The peaks were lofty and majestic, piercing the clouds.
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The base sense is 'high mountain', from which it became the name 嵩山 - the central peak of the Five Great Mountains, home of the Shaolin Temple. The same reading and tone is used whether it means 'lofty' generally or the specific mountain; capitalization only marks the proper-noun use.
Standalone 高 means 'high'. Stacked under the mountain it doubles the meaning - mountain plus height equals 'a lofty, towering peak' - while also nudging the sound.
