Phrase guide

harmonic series

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

The divergent series whose terms are the reciprocals of the positive integers; the series ∑n=1 ᪲1/n.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

The sequence of all positive integer multiples of a base frequency.

Definition source: English Wiktionary via Wiktextract

Topics: entertainment, lifestyle, music, natural-sciences, physical-sciences, physics

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

13 source translations are retained for this English entry.

  • Asturian: serie harmónica — series of reciprocals of natural numbers
  • Catalan: sèrie harmònica — series of reciprocals of natural numbers
  • Finnish: harmoninen sarja — series of reciprocals of natural numbers
  • French: série harmonique — series of reciprocals of natural numbers
  • Galician: serie harmónica — series of reciprocals of natural numbers
  • German: harmonische Reihe — series of reciprocals of natural numbers
  • Italian: serie armonica — series of reciprocals of natural numbers
  • Japanese: 調和級数 — series of reciprocals of natural numbers
  • Polish: szereg harmoniczny — series of reciprocals of natural numbers
  • Portuguese: série harmônica — series of reciprocals of natural numbers
  • Portuguese: série harmónica — series of reciprocals of natural numbers
  • Russian: гармони́ческий ряд (garmoníčeskij rjad) — series of reciprocals of natural numbers
  • Spanish: serie armónica — series of reciprocals of natural numbers