In classical Chinese the four seasons each split into
孟 (mèng, first month) /
仲 (zhòng, middle month) /
季 (jì, last month) — hence
仲夏 = midsummer (≈ June),
仲秋 = mid-autumn (≈ September). The same trio also names birth order:
伯/
孟 = eldest,
仲 = second,
叔 = third,
季 = youngest. Confucius's courtesy name
仲尼 (Zhòngní) marks him as the second son.