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I've long been fascinated with the omnipresence of power-law statistics in natural and social phenomena. A good example is Zipf's Law for the usage of English words, named for the 20th-century linguist George Kingsley Zipf. The most common word, the , is used twice as often as the second most popular word ( of ) and three times as often as the third ( and ). Similarly, the n th most popular word has a relative frequency of use of 1/ n .

Thus, the curve of popularity versus rank shows a steep decline at first, followed by a long tail that looks rather flat when plotted on a linear scale. (On a log-log plot, of course, this becomes a straight line.) A word like omnipresence is way out on the tail, at popularity position 74 228, right before the word Borodin (the Russian composer), according to WordCount (

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Deep Learning Could Bring the Concert Experience Home

The century-old quest for truly realistic sound production is finally paying off

12 min read
Image containing multiple aspects such as instruments and left and right open hands.
Stuart Bradford

Now that recorded sound has become ubiquitous, we hardly think about it. From our smartphones, smart speakers, TVs, radios, disc players, and car sound systems, it’s an enduring and enjoyable presence in our lives. In 2017, a survey by the polling firm Nielsen suggested that some 90 percent of the U.S. population listens to music regularly and that, on average, they do so 32 hours per week.

Behind this free-flowing pleasure are enormous industries applying technology to the long-standing goal of reproducing sound with the greatest possible realism. From Edison’s phonograph and the horn speakers of the 1880s, successive generations of engineers in pursuit of this ideal invented and exploited countless technologies: triode vacuum tubes, dynamic loudspeakers, magnetic phonograph cartridges, solid-state amplifier circuits in scores of different topologies, electrostatic speakers, optical discs, stereo, and surround sound. And over the past five decades, digital technologies, like audio compression and streaming, have transformed the music industry.

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