik, also der totalen Chromatik ... Ich suche dauernd
nach einer Tonalität, die nicht die modulatorische funktionale Tonalität ist. Die funktionale
Tonalität braucht das wohltemperierte Klavier, mindestens seit Bach. Ich suche alternative
Stimmungen, in einem ungesicherten Feld. Ich probiere Verschiedenes aus, Heterogenes.

From ‘György Ligeti und Manfred Stahnke: Gesprach am 29. Mai 1993’, in Manfred Stahnke,
Musik – nicht ohne Worte. Beiträge zu aktuellen Fragen aus Komposition, Musiktheorie und
Musikwissenschaft, Schriftenreihe der Hochschule für Musik und Theater Hamburg ‘Musik
und’, edited by Hanns-Werner Heister und Wolfgang Hochstein (Hamburg: Bockel-Verlag,
2000), 143.

7 Harry Partch, Genesis of a Music, 2nd edn. (New York: Da Capo Press, 1974).

80 Stahnke: György Ligeti and Harry Partch

Partch’s house in Encinitas (published in Ligeti’s Collected Writings8), some
striking common features come through (at least, this is my personal view).

Later on in his life, Ligeti considered building a kind of organ for his
home in Hamburg to give himself the possibility of playing the uneven 43-
tone Partch scale in just intonation and composing with it. This instrument
never came into being, but nonetheless we can see the dream of just
intonation that Ligeti developed from the 1980s on in his compositions,
especially in Ligeti's Hamburgisches Konzert for Solo Horn, Four Natural Horns
and Small Orchestra. The last version dates from 2001, but it is an incomplete
work, since sketches exist for other movements. Since he never used a
computer, Ligeti relied on his aural imagination to build the harmonicity of
the four natural horns, with all their crude discordances due to the mixture
of intervals stemming from disjunct fundamental tones. In his composition
class, Ligeti used the term ‘Partch effect’ to describe the sounded
confrontation of two chords with very close microtonal distances, but built
on different fundamentals. I suppose that Ligeti had something similar in
mind when constructing the Hamburgisches Konzert and its section for four
natural horns. Partch himself described the same phenomenon as ‘tonality
flux’.9

Reading Partch, it is at times almost like hearing a hypothetical
California-born Ligeti talking, as when Partch writes:

I began to hear music on Edison cylinder records when I was
ten, but I can't recall exactly what. Later, when I knew, I
reacted to certain small shafts of intense life – Hebrew chants,
Chinese theater, and Congo ritual – with a kind of intimate
passion. My painter friend Gordon Onslow-Ford speaks of

8 Ligeti, György Ligeti: Gesammelte Schriften, ed. Monika Lichtenfeld, 2 vols (Mainz: Schott,
2007), 1:469.
9 Partch, Genesis of a Music, 189.

A Tribute to György Ligeti in His Native Transylvania 81

the ‘delight in recognizing something never seen [heard]
before,’ and what might be called a wide-consciousness
intuition could account for some of my early beliefs or
imaginings as to what I actually heard.10

But there is, of course, a very big difference in the attitudes of the self-made
man Partch and the Western-taught Ligeti: Ligeti, at his compositional
beginnings, was completely settled in Western musical thinking, though he
began developing it towards unseen soundscapes through integrating non-
Western musical ideas, whereas Partch, from his very beginnings, settled in
a hybrid, undefined, to-be-defined, perhaps uniquely Californian world that
brought together scattered elements from the Far East (China, Japan) and
from Europe. Partch learned to play piano, violin, guitar, much of it self-
taught; he also read scores and began to write scores in a Western sense. It is
such a pity that he burned his early compositions, including a just
intonation String Quartet in what he called an ‘auto-da-fé’.11

Very emphatically, Partch pursued a new way of independent (or
thought-of-as-independent) thinking:

In 1919, as I recall, I had virtually given up on both music
schools and private teachers, and had begun to ransack
public libraries, doing suggested exercises and writing music

10 Partch, preface to Genesis of a Music, ix.

11 Partch, preface to Genesis of a Music, x. ‘The only other notable event within this purview
was a kind of adolescent auto-da fé – the burning of fourteen years of my music in a big iron
stove – a confession to myself, that in pursuing the respectable, the widely accepted, I had
not been faithful. I say adolescent, even though I was twenty-eight at the time, because the
act involved many adolescent dreams, and because I had written a large part of the music as
an adolescent. The works burned were a symphonic poem, a quartet, an unfinished piano
concerto, and numerous short pieces and songs. The time-span between my initial divergent
gropings (mostly theoretical) to the resolution of the fire was about ten years – ten years in
which I began to evolve my own direction, in reaching for a supernal freedom, while at the
same time enduring a kind of anguish in abandoning all that I had struggled to learn of the
old ways (and not so old!)’

82 Stahnke: György Ligeti and Harry Partch

free from the infantilisms and inanities of professors as I had
experienced them.

When I was twenty-one I finally found, in a library, the key
for which I had been searching, the Helmholtz-Ellis work, On
the Sensations of Tone. Under this new impetus, doubts and
ideas achieved some small resolution, and I began to take
wing.12

To add a last Partch comment:

Mine is a procedure more of antithesis than of simple
modification […] Sometime between 1923 and 1928 I finally
became so dissatisfied with the body of knowledge and
usages as ordinarily imparted in the teaching of music that I
refused to accept, or develop my own work on the basis of
any part of it. With respect to current usage this refusal was a
rebellion; from the standpoint of my creative work it was the
beginning of a new philosophy of music, intuitively arrived
at. Just how old this ‘new’ philosophy actually is has since
been a continual revelation to me.13

In the “Ligeti class” in Hamburg, some of us thought very deeply
about how to handle just intonation in fresh and new ways. In the mid-
1980s, Ligeti had promoted a further development of the first digital
synthesizer DX7 by Yamaha towards completely free microtonal tuning
possibilities. Ligeti convinced Yamaha Europe, located in Rellingen (close to
Hamburg) to offer members from his class some of the newly manufactured
digital synthesizers, the then-famous DX7-II. These DX7 and DX7-II
machines worked on the basis of the research conducted by Ligeti's friend,

12 Partch, preface to Genesis of a Music, vii.
13 Partch, Genesis of a Music, 4.

A Tribute to György Ligeti in His Native Transylvania 83

the composer and computer-music specialist John Chowning from Stanford
University. Chowning had discovered that it was possible to use frequency
modulation for complex audio spectra.14 Thus, he became the ‘father’ of the
first FM synthesizer using very little digital storage capacity, which was
expensive at that time. At the SMC (Sound and Music Computing)
Conference in Hamburg in 2016 Chowning pointed out in his keynote
speech that he had invited Ligeti to Stanford in 1971, and ‘to his
astonishment’, as he put it, Ligeti actually came the next year. They became
very close friends from then on. These two important encounters with
Partch and with Chowning had a big impact on Ligeti’s composition class.

From Ligeti’s class in the 1980s, Hubertus Dreyer, Hans Peter
Reutter, Mari Takano, and myself, later also Benedict Mason, all used
synthesizers to explore microtonality in its broadest sense, not only for just
intonation. I will concentrate for now on two microtonal pieces which some
of us developed in the mid-1980s. They are both ‘hybrid’ in a sense that the
aim is not the purity of just intonation, but a confrontation between the ‘just’
and the ‘strange’.

The first of these examples is Hans Peter Reutter’s ‘Hinkel’ from
Märchenbilder II.15 In this piece for microtonally played flute and DX7-II
synthesizer, Reutter superimposes just intonation thirds in 5:4 (major) and
6:5 (minor) ratios in three entangled layers. The resulting intervallic steps on
his scale are either 176C or 70C. In my scale sketch, Reutter’s intervals are
drawn in comparison to equal temperament steps (see Figure 6).

14 John M. Chowning, ‘The Synthesis of Complex Audio Spectra by Means of Frequency
Modulation’, Journal of the Audio Engineering Society 21, no. 7 (1973): 526–34. For an
overview of Chowning’s invention, see Zachary Crockett, ‘The Father of the Digital
Synthesizer’, https://priceonomics.com/the-father-of-the-digital-synthesizer/


15 Soundfile available at http://www.hans-peter-reutter.de/download.html (accessed 8
October 2016).