Figure 1. La Légende d’Eer sound analysis. [The original is in colour]
Said Athié Bonduki (Unicamp, Brazil)
Adriano Monteiro (Unicamp, Brazil)
ABSTRACT
The present research focuses on the compositional procedures that link two works that Iannis Xenakis composed during the year 1977 : La Légende d’Eer, on 7 tracks of electroacoustic tape and Jonchaies, for large orchestra. In the score of Jonchaies, Xenakis states that one of his main sources of inspiration was the compositional process of the eletroacoustic work mentioned.
The objective of this research is to further explore this relationship and to clarify how La Légende d’Eer influenced the composition of Jonchaies. In order to analyze this relationship, a method of analysis was established. The main subjects of this analysis are the matters related to sonorities obtained and reproduced, and compositional techniques. Spectrograms and sound descriptors are the analysis tools utilized to obtain data from both works. Similarities and differences are presented in both macro and microstructure.
1. INRODUCTION
Xenakis quotes in the music score of Jonchaies that this work was inspired by his results from the composition of La Légende d’Eer, both from 1977.
“This piece is inspired by results obtained and used in the « Legend of Eer », music of the Diatope of the Centre Pompidou, (…). These results stem from my theoretical work in sound synthesis and music aided by computer, work that employs a different path than that of the classical Fourier harmonic analysis (…). This difference uses stochastic walks and Brownian movements. Indeed according to this theory that I introduced twelve years ago, one starts from noise and, with the aid of these stochastic functions periodicities are injected into it.” (Xenakis, 1977).
Starting from this statement this research intends to trace the relationship between both works and demonstrate how the influence from electroacoustic media takes place over instrumental media.
In a detailed analysis of La Légende d’Eer - based on the 7 separate audio tracks from this work and on some of the composer’s preparatory sketches - Makis Solomos briefly mentions the relationship that this work might have with Jonchaies (Solomos 2004, p.13). In an article published four years later and entitled “Quelques réflexions sur les rapports entre l’électroacoustique et la musique instrumentale de Xenakis : le cas de La Légende d’Eer et Jonchaies”, Isabel Pires specifically set forth to explore the possible traces of this transfer from the electroacoustic to the instrumental medium mentioned by the composer. She concludes that, in general, the abstract nature of Xenakis’s compositional thinking and technique allows him to operate in either one of them.
Based on these previous analyses, the present article proposes to approach the matter of relations in both pieces through the sound scope, aiming to clarify how compositional choices made in Jonchaies were influenced by the compositional experience of La Légende d’Eer.
This article’s structure is as follows : after a brief presentation of the technology applied to our analysis, the relationships between both works are presented and commented, followed by a more detailed analysis of excerpts to demonstrate these relationships in depth.
2. METHODOLOGY
2.1. Sources
One of the main difficulties regarding the comparative analysis between these works is the two different medias in which they are composed for, one instrumental and the other electroacoustic. Concerning this matter, a common ground was needed, for which sound scope was chosen. From this perspective the methods of sound analysis through sound spectrum and descriptors were defined, which are procedures that can assure a methodological equality that can clarify points of relationships between both works. The CD version of La Légende d’Eer14 and a recording of Jonchaies15 were used for this analysis. It is important to state the fact that sound analysis from different recordings of Jonchaies results in differences in the sound spectrums among them. However, the overall instrumental behavior that establishes the internal movements of a texture remains the same, since the sound score defines them and the consequent variations of different interpretations aren’t sufficient to modify that. For this analysis the information that is needed to establish a valid set of data for the comparisons defined are the same with the different recordings available of Jonchaies.
As additional source material we also have Jonchaies music score as well as analysis from other authors regarding such work. For La Légende d’Eer we have Solomos’s analysis that used source documents from Xenakis’s archives. Texts form Xenakis contributed to the clarification of the musical issues that were present in both works16.
2.2. Methods of sound analysis
Spectrograms and sound descriptors were utilized for the sound analysis17. Three descriptors were combined in one graphical representation. The parameters of loudness (RMS), sound brightness (spectral centroid) and spectral bandwidth were used in order to create a spectral contour. Mikhail Malt and Emanuel Jordan first used the representation achieved by this combination, which inspired the analysis presented in this article. The extraction of information from the audio analysis had a delimited set of parameters established, resulting in a reduction of the information obtained, aiding the visualization of the behavior of the pieces in question. The parameters are : 1) The spectral centroid, which is the gravity center of energy distribution over the sound spectrum which allows the tracing of a profile of the energy movement over the excerpt analyzed. 2) The bandwidth, which is spectral standard deviation that presents the medium energy detour over the spectrum in relation to the centroid, and is represented by the thickness of the red lines through the graphics. 3) The RMS, the loudness present in the analyzed section that is indicated by red’s intensity.
This method of analysis allows the visualization of such characteristics of sound behavior that were used to clarify global similarities between both works. Spectrograms were used to obtain a more detailed set of information regarding selected elements, allowing a more in depth analysis.
3. SIMILARITIES AND IFFERENCES IN THE OVERALL FORM
Both works start with high-pitched sounds in a rarefied texture, proceeding to the development of heavily dense textures in a lower frequency region and then returning to a rarefied texture with high-pitched sounds similar to the initial ones (as seen on figures 1, 2 and 3)18, creating an overall arc form. The next examples are a result of the sound descriptor mentioned above.
From the sound analysis we have established a segmentation of 6 distinct sections for both pieces19, basing this affirmation over the differences in pitch frequency, density and sound intensity. It is clear in the figure that follows that the sections between works do not necessarily relate. Although the formal structure has similar segmentation, the common elements do not necessarily occur in the equivalent section.
Figure 1. La Légende d’Eer sound analysis. [The original is in colour]
Figure 2. Jonchaies sound analysis. [The original is in colour]
4. SIMILARITIES BETWEEN SPECIFIC EXCERPTS
4.1. Overview
For the exposition of the relationships that exist between these two works, the analysis follows a specific approach concerning common elements present in both of them.
From the information gathered from the sound analysis, Jonchaies music score, the preparatory sketches of La Légende d’Eer and previous analysis from the other authors, we have placed these 5 common elements between the 2 pieces that can be seen in the following figure. Note that some of them have sub groupings.
If we take into consideration the elements 1a, 2, 4, 5 and 1b, the presented similarities do have an equal order of occurrence for both works. The specific content of each section of Jonchaies was not defined by the order of the sections of La Légende d’Eer, with the only clear exception at the end and the beginning.
Figure 3. Correlations between elements in La Légende d’Eer (above) and Jonchaies (below). [The original is in colour]
The first marking is relative to the similarity between the high-pitched sounds at the beginning and end of both pieces. For the second marking there is a specific region with similar characteristics concerning their behavior, where in both pieces we have a texture with sonority similar to that of the Doppler effect20. The third set of correlations to consider are the high peaks ; well detached from the regions that they are in, in both respective pieces. The fourth is a region with an “L” shaped curve (based on the spectral centroid) and proportionally they have a similar duration in both works, having a larger bandwidth in La Légende d’Eer. In Jonchaies this texture is further developed until the end of the section. Having a similar profile, the fifth marking engulfs the last two sections of each work. In the following section we have a further analysis of each correlation.
The first section Jonchaies does not have any clear procedural or structural relations with La Légende d’Eer, but there is one common element that goes beyond the structural factors. This first section has a segment (between measures 10 and 63) created using harmonic sieves, from the first section of the orchestral piece. This sieve has a similar structure to the pelog scale from gamelan music (HARLEY, 2004, p. 108). Xenakis used instruments from folkloric music in La Légende d’Eer from African and Japanese traditional music such as the mbira and the tsuzumi (Solomos, 2004, p. 17). Together with these instruments there are sounds of impacted ceramics that may resemble some sonorities from gamelan music. It can be speculated that the desire to explore folkloric-based sonorities in this passage was influenced by Xenakis’s compositional experience from La Légende d’Eer.
4.2. Correlations between set of elements 1a and 1b.
Both works begin and end with high-pitched sounds shown in the sonograms below21. In spite of the glissando from the beginning of Jonchaies we have a very similar sonority between them both. The same is true at the end of them, where there is also a similar procedure of repetitions of short sounds, superimposed in Jonchaies and sequential in La Légende d’Eer.
Figure 4. High-pitched sounds in the beginning of La Légende d’Eer (left, 0’00’’ - 5’52’’) and Jonchaies (right, 0’0’’ – 0’23’’). [The original is in colour]
Figure 5. High-pitched sounds in the end of La Légende d’Eer (left, 41’48’’ – 44’45’’) and Jonchaies (right, 15’16’’ – 15’58’’). [The original is in colour]
4.3. Correlations between the set of elements number 2
There are different layers of elements in both pieces to create textures with similar sonorities, close to that of a Doppler effect. Mind that both have a gradual saturation of the spectrum, with a higher intensity in La Légende d’Eer, as a consequence of the electroacoustic media, that supports this resource with better precision than an orchestra.
In La Légende d’Eer this section is constituted by the predominance of synthesized sounds with undulated profiles that constantly ascend, which characterizes the sonority of the spirals. On the spectrogram an overlapping of layers can be seen with their continuous transpositions, creating these arcs that are seen throughout the section, first clearly and then much more diffused due to the high degree of overlap.
Figure 6. Spirals in La Légende d’Eer (24’50’’ – 33’ 08’’).
In Jonchaies the orchestra is divided into 5 instrumental groups, organized in order to obtain distinct timbristic characteristics. This allows for Xenakis to have wider control over the internal variations of this texture, mainly through variation of the metric values and overlaps, making this section extremely polyrhythmic. Xenakis used these procedures to create the sonority he desired, making it through the repetition of binary high-low cells that alternate timbristics sub-groupings inside the respective layers, thus creating variations of timbrical peaks similar to the ones found in La Légende d’Eer. The continuous variation of pitch is noticeable in the spectrogram below, which occurs together with the metric variations previously pointed out.
Figure 7. Spirals in Jonchaies (4’30’’ – 6’34’’).
4.4. Correlations between set of elements number 3a and 3b
The detached peaks taken for consideration from the third group of correlations are peaks 3a and 3b from La Légende d’Eer and Jonchaies. Below we have the peaks produced in the electroacoustic media. Note the similarity in the spectral saturation with energy until high values of frequency and, most importantly, the similarity regarding the wavy internal profile. We know that for its characteristic sonority and behavior these elements correspond to stochastic synthesis22. This profile presents a feature similar to Brownian movements23 (random walks) within a certain band limit.
Figure 8. Peaks 3a (16’23’’ – 20’30’’) and 3b (16’23’’ – 20’30’’) in La Légende d’Eer. [The original is in colour]
Figure 9. Peaks 3a and 3b in La Légende d’Eer compositional score.
In Jonchaies we have a similar wavy profile with spectral saturation and undulations through the notes that compose the texture, as seen below.
Figure 10. Peaks 3a (8’56’’ – 9’27’’) and 3b (12’22’’ – 12’53’’) in Jonchaies. [The original is in color]
In the music score of Jonchaies, the notation relative to peaks 3a and 3b use the same wavy pattern, with lines indicating free vibratos constrained inside a limited range stipulated by Xenakis. We assume that these notations are correlated and that Xenakis tried to mimic the sonority of the stochastic synthesis with these blocks of vibrato in the winds and further on the music with the metals.
Figure 11. Winds notation in Jonchaies (measures 142 – 144).
Throughout Jonchaies, Xenakis uses one of his most known instrumental characteristics, his strings glissandos, which can be seen on figure 12. This way of writing is characteristic to the writing technique used to imitate the Brownian movements, employed by Xenakis in previous works such as Mikka, Mikka S and N’ Shimma. This writing technique appears in Jonchaies almost exclusively together with the blocks of vibratos in winds or metals24, simulating the stochastic synthesis.
In the detached passage of the strings seen below there are parts played in diatonic ascending movements to high pitched notes, followed by movements in glissandos descending to lower notes, and in between these movements there are repeated notes. This sequence is repeated four times, creating a layer with an adulatory movement in the macrostructural dimension.
Figure 12. Excerpt of waveform structure (measures 141 – 160).
The procedures mentioned above for instrumental notation takes place through the second section of Jonchaies (from measures 141 to 217) with the presence of no other procedures in this section. This whole section can be considered to have been composed after the idea of exploring different ways of transcribing the behavior of stochastic synthesis to musical notation.
4.5. Correlations between set of elements number 4
The fourth element concerns two similar profiles identified in both pieces through sound analysis the “L” shaped profile. In La Légende d’Eer it is made through stochastic synthesis and in Jonchaies there is an instrumental simulation of the internal behavior of such synthesis, as previously seen in a similar example. Below we have the extracted spectrogram of the profile of the figure in L in both works, and it shows the wavy patterned frequencies (random walks in both parts).
Figure 13. Brownian movement in La Légende d’Eer (left, 33’17’’ – 37’24’’) and Jonchaies (right, 8’54’’ – 10’22’’). [The original is in color]
4.6. Correlations between set of elements number 5
The last correlation of elements is constituted of the final sections of both respective works and the similarity in their profiles. It has an initial region with distribution of the energy in a broad band on the low to the high frequencies, an intermediate region with energy predominance in the low region and an input of high-pitched elements in the end. For these similarities we have a profile with a similar centroid in both works. The two peaks of the inputs of high frequencies are respectively the peaks 3c mentioned before.
Detached in white are two peaks from Jonchaies that are not present in La Légende d’Eer. The ascending movement of the strings that are continuing the Brownian movement simulation creates the first one and that at this point they converge to high pitches. The second has relations with other elements of La Légende d’Eer that will be shown next.
Figure 14. Last section of La Légende d’Eer (above, 32’28’’ – 43’44’’) and Jonchaies (below, 12’19’’ – 15’58’’). [The original is in color]
Figure 15 is a part of the music score regarding the section where the second peak marked with a white circle occurs, specifically the element of the medium-high frequencies previously pointed out. In the music score there are ascending scales in metals with a posterior note sustentation.
Figure 15. Jonchaies (measures 221 - 224).
This ascending element followed by pitch stability over a note performed by the metals in Jonchaies has the same profile from elements of a passage in La Légende d’Eer, glissandos followed by random walks, which are steadier in the register, and can be seen in figure 16. The similarity of this texture with a stochastic synthesis presented in La Légende d’Eer in the region of the group of peaks 3a is noticeable, and is present in the comparison below. The spectral saturation is a result of the cymbals in Jonchaies and of white noise generated by the stochastic synthesis in La Légende d’Eer.
Figure 16. Upper graphics : Piece’s Global Maps - La Légende d’Eer (left), Jonchaies (right). Middle Graphics : Peaks 3a (16’23’’ – 20’30’’) in La Légende d’Eer and 3c in Jonchaies (12’19’’ – 15’58’’). Bottom graphics : Zoom in the Peaks’ Internal structure : Peaks 3a (18’44’’ – 18’51’’) in La Légende d’Eer and 3c in Jonchaies (14’18’’ – 14’40’’). [The original is in color]
We can assume that this is another method employed by Xenakis of recreating into instrumental media the elements generated electronically by his synthesis. In this case he recreates in the instrumental music the profile of the sound generated by the synthesis. This profile, with an ascendant movement followed by stability (or random walk), happens again in other elements in different levels of organization, either micro or macrostructural.
5. CONCLUSION
Starting from the information that the process and compositional result of La Légende d’Eer have influenced the composition of Jonchaies, we employed a methodology, the use of distinct audio analyses, which has yielded information regarding possible points where this influence may have taken part. Xenakis obtained substratum concerning stochastic synthesis procedures and sonorities through his practice during the composition of La Légende d’Eer, and then he could later employ them in Jonchaies. For instance, by simulating the synthesis sonority or by applying a frequency profile that is resultant from the stochastic synthesis as a model for the macrostructural organization in Jonchaies, as seen on the strings. Formal structures and textural behaviors from La Légende d’Eer were again explored in Jonchaies, allowing the composer to re-elaborate his approach over new prisms generating a composition that produces many elements derived form the same foundation.
It is important to consider that these similarities may have occurred in a casual way, without Xenakis’s conscious intentions. However, we obtained consistent results, allowing the possibility for a future study with a new perspective on the subject, such as analyzing Xenakis’s manuscripts to verify the range of the proposed analysis.
6. REFERENCES
Harley, James (2004), Xenakis : his life in music, New York, Routledge.
Pires, Isabel (2008), « Quelques réflexions sur les rapports entre l’électroacoustique et la musique instrumentale de Xenakis : le cas de La Légende d’Eer et Jonchaies », Proceedings of EMS08 – Eletroacustic Music Studies – Musique Concrète – 60 ans plus tard, Paris.
Solomos, Makis (2004), « Le Diatope et La Légende d’Eer », www.iannis-xenakis.org/fxe/actus/Solom3.pdf.
Xenakis, Iannis (1977), Jonchaies, Paris, Editions Salabert.
Xenakis, Iannis (1992), Formalized Music (translations Christopher Butchers, G. H. Hopkins, John Challifour ; new edition augmented by Sharon Kanach), Stuyvesant (New York), Pendragon Press.
Xenakis, Iannis (1985), « Music Composition Treks », in William Kaufmann (ed.), Composers and the Computer, p. 170–192.
13 Special thanks to Dr. Stéphan Schaub for supervising this research and also our financial supporters, where Bonduki had a scholarship from CAPES and Monteiro from FAPESP and later CAPES.
14 The reording used for the sound analysis is from the album Orchestral CD Xenakis Eletronic works, vol.1 La Légende d’Eer, mode, 2005.
15 The reording used for the sound analysis is from the album Orchestral works, vol. II Jonchaies, Shaar, Lichens, Antikhthon. Orchestre Philharmonique du Luxembourg, dir. Arturo Tamayo, Timpani, 2001.
16 There are also the analyses from James Harley, where he analyzes both works separately (Harley, 2004, p. 108, p. 110).
17 The software’s used are Sonic Visualiser for the spectrograms and Pure Data for the descriptors.
18 Both works have distinct time durations, so the graphics window has been made so that they would result in functions with the same number of values. La Légende d’Eer has approximately 2.8x times the duration of Jonchaies, for that the analysis window in La Légende d’Eer is approximately 2.8x bigger than that of Jonchaies.
19 In Jonchaies the third and second sections presented can be considered as one, since the third section is a continuation of the second section. There is a constant and gradual transformation of the layers involved in this passage that starts the second section and ends with the third section. Nonetheless there are differences in the spectral contour, with a decrease of intensity and increase of the bandwidth between these two sections, and these parameters are taken into consideration for this research.
20 Solomos refers to this sonority in La Légende d’Eer as spirals.
21 Note that in this figure the upper distinct region of frequencies are harmonics from the fundamental group frequencies being used in this section.
22 La Légende d’Eer is the first eletroacoustic work from Xenakis where he uses the stochastic synthesis.
23 Solomos makes a transcription of this brownian movent is his article Le Diatope et La Légende d’Eer, 2004, p.11.
24 Only exception is the glissando from the beginning of Jonchaies.