Meaning of the word "Harmonic" in different contexts

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Discussion Overview

The discussion revolves around the various meanings and contexts of the term "harmonic," including its applications in mathematics, physics, and music. Participants explore the definitions related to harmonic functions, harmonic oscillators, and the implications of these terms in different fields.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant defines a harmonic function as one that satisfies Laplace's equation but notes that sine and cosine functions, considered harmonic in the context of vibrations, do not solve this equation.
  • Another participant suggests that the term "harmonic" likely has multiple definitions across different contexts, acknowledging the confusion this can cause.
  • A different viewpoint proposes that the term "harmonic" may share a common etymology related to stringed instruments, referencing connections made in a Wikipedia article about harmonic series in music and other related concepts.
  • One participant mentions the issue of overloaded notation in mathematics, drawing a parallel to the varying meanings of the term "normal."

Areas of Agreement / Disagreement

Participants generally agree that the term "harmonic" has multiple definitions across different contexts, but the discussion remains unresolved regarding the specific relationships between these definitions.

Contextual Notes

There are limitations in the discussion regarding the assumptions underlying the definitions of harmonic functions and the potential connections to harmonic oscillators, which remain unclear and unresolved.

JTC
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A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that.

However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation.

And then there are words like: harmonics (for higher frequencies) or "harmonic oscillators" that repeat their motion.

Could someone provide a suite of definitions of the word harmonic?

At the moment, I am confused and thinking that the functions that solve Laplace are related to harmonic oscillators. Am I dealing with multiple definitions?
 
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JTC said:
Am I dealing with multiple definitions?
Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.
 
I'd guess that harmonic in each case may have a common etymology from stringed instruments.

The wikipedia article here makes the connection between the harmonic series in music, harmonic mean, harmonic oscillators, etc. I don't know about the Laplace's equation piece of it though.
 
jtbell said:
Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.
Talk aboutthe use of the term " Normal" in Mathematics: https://en.wikipedia.org/wiki/Normal#Mathematics

Talk about overloading notation.
 

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