Long-range correlation and multifractality in Bach’s Inventions pitches

Jafari, G. R.; Pedram, Pouria; Hedayatifar, Leila

doi:10.1088/1742-5468/2007/04/p04012

Cited by 77 publications

(70 citation statements)

References 49 publications

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“…(3) will be an fractional Brownian motion (FBM) signal, so that 0 < < 1 0. The exponent h is known as the Hurst exponent H [10,11,14]. But for a non-stationary signal, such as FBM noise, Y ( ) will be a sum of FBM signal, so the scaling exponent of F ( ) is identified by > 1 0 [10,11,14].…”

Section: Analysis Techniquesmentioning

confidence: 99%

“…In addition, it is shown Scaling behavior of earthquakes' inter-events time series that the autocorrelation function can be characterized by a power law C ( ) ∼ γ with exponent γ = 2 − 2H and the power spectra scales by S(ω) ∼ ω −β with frequency ω and γ = 2H − 1. For the non-stationary signals, the correlation and the power spectrum scaling exponents are γ = −2H and β = 2H + 1, respectively [10,11,14].…”

Section: Analysis Techniquesmentioning

confidence: 99%

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Scaling behavior of earthquakes’ inter-events time series

et al. 2009

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Abstract:In this paper, we investigate the statistical and scaling properties of the California earthquakes' inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0 34 + 1 53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0 50, which is for independent events. PACS

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Section: Analysis Techniquesmentioning

confidence: 99%

Section: Analysis Techniquesmentioning

confidence: 99%

Scaling behavior of earthquakes’ inter-events time series

et al. 2009

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“…Similar analysis was performed by Hsü & Hsü (1990, 1991. Jafari et al (2007) analysed power-law behaviour in the frequency series of Bach's pitches, finding that fat tails in the probability density function has more effect than long-range correlations in the multifractality. Long-range correlations in Mozart's music scores were investigated by Dagdug et al (2007), revealing the presence of correlations for relatively small note distances, with a tendency towards non-correlated behaviour for long note distances.…”

Section: Introductionmentioning

confidence: 73%

“…These pitches indicate a frequency, which is measured in hertz (Hz), they are related to each other and are defined around a central note pitch, with a frequency of 440 Hz. The frequency of any other note pitch is given by n = 440 × 2 n/12 Hz, where n indicates the integer number of half-steps away from the central note pitch (Jafari et al 2007). Each Sinfonia is characterized by three voices.…”

Section: Discussionmentioning

confidence: 99%

Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

Telesca

Lovallo²

2011

Proc. R. Soc. A.

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The one-, two-and three-dimensional multifractal detrended fluctuation analysis (MF-DFA) was applied to Bach's Sinfonias, which are characterized by the superposition of three different voices. Each voice, represented as a time series, can be considered as a component of a one-, two-or three-dimensional vector. The one-dimensional MF-DFA was applied to any single voice, while the two-and three-dimensional MF-DFA was applied to the couples of voices and to the triple, respectively. Each voice is characterized by a multifractal degree (MD), indicated by the range of the generalized Hurst exponents; the higher the MD, the larger the amount of heterogeneity and irregularity. Competitive scaling multifractal behaviours in Bach's Sinfonias were revealed; although one (or two) voices showed a relatively high MD, the other two voices, or voice, are characterized by a low MD. Nevertheless, the overall effect of the Sinfonia, measured by the MD of the triple, tends towards homogeneity, or at least to an average between the different competitive scaling behaviour shown by the different voices.

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“…Multifractal structures were identified in systems from various areas such as physics [2][3][4][5], biology [6][7][8], chemistry [9,10], economics [11][12][13] and even music [14][15][16][17][18][19]. One of the most popular methods of the multifractal analysis is multifractal detrended correlation (MFDFA) [20][21][22] and cross-correlation analysis (MFCCA) [23,24].…”

Section: Methodsmentioning

confidence: 99%

Quantitative Characteristics of Correlations of Meteorological Data

Rak

Bwanakare

2016

Acta Phys. Pol. A

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This paper presents the quantitative characteristics of correlations (and cross-correlations) of plant main ecofactors i.e. the ground and over-ground temperature, the wind speed, and the humidity. The study is based upon hourly data statistical observations collected in the region of Lublin, in Poland for the period 2001.05. 07-2009.04.10. This paper indicates that plant growth conditions constitute an emergent response to the above direct eco-factors. Then, the dynamics properties of each eco-factor is first analyzed alone for its multifractal structure. We apply the multifractal detrended correlation analysis and multifractal detrended cross-correlation analysis. We show that the widest multifractal spectrum is for over-ground temperature and the strongest power-law cross-correlations exist between ground and over-ground temperature. Next, an impulse response analysis is carried out to measure dynamical inter causalities within all the considered variables. As far as cross-impact between different eco-variables is concerned, one observes that the wind speed, the ground temperature and the air humidity dynamics are the most influenced, in terms of memory length time, by external temperature.

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Long-range correlation and multifractality in Bach’s Inventions pitches

Cited by 77 publications

References 49 publications

Scaling behavior of earthquakes’ inter-events time series

Scaling behavior of earthquakes’ inter-events time series

Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

Quantitative Characteristics of Correlations of Meteorological Data

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