Visualizing the emotional power of music

February 23, 2016
Credit: Wikipedia.

Musical styles and genres differ around the world, but the emotional power of music is universally felt. To understand this evocative force, researchers in many fields, including information science, neural perception, and signal processing, investigate music's underlying structure, examining features such as the tone, timbre, and auditory and rhythmic features of a piece.

Now a team of Japanese scientists from the University of Tokyo has developed a new approach to analyzing musical structure. The new method overcomes many of the limits of previous tools. The researchers publish their results in the journal Chaos.

"The new and important point of our method is that it analyzes the local and global features in one framework without corrupting the underlying regularities of the original time series," said Miwa Fukino, a doctoral student at the University of Tokyo and first author on the paper. "For example, when one uses Fast Fourier Transform to get the frequency spectrum and then uses it to calculate the feature vectors of tonality, the timing information is lost in the resulting data. So, the result cannot be used for further analysis related to the timing factors," she said.

Fukino and her colleagues' new approach is based on a graphing technique called a recurrence plot, a two-dimensional analytical tool that visualizes recurrences of data. Recurrence is a basic property of complex systems, first described mathematically in the late 19th century by French mathematician and scientist Henri Poincaré, in which systems return close to their initial state after a finite amount of time. The new twist the Japanese researchers added is to make a recurrence plot of recurrence plots. This provides layers of time series data to visualize simultaneously both local and global attributes of . The researchers applied their new approach to selected classical piano pieces by Bach, Beethoven and Mozart.

Structural knowledge of music is useful for many professional applications, from composition of performance pieces to to music therapists seeking a healing response. The researchers are continuing their work to reveal a scientific understanding of its evocative power.

Explore further: Genes may help explain why some people are naturally more interested in music than others

More information: "Coarse-graining time series data: recurrence plot of recurrence plots and its application for music," by Miwa Fukino, Yoshito Hirata and Kazuyuki Aihara, Chaos: An Interdisciplinary Journal of Nonlinear Science Feb. 23, 2016. DOI: 10.1063/1.4941371

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1 / 5 (1) Feb 23, 2016
Suppose we hear an A4 @ 440 Hz, accompanying an A2 @ 110 Hz - both pure tones (sine waves):

- we resolve each tone individually - a lower pitch and a higher one. The sensory data is fine; there is no interference between the two stimuli.

- yet we perceive octave equivalence - we might not know we're hearing the pitch class of "A", but we still have a percept of "sameness" regardless.

So if the stimuli data remains intact - as it is - what is this property of "equivalence" - what is "the same" as what? They're clearly two distinct pitches!

Evidently it's something internal, not external. It's a value we ascribe to the relationship between spatial frequencies. To wit, it is metadata!

it is information "about" a frequency relationship, and it is registering as "zero" - there is no information about a difference, hence the sense in which they're equivalent.

So there is no tonal consonance or dissonance, only degrees of inequivalence.

Intriguing eh?
1 / 5 (1) Feb 23, 2016
In resolving this classic paradox it becomes evident that we're processing information and representing it internally in terms of physiological entropies.

Notes are just sound. But the metadata we're assigning their relationships is not borne of some specialised musical affinity - on the contrary, audition is bound to universal principles of processing.. IOW, this equivalence (or lack thereof) between tones is much more fundamental than audition itself.

It must be the "stuff" - the ones and zeros - of meta information generally, across the board.

And as much for the limbic system as for thalamus and cortex.

Spatial and temporal frequency relationships most likely correlate to connective and impulse rate entropies, respectively; relationships lying in a factor of two to a fundamental (NOT simply doubles and halves) are maximally simple WRT their respective physiological processes.

Octave-sized bandwidths are the emergent paper upon which all else is written...

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