Tonal Center Research Articles

A Research on the Tonal Structures of ‘Bonnyeongsan’ of Jeongeup Julpungnyu

정읍줄풍류는 지역의 줄풍류에 국한되지 않고 영ㆍ호남지역의 풍류에 영향을 끼친 줄풍류이다. 정읍줄풍류의 음악적 특징과 활동한 인물 그리고 지역의 풍류 활동에 미친 영향 등을 고려하면, 정읍줄풍류의 음악적 중요성은 높다. 정읍줄풍류의 첫 번째 곡 상령산(上靈山) 즉, 본령산(本靈山)는 본풍류에서 뒷풍류까지 연주된 악곡의 출발점이며, 영산회상 관련 파생곡들에 영향을 준 중요한 악곡이다. 본 연구는 정읍줄풍류 중 본령산의 대금 음조직을 연구하기 위하여 정읍줄풍류와 국립국악원 줄풍류를 대상으로 비교・분석하였다. 그리고 전계문의 풍류대금 가락을 전수한 것으로 알려진 신달룡의 대금 가락도 일부 포함하였다. 본령산 대금선율에 함의된 음조직(Tonal System) 즉, 출현음ㆍ골격음(Structure Tone)ㆍ주음(Tonal Center)ㆍ음계(音階)ㆍ음의 시종(始終) 등을 분석하였다. 본 연구를 통하여 정읍줄풍류 중 본령산에 출현하는 대금 음조직의 특징은 첫째, 정읍 본령산 12음과 국악원 상령산 10음에 해당하는 출현음에 사용하는 장식음에 관한 악상기호는 총 6종이다. 본령산에서는 니레(∧)만 사용되었다. 둘째, 정읍 본령산 핵음은 黃, 국악원 상령산은 仲이다. 셋째, 본령산과 상령산의 기본 7음은 㑣ㆍ 㒇ㆍ黃ㆍ太ㆍ仲ㆍ林ㆍ無 이다. 본령산과 상령산의 음은 7음을 중심으로 옥타브 위의 음으로 확장되는 현상이 각각 2회 나타나지만, 확장의 결과는 상이 하다. 확장의 결과 본령산은 12음을 사용하지만 상령산은 10음에 그치고 있다. 상령산에서 淋ㆍ潕음은 사용하지 않았다. 정읍줄풍류 중 본령산의 음조직은 국립국악원 상령산과 유사하지만 기본음의 출현빈도와 음의 확장 그리고 주요 시김새의 사용방법 등에서 일부 차이점이 발견되었다Jeongeup Julpungnyu has widely influenced the chamber music in Yeongnam (Gyeongsang-do) and Honam regions (Jeolla-do) without confining the range to its indigenous music. Its musicality is significant considering its musical features, performers, and influences over the pungnyu activities in different regions. Sangyeongsan, the first piece also known as Bonnyeongsan, is the starting point played from the main piece to the last four pieces of the suite, which is a significant piece that influenced other derivatives of Yeongsanhoisang. This paper compares and analyzes the Jeongeup Julpungnyu and the Julpungnyu by National Gugak Center partly including the daegeum melodies by Shin Dal-lyong who is known to have initiated Jeon Gye-mun into the pungnyu daegeum melodies, in order to study the tonal structures of daegeum in Bonnyeongsan of Jeongeup Julpungnyu. The analyses include the tonal system implied in the daegeum melodies of Bonnyeongsan, that is, the structure tone, the tonal center, the scale, the beginning and terminating tones. The study results reveal the features of the tonal structures of daegeum in Bonnyeongsan of Jeongeup Julpungnyu as the following: Firstly, there are 6 musical symbols for ornaments for the 12 keys presented in Bonnyeongsan of Jeongeup Julpungnyu and the 10 keys in Sangyeongsan of Julpungnyu by National Gugak Center. Only one symbol, nire (∧) is used in Bonnyeongsan. The main key of Bonnyeongsan is ‘do’ (the Hwang key) while that of Sangyeongsan is ‘mi’ (the Jung key). Secondly, the basic 7 keys of Bonnyeongsan and Sangyeongsan are sol, la, do re, mi, sol , la . Although both pieces extend the 7 keys to an octave higher ones two times, the consequences are different. Sangyeongsan resultingly uses only 10 keys excluding the octave higher sol and la whereas Bonnyeongsan uses 12 keys. Bonnyeongsan is similar to Sangyeongsan in the tonal system but reveals some differences in the frequency of the basic keys in appearance, the tonal extension, and the usage of ornaments.

C, F-sharp and E-flat: The tragic, the sublime and the oppressed (with C-sharp as Nemesis): Reflections on Eine kleine Trauermusik by Milan Mihajlović

In the present paper, I will discuss tonal centers and referential sonorities in the composition Eine kleine Trauermusik (1992) by one of the leading Serbian composers Milan Mihajlović. Even though its pitch structure may appear rather straightforward with its octatonic scale and the primary tonal center in C, and with referential (quasi-tonic) chords derived from the harmonic series, I intend to highlight intricate narrative trajectories and dramatic conflicts between various tonal centers (treated as actors/characters). These narratives can be related to certain archetypal plots, with the conclusion that there exists ambiguity between the tragic and the ironic archetype. On a higher plane, similar conflict/interplay/ambiguity exists between different principles of pitch organization, i.e. the octatonic and functionally tonal. The unresolved ambiguities and simultaneity of conflicting interpretations are examined from the psychoanalytic perspective, which postulates isomorphism between musical structures and processes and the processes unfolding in the unconscious mind. Finally, the effect of these narratives, especially the overwhelming impact induced by the excerpt from Mozart's piano concerto is linked with the idea of sublime as conceived by Kant, but also including other approaches (Burke, Lyotard etc.).

Tonality Without Structure

In most Western music, notes in a melody relate not only to each other, but also to a “key”—a tonal center combined with an associated scale. Music is often classified as in a major or minor key, but within a scale that defines a major key, emphasizing different notes as the tonic yields different “modes.” Thus, within a set of notes, changing the tonal center changes the putative role of any given note. In this experiment, we eliminated all structural cues to the tonic within a melody by presenting notes randomly selected from the C major scale. A “mode” was established by a continuous drone note lower than the melody. Subjects rated mood (happy versus sad) and tension of each pseudo-melody. Consistent with Temperley and Tan (2013)—in which multiple structural cues were present—different modes produced reliable differences in judged mood and tension. Notably, modes with a major 3rd from the tonic (Ionian, Lydian, Mixolydian) were perceived as happier and less tense than modes with a minor 3rd (Dorian, Aeolian, Phrygian, Locrian). The results confirm that the perception of notes in a melody, and their consequent emotional connotation, depend at least in part to their relationship to a tonal center.

The fret-harmonic content of the Chinese melos (on the example of samples for the voice and piano in the modern arrangement)

The fret-harmonic content of the Chinese melos (on the example of samples for the voice and piano in the modern arrangement)

The fret-harmonic content of the Chinese melos (on the example of samples for the voice and piano in the modern arrangement)

The fret-harmonic content of the Chinese melos (on the example of samples for the voice and piano in the modern arrangement)

Feedback and Feedforward Models of Musical Key

This study begins by drawing a distinction between two ways of framing the concept of musical key.Feedforwardmodels understand key as arising from immediately apparent surface characteristics like the distribution of pitch classes or a melody’s intervallic content.Feedbackmodels, on the other hand, understand key as being determined in tandem with other domains. Here, key arises from the surface being organized into other more complicated musical groupings or schemata—harmonic progressions, cadences, prolongations, meter, etc.—that themselves are informed by the music’s tonal center. While much music theory and theory pedagogy have acknowledged that feedback occurs in various approaches to tonality, formal modeling in the fields of music cognition and computation has focused primarily on feedforward systems. This article attempts to right this imbalance by presenting a corpus-based feedback computational model that can be tested against human behavior. My model will identify a passage’s key by organizing a surface into its constituent harmonies. Here, harmonic organization and key will be integrated into a feedback system with the ideal key being that which produces the ideal harmonic analysis, and vice versa. To validate the resulting model, its behavior is compared to that of other published tonal models, to the behaviors of undergraduate music students, and to the intuitions of professional music theorists.

Quantifying the manipulation of F0 as an acoustic correlate of stress in Rebkong Amdo Tibetan

Quantifying the manipulation of F0 as an acoustic correlate of stress in Rebkong Amdo Tibetan Rebkong Amdo is a non-tonal variety of Tibetan spoken in Rebkong County, Qinghai Province, PRC. Speakers draw on varied acoustic resources to convey stress in disyllabic words, which are highly frequent in the language. Non-verbs (nouns, adjectives, and numerals) are stressed on the second syllable (S2); the primary acoustic correlate of stress is F0. Verbs are stressed on the first syllable (S1); stress is conveyed by both intensity and F0. For non-verbs, speakers manipulate F0 in different ways to convey S2 prominence. The pitch contour may (a) be flat in both syllables but higher in S2; (b) be flat or slope gently in S1 but fall sharply in S2; or (c) be generally flat in S1 but define a prominent arcing curve in S2. These three patterns, which occur in free variation, require different analytical approaches in order to quantify relative acoustic prominence across syllables: (a) mean F0 (Hz) is measured for each syllable; (b) pitch slope (in Hz/100 ms) is measured for each syllable; (c) F0 curves are characterized using a principal components analysis, and by determining the tonal center of gravity. In each approach, measurements are paired to determine the magnitude of the F0 contrast across syllables in individual words; these are then aggregated, demonstrating that speakers’ use of F0 to convey S2 prominence is statistically as well as perceptually significant.Quantifying the manipulation of F0 as an acoustic correlate of stress in Rebkong Amdo Tibetan Rebkong Amdo is a non-tonal variety of Tibetan spoken in Rebkong County, Qinghai Province, PRC. Speakers draw on varied acoustic resources to convey stress in disyllabic words, which are highly frequent in the language. Non-verbs (nouns, adjectives, and numerals) are stressed on the second syllable (S2); the primary acoustic correlate of stress is F0. Verbs are stressed on the first syllable (S1); stress is conveyed by both intensity and F0. For non-verbs, speakers manipulate F0 in different ways to convey S2 prominence. The pitch contour may (a) be flat in both syllables but higher in S2; (b) be flat or slope gently in S1 but fall sharply in S2; or (c) be generally flat in S1 but define a prominent arcing curve in S2. These three patterns, which occur in free variation, require different analytical approaches in order to quantify relative acoustic prominence across syllables: (a) mean F0 (Hz) is measured for eac...

New Notes on the Rise-Fall Contour

Abstract This study examines the production and use of the rise-fall contour by three Yiddish/English bilinguals in a small American Jewish community. Acoustic analysis shows that the Yiddish rise-falls have higher peaks, larger rise spans, and later Tonal Centers of Gravity compared to a similar intonational contour in English. These results hold for all three speakers despite their diverse linguistic histories. Additionally, evidence is provided that rise-falls with higher peaks have social meaning in both languages. English rise-falls are produced with higher peaks during meetings of a local Yiddish club than during one-on-one interviews, and rise-falls with high peaks are used in both Yiddish and English during an exchange in which one of the speakers discusses his relationship to Passover. The social meaning of the phonetically extreme rise-falls is posited to be the reason why all three speakers have either successfully acquired or maintained phonetic distinctiveness between their English and Yiddish.

Reports of equitonic scale systems in African musical traditions and their implications for cognitive models of pitch organization

Psychological research into musical behavior has mostly focused on Western music, explored with experiments utilizing Western participants. This ethnocentric bias limits the generalizability of many claims in the field. We argue that our current understanding of the cognition of pitch organization might be helpfully informed by data gathered in non-Western contexts. In particular, musical traditions featuring equal-spaced scales (where all scale-step interval sizes are equal) are suggested to pose a challenge to popular models of pitch organization, in which unequally spaced scales are suggested to provide cognitive anchor points for on-the-fly pitch orientation. This article presents a summary and theoretical consideration of all available evidence on equal-spaced scales, the vast majority of which appear in east Africa. It is noted that despite equal spacing, there is evidence to suggest that tonal centers are still perceived by idiomatic listeners. We then proceed to propose how such tonal center perception is possible within equal-spaced tonal environments. In short, the existence of equal-spaced scale systems shifts the focus of research from interval uniqueness to alternative explanations for the perception of tonal centers, such as implicit statistical tracking, secondary parameters, recognition of learnt patterns as tonal cues, and so on. Throughout, we note that interdisciplinary work involving ethnomusicologists and psychologists would be beneficial in answering questions about music cognition, and by extension, human cognition in general.

A study on the characteristics of neoclassicism in Polish music under new political circumstances in 20 th Century

신고전주의의 경향은 제1차 세계대전이후 전 유럽의 작곡가들에 의해 나타났으며, 인상주의 사조, 표현주의 사조로 확산되어져갔다. 그 확산되어진 사조의 중심에는 폴란드 출신의 많은 작곡가들이 있었고, 그들은 20세기 현대사조를 준비하는 음악사적 위치에서 나름 중요한 차지하고 있었음으로 이에 관한 연구는 중요한 작업이라 사료된다. 폴란드 음악의 신고전주의는 파리에서 유래되었고 스트라빈스키가 아닌 오네게르와 미요의 사조를 따랐다. 카롤 시마놉스키를 비롯한 당시 중요한 폴란드신고전주의 악파들은 폴란드 민속음악의 다양한 요소들을 가미하여 그들만의 독자적인 신고전주의 기법에 의한 작품들을 쏟아내는데, 훗날 이들에 의한 신고전주의 작풍은 전후 40~50년대까지 폴란드 현대음악 전반에 걸쳐서 주류적인 기반이 되었다. 이는 20세기 폴란드 현대음악 사조의 대표적 특징들인 ‘새로운 선법’ · ‘새로운 조성’ · ‘새로운 민속주의’ · ‘새로운 단순화주의’ 등의 작품기법들이 루토스왑스키 · 펜데레츠키 · 구레츠키 · 킬라르 등 많은 폴란드 출신의 세계적인 작곡가들 의 작품사조에 중요한 기여를 했다는 점에서 폴란드 음악의 신고전주의는 20세기 폴란드 현대음악의 역사와 그 맥을 같이 하고 있다고 말할 수 있겠다. ‘폴란드 음악의 신고전주의’에 관한 역사적인 고찰을 위하여 그 당시 주요 작풍이었던 ‘민속주의’ · ‘다양한 리듬형태’ · ‘다양한 선율형태’ · ‘구조’ 등을 세계적으로 많은 활동을 한 주요 작곡가들의 작품을 통하여 살펴보았다.Polish musical neoclassicism, although oriented towards Paris, did not imitate the creative method of Igor Stravinsky, but rather the method of Arthur Honegger and Darius Milhaud. This was manifest in its poly-tonality, the harmonies of tonal centers, a limpidity of texture, the augmented role of hythm(incidentally, more motive forces than metro-rhythmic complications), the reduced influence of melody, the emphasis on an ironic approach to ‘Romantic relics’, i.e. the melodic and the lyrical. Polish neoclassicists readily braided into their music dance rhythms or melodic motifs characteristic of Polish Folklore. In contrast to the model of neoclassicism presented by Stravinsky, Poles were not inclined towards parody, grotesque or pastiche. Neither did not they adhere to the technique of processing material derived from the work of composers from other ears; they employed neither quotation nor imitation. Their simplification of language and texture was not so radical as that of the French composers of the ‘Groupe des Six’. The shift in the center of gravity from the Romantic aesthetic in which the output of Karol Szymanowski took shape to the new aesthetic(neoclassicism) launched in Paris took place within his lifetime. After Karol Szymanowski, virtually almost Polish composers turned towards the neoclassical aesthetic, which also became dominant across Europe, in spite of quite strong opposition from dodecaphony.

Perception of Modulations in South Indian Classical (Carnātic) Music by Student and Teacher Musicians

Modulation, a shift in mode (rĀgam), is important in South Indian classical (Carnātic) music. Here we investigate the sensitivity of Carnātic and Western listeners to such shifts. Carnātic music has two kinds of shifts: rāgamālikā (retaining tonal center, resembling a shift from C major to C minor in Western music) and grahabēdham (shifting tonal center, resembling a shift from C major to A minor). Listeners heard modulating pieces of music and indicated the point of modulation, and were measured for accuracy and latency. Indians were more accurate than Westerners with both types of modulation but Westerners were faster with grahabēdhams. Cues could explain performance differences between nationalities: Indians were more familiar with rāgamālikā-type modulations whereas Westerners’ culture made them more familiar with grahabēdham-type modulations. Increased caution toward the less familiar grahabēdhams for Indians could explain their slower response time compared to rāgamālikās. With grahabēdhams, hit rates for both groups were comparably high, but Westerners’ lower level of accuracy was due to higher false-alarm rates to lures that were superficially similar to actual modulations. This indicated their dependence on surface-level cues in the absence of familiarity and culture-specific information. Music training helped teachers in both groups make fewer errors when compared to students. Older listeners’ performance was comparable to that of younger listeners.

Review of Eric Chafe. 2000. Analyzing Bach Cantatas . New York: Oxford University Press

This analysis of the two tasks of suggestive theory help in making a precise assessment of Eric Chafe’s 2000 book, Analyzing Bach Cantatas. With Analyzing Bach Cantatas, Chafe continues to develop his theory of the allegorical use of tonal centers in Bach’s vocal music, also the subject of his 1991 book Tonal Allegory in the Vocal Music of J S. Bach (henceforth Tonal Allegory). These works advance, defend, and illustrate the hypothesis that Bach used relationships among tonal centers in the allegorical representation of the theological contents of the vocal works. Analyzing Bach Cantatas is an extremely ambitious work in that it attempts three simultaneous advances over Tonal Allegory: it seeks to broaden the audience for Chafe’s ideas; it deepens the historical contextualization of the cantatas; and it uses the concept of tonal allegory with greater flexibility. While a fuller picture of Chafe’s success in reaching these goals will emerge over the course of this review, an initial assessment is offered here.

Memory of a Tonal Center After Modulation

This study examines how long the percept of a tonal center is retained in memory following a modulation to a new key, and how harmonic context in the new key area affects recall of the original key. In Experiment 1, musically trained listeners (N = 50) were asked to rate perceived harmonic tension while listening to chord sequences that consisted of three parts: the first section established an initial key, the second section modulated to a new key, and the last section modulated back to the original key. The duration of the new key section ranged from 3 to 21 seconds. The tension slopes following the modulations indicated a gradual decay in the memory of the previous key as the length of the new key section increased. When sequences lacked cadences, traces of the initial key appeared to persist longer. In Experiment 2, musically trained listeners (N = 31) were asked to rate harmonic tension while listening to sequences with longer timescales of up to 45 s in a new key area. Additionally, responses to “closed” modulations, which returned to the original key, and “open” modulations, which departed from both the original and new keys, were compared. The combined results of Experiments 1 and 2 showed that the original key was retained in memory after 15-20 s in a new key. However, there was not enough evidence to conclude it persisted beyond 20 s.

Cognition of stability in atonal music in teenagers with no musical experience.

Musical understanding arising any musical stimulus is generally a complex task, as it is the product of cognition, of the subsequent emotional response, as well as of the complementary interaction between cognitive and aesthetic understanding (Eggebrecht, 2010). Levinson's (1997) Statement and Elaboration of Concatenationism suggests that musical understanding is achieved when listeners are able to distinguish between four separate yet interrelated points: (a) comprehension on a small scale, (b) enjoyment of the successive parts of a piece of music, and their relationship, (c) the way in which the parts interrelate, and (d) the appreciation of the musical value of individual parts and the cogency of their succession.The body of knowledge on musical understanding is not complete without considering Architectonicism, the ability to grasp large-scale musical form and structure that enhances musical appreciation (Levinson, 1997, 2006) and, according to Kivy (2001), translates into intellectual pleasure rather than musical pleasure. Hence, this type of listening experience always involves the unfolding of successive events (expectation-delay-resolution), where sound stimuli are perceived by the listener as being inconclusive and ambiguous, that is, psychological formalism. As a result, the listener will feel the urge to clarify the ambiguity in order to experience satisfaction (Meyer, 1956).Listener expectations can unleash distinct emotional states. According to Huron, the emotions evoked . . involve five functionally distinct physiological systems: imagination, tension, prediction, reaction and appraisal. Each of these systems can evoke responses independently (Huron, 2006, p. 7). Huron considers that these issues may to a great extent point to the difficulty of understanding the musical message, and indeed this difficulty is further increased when the analysis focuses on contemporary music, that is, 20th and 21st century music, which is marked by a lack of formal structuring and the unconventional use of musical parameters, such as dissonance, rhythm, timbre, or melody intrinsic difficulties.Given the breadth of the concept, for the purpose of this study, the term atonal is restricted to music that rejects tonal functions and relationships (Alain, 1981, p. 109; von der Weid, 1997, p. 35), and is mainly represented by the styles of the Second Viennese School composers (Schoenberg, Berg, and Webern) and their music composed from 1908 until the dodecaphonic system was developed in 1923 (Bosseur, 1996, p. 20). This may explain both the lack of popularization of contemporary music and the limited exposure of the population to this type of music, namely, its extrinsic difficulties. Nevertheless, it is . . the logical culmination of a tendency that started during Romanticism (Bennett, 2003, p. 26).The scientific literature in the field of comprehension manifests the aforementioned intrinsic (cognitive difficulty) and extrinsic difficulties (lack of familiarity and exposure). According to some authors (Lerdahl & Jackendoff, 1983; Raffman, 2003), the inability to understand this type of music is due to the fact that the listener lacks a measure of relative pitch stability. He or she is unable to accept the absence of tonal centers or to establish a regular metrical hierarchy, for example.Difficulties Caused by Auditory HabitsAnother group of authors (Hargreaves, 1986; Meyer, 1956; Zajonc, 1968) believe that the limited dissemination of pieces is the result of poor listening habits. As such, listeners are unable to refer to past experiences, and their lack of reference points provokes a rejection of music because they fail to understand it. In this vein, Krumhansl (1990) indicates that the primary reason behind a lack of reference points (cognitive opacity) is that musical cognition inclines toward forms of tonal structuring in acoustic material. …

A Cross-Cultural Grammar for Temporal Harmony in Afro-Latin Musics: Clave, Partido- Alto and Other Timelines

Introduction This article presents an in-depth study of musical concept called direction. The significance and regulative role of and similar cyclical timelines (1)in Afro-Latin have been established by many scholars, including Ned Sublette, Tomas Cruz, H.W. Soebbing, Rebecca Mauleon-Santana, and Ronald Herder. (2) Clave is typically identified as rhythmic anchor of Cuban music. Furthermore, Eugene Novotney, Hugo Foca Machado, Willy Munoz, Jorge Sadi, and Chris Washburne, among other musicians and scholars, have argued that is central not only in Cuban but in all Afro-American music. (3) Although there is agreement on importance of concept, previous work has either been precise but culturally narrow in scope, or broad in scope but imprecise in its details. The present work builds on these earlier efforts to establish an understanding of direction that is precise, parsimonious (only two concepts suffice), and widely applicable. My analysis proceeds from hypothesis that musics emerging from transatlantic slave trade with significant Yoruba influence share common traits including what has come to be called Ruth M. Stone links observations of musical role of clave-type patterns to geographical origins of patterns in West Africa, and emphasizes that this pattern-as-concept was brought to Americas with transatlantic slave trade. In particular, she states that fits, of course, with other patterns played at same time ... Therefore, it has role in keeping everything appropriately linked. Players use it as reference point to synchronize drum, bell, and vocal parts (Stone 2005:81). (4) D. A. Tobias has written that the is foundation of Latin-American rhythm and practically all of other instruments are guided by this beat (Tobias 1965:270). More recently, Arturo Rodriguez has argued that is key to understanding how Afro-Cuban is arranged and flows and that it is a concept that is fundamental to Afro-Latin music (Rodriguez 2003:41). Consequently, should be understood not only as pattern but also as critical musical concept (Rodriguez 2003:41-45; Mauleon-Santana 2005:5-8; Spiro and Ryan 2006:12-17). The word clave has several meanings, (5) so it is important to specify which I am addressing here. Three of these meanings are well-known: (1) claves, instrument; (2) in harmonic sense, as in the key of C major (in Spanish); and (3) small family of patterns, which is what musicians typically have in mind for clave. I refer to latter as proper. This article focuses on fourth meaning of clave, one frequently discussed but rarely investigated. I refer to this as direction. Clave direction is concept and rhythmic-regulative principle. It is analogous to key of piece of music, but instead of governing tonality, it governs fine-scale local timing (mostly without regard to pitch (6)). Clave direction gives composer or improviser set of preferred timing options and appropriate places within each phrase to place them (a sort of micro-phrasing), along with acceptable ways to break these rules (more freely in batucada than in Candomble, more so in axe than in samba, in timba than in songo, etc.). Just as key determines tonal center of piece, direction is overarching determinant of timing preferences for piece, but like its tonal counterpart, it allows for variety in musical expression, and even tricks, puzzles and multi-layered playfulness in its execution. In order to make most artistic and culturally sensitive use of this principle, I offer an approach to understanding direction that I call wide-sense clave. In this wider sense, clave-the-concept denotes not just existence of specific patterns, but relationships that any pattern may have with family of associated patterns. …

The Concept of Mutability in Russian Theory

In the last several decades, some important studies, such as those by Christopher Lewis, Harald Krebs, William Kinderman, and William Rothstein, have explored alternatives to monotonality in tonal music. In this paper, I discuss the concept ofperemennost’(mutability), which addresses the same problem from a Russian perspective. Mutability is generally defined as a fluctuation between two diatonically related tonal centers, usually a third apart. However, this somewhat narrow definition does not capture the notion in all its richness; the concept of mutability evolved significantly over the course of the last century. I explore this concept in the writings of six twentieth-century Russian theorists: Boleslav Iavorskiĭ, Lev Mazel, Viktor Berkov, Igor Sposobin, Iuriĭ Kholopov, and Andrei Miasoedov.

Emotional processing in music: Study in affective responses to tonal modulation in controlled harmonic progressions and real music.

The pitch material of virtually all the musics of the world is organized into tonal hierarchies in which the pitch classes of a tonal scale divide the octave into (typically) five to seven steps of a tonal scale, with a stable home base in the tonic pitch, and a variety of tonal functions and tendencies assigned to the remaining pitch classes (Dowling & Harwood, 1986). In western music, the tonal hierarchy is organized in terms of two principal modes, major and minor, defined in terms of tonal scales of seven pitch classes (Krumhansl, 1990). The seven pitch classes of a mode are selected from the set of 12 logarithmically equal steps (semitones) into which the octave has been divided by the system of equaltempered tuning adopted in Europe beginning in the early 18th century (Robinson & Needham, 1962). All the intervals defined by a mode are defined in terms of numbers of semitones, so any of the 12 possible pitch classes can be chosen as the tonic pitch of a musical (e.g., C major or E minor). Hence, a melody played in one key can be shifted to another key without distorting its melodic intervals. This system makes possible a shift of keys within a piece, which is called modulation.Tonal modulation involves a shift of tonal center within the same musical composition, involving a transition to a different key (tonality) with a new scale of pitch classes. Modulation is one of the main structural and expressive aspects of music in the European musical tradition. Relationships among tonalities are described in terms of the circle of fifths (Diletsky, 1677; see Figure 1). The circle of fifths arises because you can start with any pitch class and go up or down by 7 semitones (a musical fifth) and arrive at a tonal center whose major scale differs from the original scale by just one altered pitch. In Figure 1, this is illustrated by going from C up a fifth to G. The key of G major has one altered pitch (F#) with respect to the key of C major. The second example in Figure 1 shows what happens if we go up clockwise by five fifths around the circle, landing on B and adding five sharps (#) to alter the pitches of the scale. The more steps (in the shortest direction) between two pitches on the circle of fifths, the more differences between the two pitch sets that define the tonalities represented by these letters. Modulations can thus vary in the distance over which they travel in tonal space from one key to another. The greater the distance, the more complicated and surprising they are likely to be.Modulations can also vary in the relationships between the original and target modes. Each of the 12 available steps around the circle of fifths can be the center for two tonalities, one in a major mode and another in a minor mode, so that there are four possible modal relationships involved in modulations: Major- Major, Major-minor, minor-Major, and minor-minor. The major mode is generally characterized as happy, and the minor mode as sad. The affective influence of the major and minor modes has been thoroughly investigated (Gagnon & Peretz, 2003; Halpern, Martin, & Reed, 2008; Hevner, 1935; Kastner & Crowder, 1990; Panksepp & Bekkedal, 1997; Webster & Weir, 2005).Previous studies have demonstrated that listeners are able to track modulations in that their cognitive responses in terms of tonal-hierarchy profiles and ratings of tonal distance or tension are differentially affected (Firmino, Bueno, & Bigand, 2009; Krumhansl & Kessler, 1982; Lerdahl & Krumhansl, 2007; Thompson & Cuddy, 1989, 1992; Toiviainen & Krumhansl, 2003). The process of following the reorientation of a tonal center is guided by musical expectations and by perceived tonal tension (Lerdahl & Krumhansl, 2007; Meyer, 1956). In modulation, the degree of the perceived change in tonal tension increases with key distance (Bigand & Parncutt, 1999; Firmino et al., 2009) and is greater with clockwise (vs. …

The Off-Board String on the Medieval Fiddle

Drawing on explicit descriptions, iconographic representations, and contemporary narrative, this essay analyzes playing techniques and repertories plausible for one type of medieval fiddle and suggests that notions of historical fiddle performance may need to expand to accommodate the aesthetics and techniques implied by the off-board fiddle. While it has been widely assumed that the left thumb was used to pluck the laterally divergent string described by Jerome of Moravia, the complete body of evidence suggests an alternative interpretation: the thumb can be used to stop this off-board string, extending the melodic range of the instrument down to a step below the tonal center and providing potential for non-diatonic ornamentation. Ornamentation facilitated by the off-board string helps explain the emotional impact hinted at by theorists, a component underscored and clarified in visual representations of the instrument, where the off-board fiddle is associated with passion, whether sacred or profane. Similarly, this instrument is well suited to accompanying contemporary romances, which are associated with fiddle performance; the off-board string offers a singer a range of tools to heighten emotional tones and dramatic action.

A geometrical distance measure for determining the similarity of musical harmony

In the last decade, digital repositories of music have undergone an enormous growth. Therefore, the availability of scalable and effective methods that provide content-based access to these repositories has become critically important. This study presents and tests a new geometric distance function that quantifies the harmonic distance between two pieces of music. Harmony is one of the most important aspects of music and we will show in this paper that harmonic similarity can significantly contribute to the retrieval of digital music. Yet, within the music information retrieval field, harmonic similarity measures have received far less attention compared to other similarity aspects. The distance function we present, the Tonal pitch step distance, is based on a cognitive model of tonality and captures the change of harmonic distance to the tonal center over time. This distance is compared to two other harmonic distance measures. We show that it can be efficiently used for retrieving similar chord sequences, and that it significantly outperforms a baseline string matching approach. Although the proposed method is not the best performing distance measure, it offers the best quality–runtime ratio. Furthermore, we demonstrate in a case study how our harmonic similarity measure can contribute to the musicological discussion of the melody and harmony in large-scale corpora.

Ordered Step Motives in Jazz Standards

The focus of this study is the melodic motive. It uses a tool called the Ordered Step Motive (OSM) to investigate the way linear motives give shape to jazz compositions that have frequently changing tonal centers, nonfunctional chord connections, no clear global tonics, or structurally open, circular forms. This study contributes to the written body of theoretical knowledge about jazz composition by engaging with current scholarship on tonal ambiguity, circular form, and motivic associations between melody and harmonic organization. This study also invites further research into the relationship between common riffs and underlying structure in jazz composition, which may reveal crucial differences between standards written by Broadway and Tin-Pan-Alley composers and those written by practicing jazz musicians.