Intervallic Scaling in the Bach Cello Suites

Brothers, Harlan J.

doi:10.1142/s0218348x09004521

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…A similar pattern is found in the distribution of colors among paintings in a given period of art history (111). In music, Zipf's law has been observed in the melodic intervals of Bach, Chopin, Debussy, Mendelssohn, Mozart, and Schoenberg (112)(113)(114)(115)(116); in the loudness and pitch fluctuations in Scott Joplin piano rags (117); in the harmonies (118)(119)(120) and rhythms of classical music (121); and, as Zipf himself noted, in melodies composed by Mozart, Chopin, Irving Berlin, and Jerome Kern (108).…”

Section: Melodic and Rhythmic Bigrams Are Distributed According To Po...supporting

confidence: 60%

Universality and diversity in human song

Mehr

Singh

Knox

et al. 2019

Science

393

390

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What is universal about music, and what varies? We built a corpus of ethnographic text on musical behavior from a representative sample of the world’s societies, as well as a discography of audio recordings. The ethnographic corpus reveals that music (including songs with words) appears in every society observed; that music varies along three dimensions (formality, arousal, religiosity), more within societies than across them; and that music is associated with certain behavioral contexts such as infant care, healing, dance, and love. The discography—analyzed through machine summaries, amateur and expert listener ratings, and manual transcriptions—reveals that acoustic features of songs predict their primary behavioral context; that tonality is widespread, perhaps universal; that music varies in rhythmic and melodic complexity; and that elements of melodies and rhythms found worldwide follow power laws.

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Section: Melodic and Rhythmic Bigrams Are Distributed According To Po...supporting

confidence: 60%

Universality and diversity in human song

Mehr

Singh

Knox

et al. 2019

Science

393

390

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show abstract

“…If this were true, one would expect similar types of beauty-related stimulus structure, for example self-similar (fractal) patterns, across sensory modalities. Indeed, fractal structure has been demonstrated for particular types of music ( Voss and Clarke, 1978 ; Hsu and Hsu, 1990 ; Su and Wu, 2007 ; Brothers, 2009 ), but these findings remain anecdotal and await a more systematic investigation across different types of music and cultures. In the area of brain imaging, comparative studies of different domains are more advanced.…”

Section: Implications Of the Model And General Discussionmentioning

confidence: 99%

Combining universal beauty and cultural context in a unifying model of visual aesthetic experience

Redies

2015

Front. Hum. Neurosci.

112

127

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In this work, I propose a model of visual aesthetic experience that combines formalist and contextual aspects of aesthetics. The model distinguishes between two modes of processing. First, perceptual processing is based on the intrinsic form of an artwork, which may or may not be beautiful. If it is beautiful, a beauty-responsive mechanism is activated in the brain. This bottom–up mechanism is universal amongst humans; it is widespread in the visual brain and responsive across visual modalities. Second, cognitive processing is based on contextual information, such as the depicted content, the intentions of the artist or the circumstances of the presentation of the artwork. Cognitive processing is partially top–down and varies between individuals according to their cultural experience. Processing in the two channels is parallel and largely independent. In the general case, an aesthetic experience is induced if processing in both channels is favorable, i.e., if there is resonance in the perceptual processing channel (“aesthetics of perception”), and successful mastering in the cognitive processing channel (“aesthetics of cognition”). I speculate that this combinatorial mechanism has evolved to mediate social bonding between members of a (cultural) group of people. Primary emotions can be elicited via both channels and modulate the degree of the aesthetic experience. Two special cases are discussed. First, in a subset of (post-)modern art, beauty no longer plays a prominent role. Second, in some forms of abstract art, beautiful form can be enjoyed with minimal cognitive processing. The model is applied to examples of Western art. Finally, implications of the model are discussed. In summary, the proposed model resolves the seeming contradiction between formalist perceptual approaches to aesthetic experience, which are based on the intrinsic beauty of artworks, and contextual approaches, which account for highly individual and culturally dependent aspects of aesthetics.

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“…In summary, we have demonstrated an interesting characteristic of the music harmony. Previous studies have demonstrated the scale-free properties of the pitch [ 15 , 18 , 43 ], rhythm [ 13 ], intensity [ 44 ], melody [ 15 – 17 ] and structure [ 45 ] of a large number of musical compositions. The current findings show for the first time that consonance fluctuation in music obeys the same law.…”

Section: Discussionmentioning

confidence: 99%

Bach Is the Father of Harmony: Revealed by a 1/f Fluctuation Analysis across Musical Genres

Kendrick

Levitin

et al. 2015

PLoS ONE

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Harmony is a fundamental attribute of music. Close connections exist between music and mathematics since both pursue harmony and unity. In music, the consonance of notes played simultaneously partly determines our perception of harmony; associates with aesthetic responses; and influences the emotion expression. The consonance could be considered as a window to understand and analyze harmony. Here for the first time we used a 1/f fluctuation analysis to investigate whether the consonance fluctuation structure in music with a wide range of composers and genres followed the scale free pattern that has been found for pitch, melody, rhythm, human body movements, brain activity, natural images and geographical features. We then used a network graph approach to investigate which composers were the most influential both within and across genres. Our results showed that patterns of consonance in music did follow scale-free characteristics, suggesting that this feature is a universally evolved one in both music and the living world. Furthermore, our network analysis revealed that Bach’s harmony patterns were having the most influence on those used by other composers, followed closely by Mozart.

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Intervallic Scaling in the Bach Cello Suites

Cited by 6 publications

References 5 publications

Universality and diversity in human song

Universality and diversity in human song

Combining universal beauty and cultural context in a unifying model of visual aesthetic experience

Bach Is the Father of Harmony: Revealed by a 1/f Fluctuation Analysis across Musical Genres

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