Spectral characteristics in linguistics

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Forbes
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In the Wikipedia article on prosody in linguistics it says:

There is no agreed number of prosodic variables. In auditory terms, the major variables are:
  • the pitch of the voice (varying between low and high)
  • length of sounds (varying between short and long)
  • loudness, or prominence (varying between soft and loud)
  • timbre or voice quality (quality of sound)
In acoustic terms, these correspond reasonably closely to:
  • fundamental frequency (measured in hertz, or cycles per second)
  • duration (measured in time units such as milliseconds or seconds)
  • intensity, or sound pressure level (measured in decibels)
  • spectral characteristics (distribution of energy at different parts of the audible frequency range)
I have no problem with frequency, duration and intensity. However, I am at a loss to grasp what spectral characteristics refers to. I have done some Googling, but the explanations are too technical for me. Can someone please explain what spectral characteristics involve which is not covered by frequency and intensity?
 
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My understanding is that each instrument produces a range of frequencies and not a single frequency. Even if the range is closely distributed around a mean frequency.

The way we identify different instruments playing the same note is by the distribution of energy across this range.

I found this relevant Wikipedia page on pitch

https://en.m.wikipedia.org/wiki/Pitch_(music)
 
For instance the trumpet and the flugelhorn have the same length tube (something like 5 ft), but the conical taper is quite different. This makes the overtone (octave) mixture quite different in emphasis (and very slightly in tone) which our ear hears as timbre.
 
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I understand overtones/harmonics. So is that all spectral characteristics refers to when it comes to sound?
 
Spectral characteristics means the magnitude and phase of the various frequency components into which any sound can be decomposed (this is known as Fourier analysis). I am not going to parse your question for the meaning of "is that all"
 
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Thank you. I am now not so bemused as I was.
 
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