They are separated by 0.1° in the sky.
They are separated too into different asterism in Chinese astronomy. μ¹ Scorpii was a member of asterism 尾 (Wěi), Tail and μ² Scorpii was the sole star in asterism 神宮 (Shéngōng), Changing Room (of the temple). Both asterisms are part of the Tail mansion.
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