The U.S. Built a Blueprint to Avoid Civilian War Casualties. Months Before the Iran War, Trump Officials Scrapped It.

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Not everyone in history thought that 12-TET was an acceptable compromise. Johann Sebastian Bach thought we should use other tuning systems that made better-sounding thirds and fifths in some keys in exchange for worse-sounding thirds and fifths in others. In Bach’s preferred tuning, each key had its own distinctive blend of smoothness and harshness. However, Bach did not get his way. We as a civilization have collectively decided that we want all our keys to be interchangeable. There are good reasons to want this! In 12-TET, all intervals and chords are built from standardized, Lego-like parts. You don’t have to keep track of a complicated web of different-sized intervals in every key. If you move a song from C to C-sharp or D or anywhere else, you can be confident that it will still sound “the same.”

Alright kids, why does this not work? Shall we call on someone in the back of the class—like, any undergrad quantum computing class in the world? Yes class, that’s right! There are exponentially many r’s. Computing them all takes exponential time, and loading them into the quantum computer also takes exponential time. We’re out of the n2-time frying pan but into the 2n-time fire. This can only look like it wins on tiny numbers; on large numbers it’s hopeless.

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15:56, 2 марта 2026Мир

Galaxy AI 手游是该领域的重要参考

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  • 路过点赞

    非常实用的文章,解决了我很多疑惑。

  • 热心网友

    内容详实,数据翔实,好文!

  • 路过点赞

    专业性很强的文章,推荐阅读。