Saariaho'nun "New Gates" adlı eserinde küme yapıları, organizasyonu ve dönüşümleri
Set structures, organization and transformations in Saariaho's piece "New Gates"
Yazar: GÜNEŞ YAKARTEPE
Danışman: DR. ÖĞR. ÜYESİ RECEP GÜL
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Müzikoloji ve Müzik Teorisi Ana Bilim Dalı / Müzik Teorisi ve Kompozisyon Bilim Dalı
Derece: Yüksek Lisans, 2024
Konu: Müzik = Music

Özet:
Tonal dönem sonrası müzikleri analiz edebilmek için Allan Forte, 1964'te matematikteki küme teorisini on iki ton sistemine uygulama fikrini ileri sürmüştür. 1973 yılında yayımladığı kitabında da bu fikri, tonal dönem sonrası müziklerin analiz edilmesi için uygulanabilir hale getirmiştir. Forte'nin öne sürdüğü kavramlar Joseph Straus'un 1990 yılında yayımlanan kitabında oldukça kapsamlı ve daha erişilebilir hale gelmiştir. Bu kavramlar ile müzikte nota organizasyonundaki perde/perde sınıfı ilişkilerinin ortaya çıkarılması amaçlanır. Ancak bu teori her ne kadar belirli bir akım ile ilişkilendirilse de dönemimizin önemli teorisyenleri Roig-Francoli (2007) ve Straus (2022) çeşitli akımlarla ön plana çıkmış farklı bestecilerin müziklerini de bu teori ile analiz etmiş ve önemli bulgular elde etmiştir. 20. yüzyılın en önemli bestecilerinden biri olan Kaija Saariaho'nun müzikleri her ne kadar elektronik ve spektral müzikle ilişkilendirilse de iki teorisyen de analizlerinde besteciye yer vermişlerdir. Çünkü nota organizasyonunun sadece spektral müzik besteciliğinde kullanılan tekniklerle açıklanabileceği iddia edilemez. Saariaho'nun perde organizasyonunun müzikal dili bağlamında çok önemli bir yer tuttuğu gözlemlenebilir.
Finlandiya'da tanınan post-seriyalist  bestecilerinden olan Paavo Heininen ile kompozisyon çalışan Saariaho; müzik çevresinde spektral ve bilgisayar müziği çalışmalarıyla adından söz ettirmekle beraber, müziklerinin kurgusunda yıllarca eğitim aldığı seriyalist yaklaşımın izlerini barındırmakta olduğu varsayılabilir. Bu tezde Saariaho'nun flüt, arp ve viyola için bestelediği "New Gates" adlı eseri post-tonal teoride kullanılan bazı teknikler ile incelenmiştir. İlk bölümde Saariaho'nun bestecilik hayatının bir özeti verildikten ve seriyal müzik ile olan ilişkisi ortaya konduktan sonra her bölümde farklı bir küme teorisi kavramı açısından eser ele alınmıştır. Sırasıyla alt küme-üst küme ilişkisi, simetri, aralık permütasyonu ve ses yönelimi kavramlarının temel metodolojisi ortaya koyulduktan sonra bu kavramların Saariaho'nun nota organizasyonunu açıklayabilme kapasitesi irdelenecektir. 1996 yılında Sabeth Trio için bestelemiş olduğu "New Gates" adlı eseri gerek aralık ilişkilerinin kurgusu gerekse küme sınıfları açısından oldukça karmaşık bir yapıda olmakla kalmayıp, bu kümelerin ilişkiler ağı bağlamında da verimli bir içerik sergilemektedir. Bu tez sayesinde Saariaho'nun post-tonal bestecilik anlayışına dair daha detaylı bilgi edinilmesi amaçlanmaktadır. Saariaho'nun nota organizasyonunu küme teorisi ile analiz etmek ve bu teorinin tekniklerinin farklı bestecilik anlayışlarında gelen bestecilerin eserlerini açıklayabilmek adına da uygulanabilir olduğuna dair bir çalışma üretmektir.

Abstract:
Kaija Saariaho, one of the most significant composers of the 20th century, is primarily known for her electronic and spectral music (Moisala, 2019). Despite her recognition in spectral studies, it can't be claimed that her note organization relies solely on techniques used in spectral music composition. The analyses in this study indicate a compositional approach that diversifies pitch organization using various techniques.
Set theory, initially proposed by Allen Forte (1970) to explain the note organization in serial music, is an analytical technique. Although this theory is associated with a specific movement, prominent theorists of our time like Roig-Francoli (2007) and Straus (2022) have analyzed composers' music from various movements using this theory, obtaining significant findings. Saariaho's music has been part of the analyses by these theorists. It's observable that Saariaho's pitch organization holds a crucial place in the musical language. Hence, considering both the history of spectralism and serialism and the composer's musical language, it was thought that analyzing one of Saariaho's pieces could provide significant data.
The purpose of this thesis is to analyze Saariaho's note organization using set theory and to create a study suggesting the applicability of these techniques in explaining works of composers from diverse compositional approaches. This aims to propose that set theory, often used in analyzing early atonal music, remains an vital tool in today's music, serving as a more widely applicable technique.
In the first section, important aspects of Saariaho's life, her connections to serialism, and findings about the creation process of the piece "New Gates" are presented. It's observed that Saariaho worked with Klaus Huber, a prominent serial composer in Finland, during her early years as a composer, which could be presumed to significantly shape a composer's musical language.
The second section delves into the fundamental concepts of set theory, particularly examining subset-superset relationships. It's noted that the superset 8-2 (01234568) acts as a generator, giving rise to many sets used in the piece. Sets like 4-2 (0124) , 4-3 (0134), 4-12 (0236), and 4-13 (0136) hold significant importance in note organization. The relationships between subsets and the superset are analyzed, indicating that Saariaho initially formed subsets from her own sets and later expanded them through shared tones. The composer utilized specific subsets multiple times with various instrumentation, ensuring consistency while creating diverse tonal colors. Additionally, the same sets were diversified with different articulations and rhythmic values. In some sections of the piece, subsets were treated as if they were supersets and used as smaller structures.
The third section explores the concept of symmetry, identifying symmetric sets and attempts to establish center symmetry. As a result, it's noticed that Saariaho forms sets through two methods: one involving symmetric sets themselves and the other by adding an interval of m2 or M2 to a set containing its own symmetry, maintaining both symmetry and partial distortion. Saariaho's use of sets possessing this feature showcases a high level of creativity.
In the fourth section, efforts are made to identify relationships constructed through interval permutation technique. Despite different structures, the sets used in the piece exhibit considerable auditory similarity. Considering the occasional inadequacy of classical set theory analysis methods, it's deemed appropriate to mention this analysis technique. Consequently, connections among many sets are established using two specific types of interval permutations, namely rotation and transposition. In this context, these sets are analyzed throughout the piece, and interval series are identified, revealing significant relationships.
The fifth section tackles the concept of pitch direction and examines methods of connecting pitches. For this purpose, pitch orientations are examined in terms of P and S relationships suggested by Callender (1998).
In thesis, prior to commencing the analysis and literature review, the piece titled "New Gates" was meticulously transcribed directly from the Sibelius program. This procedure enhanced familiarity with the musical segments, enabling a detailed examination of notation. Consequently, potential areas for segmentation or dissection were identified, providing preliminary insights before delving into the analysis. To comprehend Saariaho's compositional journey, extensive research was conducted into her life and oeuvre. Considering her oeuvre's frequent association with spectralism, information was gathered regarding its relationship with serialism, a movement where pitch organization takes precedence. Additionally, thorough investigation was conducted into the era during which the piece "New Gates" was composed. This exploration drew upon secondary sources such as biographies, interviews, and analytical essays.
In formulating the theoretical framework, concepts within set theory were explored. Straus's seminal work (1994) was primarily adopted as the cornerstone owing to its linguistic clarity and the abundance of examples provided in notation. A literature review was conducted on analyses employing set theory, allowing for an understanding of elements to be considered in note organization. Furthermore, close attention was paid to how analogous analyses of textures present in Saariaho's composition were approached.
Following these preliminary endeavors, contemplation revolved around set theory concepts best suited for elucidating relationships within the composition. Concepts such as subset-superset relationships, symmetry, interval permutations, and voice leading were delineated. The selection of these concepts considered their influence on various facets of note organization and their interrelatedness, ensuring their potential to facilitate an in-depth analysis. Each topic underwent a preliminary literature review, summarizing existing scholarship, and additional methodologies were incorporated to represent analyses unaddressed in the existing literature. To facilitate the coherence of the thesis, it was deemed suitable to present the summarized literature not at the outset but at the beginning of each section, corresponding to the theoretical concept under examination.
This thesis discusses the influence of serially rooted composers on Saariaho's compositional language in her educational background. While known for her work in spectral or computer music, traces of serialism can be observed. Despite acknowledging influences from the Musique Concrete movement, significant findings have emerged through the application of set theory concepts in her music. The composition techniques unveiled through set theory in this music are expected to guide future studies in this field.
Examining the note organization within the composition reveals substantial evidence, despite it not being composed with a serial understanding. Additionally, the findings present unique examples not previously encountered in serial compositions. The composer's original language has been effectively explained in conjunction with this theory.
In Saariaho's piece "New Gates," the pitch sets and their usage can be analyzed using set theory concepts. The significant findings derived from this analysis can be summarized as follows:
1. Saariaho treats the upper set as generative, shaping the note organization with lower subsets, identifying commonly used 4-2 (0124) , 4-3 (0134), 4-12 (0236), 4-13 (0136), and 4-z15(0146) sets as actually being lower subsets.
2. Structuring the note organization with symmetric sets or creating them by adding minor or major second intervals internally, establishing pitch organization through central symmetry in some passages.
3. Utilizing interval permutation techniques in the transformation of prominent sets in the note organization, demonstrating that 4-2 and 4-3 sets, along with 4-12, 4-13, and 4-z15 sets, are rotations of each other. Saariaho frequently expanded sets using the divergence method, directing pitches according to sound regions in certain sections.
4. Creating different sets based on voice leadings within sound fields and modernizing traditional counterpoint techniques while employing this method.
Set theory remains one of the most valid analytical techniques. It has been demonstrated that post-tonal methods can still be applied in analyzing non-serially composed pieces. This method, commonly used in analyzing twelve-tone music, has proven effective in Saariaho's compositions. It has yielded remarkable results not only in analyzing music belonging to a specific period or style but also in analyzing a wide range of different music.
Following this study, I believe that analyzing works of post-serial composers associated with movements such as spectralism, musique concrete, etc., using set theory concepts will yield many important results in terms of note organization, leading to these studies being featured in the international literature.