Sangeeta is from the Sanskrit संगीता (Saṅgītā — music, song, complete musical art) — from Sanskrit sam (together) + gīta (song). Sangeeta is one of the Sanskrit feminine names — central to traditional Hindu musical heritage. Sanskrit feminine name reflecting Hindu musical heritage.
Sangeeta does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
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In Pythagorean numerology the letters of Sangeeta reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.