Did the ancient Greeks know the natural overtone series?

Music theory, which developed in the course of a single musical-mathematical-astronomical synthesis, does not give a direct answer to the question posed – "did the ancient Greeks know the natural overtone series" as a reasonable system. Nevertheless, the musical theory in the preserved sources-original works, their fragments, compilations – came quite close to understanding of the existening of the phenomenon much later called "natural overtone series". The article attempts to find a correspondence between individual mathematically calculated intervals, the main system-forming generic tetrachordal structures (diaton, chroma, enharmony) and segments of the natural overtone series as evidence of the unity of the scientific and empirical (auditory) approach to achieving the best sound of Music, universal Harmony. The article is a revised and expanded version of the Lecture for students and teachers of conservatories "Musical acoustics in the works of ancient scientists" (Novosibirsk, 2009).

Meditations for organ: parallels to musical creativeness

The purpose of the article is to determine genre parameters of meditation for the organ on the example of the pieces of composers of the early 21st century. It is proposed to concretize the prerequisites of meditation for organ as an independent genre and to compare the strategies of reading the genre by representatives of different national schools of composition (Italy, Ukraine, Brazil). Among the research methods there were used: historiographic (restoring the historical retrospective of genre formation), the method of genre analysis (confirming the genre status of meditation), the method of style determination in combination with the comparative method (comparing the strategies of reading the genre by composers of different nationalities). The novelty of the proposed topic lies in the identification of the genre status of meditation for the organ and the introduction into the musicological discourse of works that have not previously come to the attention of Ukrainian researchers. Conclusions. Meditations “Shiva” by K. Ferrari, “And there was night, and there was morning, and there were quiet heavenly flutes...” by M. Shukh and Prelude-Meditation by F. Costa make it possible to define meditation as an independent genre of organ art with a constant set of stable indicators. Meditation for the organ is a concert piece that belongs to the genres of cult-ritual music and is characterized by an introverted structure of the communicative act. All works with a similar genre name are united by a single semantic field of religious contemplation. The compositional foundations of meditation as a genre consist in the multiple repetition of structures (of different scales) with a clear “looseness” of the form, which guarantees the tightness of the same sound environment and the monochromatic text. Stylistic characteristics became variable components of the meditation: the meditative profile of “Shiva” by C. Ferrari is emphasized by the using of techniques of minimalism, in the piece by M. Shukh the emphasis is transferred to the timbre of the organ with appeal to the intonation of oriental music, and in the Prelude-meditation by F. Costa attempts to build a new sound universe, as extended scale of the overtone series.

New Musical Resources

New Musical Resources is a book written by Henry Cowell in 1919, unpublished until 1930. In it, Cowell proposes a theory of musical relativity in which pitch, rhythm, and the progress of music history are grounded through reference to the structure of the overtone series: the "living essence from which musicality springs." Ethnomusicologist Charles Seeger encouraged a young Cowell to rationalize the compositional tools he had been developing, which ultimately led to the creation of this book. In the book’s first section, Cowell presents the development of Western harmony as progressive upward movement through the overtone series. He suggests the continuation of this same logic into chords based on the ratios beyond the minor seconds that he was using to create "cluster chords." His rhythm chapter proposes the whole-note as the basic unit of time, encouraging division beyond the standard multiples of two into the next numbers in the harmonic series—creating third-notes, fifth notes, etc. This method enables the composition of rhythmic patterns that rely on the same ratios as are present between various melodic and harmonic intervals. Many American composers—notably Conlon Nancarrow—have utilized Cowell’s concepts, which predate the development of similar ideas in integral serialism by several decades.

Tenney, James (1934–2006)

American composer James Tenney produced a wide range of innovative works, including computer music, Fluxus-inspired text scores, and chance-based instrumental pieces founded on the overtone series. Tenney’s music is characterized by a fascination with sound and how listeners perceive it. In addition to his creative work, Tenney is the author of important theoretical writings on the psychology and phenomenology of musical experience. Like John Cage, Tenney intentionally avoids rhetorical gestures in his music, following his dictum that "[T]he focus should be on the sound itself and not on the ideas and emotions of the composer" (Tenney, 2005). Tenney was born in Silver City, New Mexico, but moved to New York in the 1950s to study piano with Eduard Steuermann and composition with Chou-Wen Chung. Later studies at Bennington College and the University of Illinois brought him into contact with Carl Ruggles, Lionel Nowak, Kenneth Gaburo, and Lejaren Hiller. In works from this period, such as Seeds (1956–61), composer Larry Polansky identifies the strong influence of Anton Webern and Edgard Varèse, two of Tenney’s early inspirations.

„nicht tonal und nicht atonal“ Zur Bedeutung der Quinten in Ligetis Etüde Nr. 8 „Fém“

Ligeti’s claim that his etudes are neither tonal nor atonal can be demonstrated with the functions of the fifths in the etude No. 8 “Fém.” The fifths are integrated into the musical relationships partly in a traditional and partly in a modern manner. Customarily, the interval of a fifth is added to single tones in order to establish tonal spaces and implying fundamentals. A peculiarly modern aspect is the use of fifths as parts of the overtone series.

The Song of the Sirens

In Homer’s account of the adventurous journey of Odysseus, the song of the sirens was so appealing and tempting that it lured sailors to their deaths. Warned by the goddess Kirke, Odysseus overcame the trap by plugging his crew’s ears with wax. An archaeo-acoustical research expedition undertaken by members of Humboldt University Berlin made sound propagation experiments at the supposedly historical scene at the Galli Islands where it’s said that the sirens originally sung. At the site we broadcasted both synthetic signals and natural voices via loudspeakers in the direction Odysseus most probably should have approached the Siren’s island. Subjective listening as well as objective acoustic analysis of the recorded signals revealed evidence for a combination of site-specific acoustic effects, which may explain the nature and origin of the song of the sirens in Homer. The local arrangement of the three islands deforms the acoustic signals by amplification and by changes in timbre. Two female singers from the Berlin State Opera were asked to sing differently pitched musical intervals to be tested in the Li Galli environment. The experiment evinced that the first overtones (octave, fifth, and fourths) would be merged by the echo of the rocks; yet when singing pure thirds and less consonant intervals, which yield higher orders in the overtone series, the voices appear recognisable as being two. As a result, and particularly because Homer stresses the number of exactly two sirens several times, the evidence of our research supports the musicological theory for a rather early existence of enharmonic tunings and most prominently a two-part polyphonic singing of Greek songs. Given that the rocky formation of the Galli Islands most likely didn’t change during the geological tick of just 2,700 years, we conclude that there has been a real acoustic basis for the myth reported by Homer and that a “song of the Sirens”, most probably based on natural voices, was transformed by the particular acoustic conditions of the landscape in such a way that signals were amplified and sent out in one concrete direction. Based on these results, we continue to discuss further leading acoustic theories that offer new insights into the mythology and which were essential to motivate our expedition in the first place. After all, the question remains open what kind of beings the first emitters of the song might have been.

MICROTONAL INTONATION FROM COMPOSER’S, PERFORMER’S AND CONCERT-AUDIENCE’S PERSPECTIVE: THE CASE OF GYÖRGY LIGETI’S Hora lungă FOR VIOLA SOLO

The aim of this study is to explore the microtonal intonation, i.e., pitch lowered by a quarter-tone, in György Ligeti’s (1923-2006) „Hora lungă” for viola solo. It is examined from three points of view: composer’s, performer’s, and concert-audience’s. The artistic reasons for the use of microtonality in this piece were explored in Ligeti’s own and other written sources. The difficulties performer encounters hitting the microtonal pitch on viola (corresponding to the 11th harmonic in the overtone series) were investigated practicing the piece by the author of this paper herself. Two methods of practicing microtonal intonation were tested. Firstly, the out-of-tune (“false”) sounding pitch was searched by ear. Secondly, the validity of the second method – listening to harmonics of open C string was proofed, measuring pitch frequencies of open string harmonics in 16 recordings, including the author’s. Finally the perception of microtonal intonation by 26 subjects in live concert setting was tested. Pitch frequencies of performed excerpts were also analysed. Additionally, 17 subjects were interviewed about the perception of microtonal intonation. It was concluded that the appropriate way to practice microtonal intonation is to search the out-of-tune sounding pitch by ear, while other method – listening to open string harmonics, could be questionable as frequency measurements of harmonics showed that 11th harmonic deviated largely from the target. Perception test results have shown that both musicians and non-musicians were able to hear by a quartertone lowered pitch in the author’s performance. Frequency analysis has shown that microtonal intonation in the author’s performance was reliable. From answers in questionnaires and additional interviews it could be concluded that the composer’s intention to create the impression of a „strange, magical, nostalgic world” through the use of microtonal intonation worked, although it remains unclear, if the result would be similar without preparatory explanations before the interviews.