I'm struggling with the terminology for all the concepts related to sounds and notes. Most of the texts I read are not very precise in their usage of different terms, which makes it hard for me as a beginner to fully grasp the different concepts and get a clear understanding of their differences.
From a theoretical point of view, I'd like to distinguish the following concepts:
- Anything we can hear (i.e. an osciallation of pressure in a compressible media)
- The same as #1, but consisting of only a single frequency (e.g. a 440Hz wave, this is a purely theoretical construct)
- The same as #2, but including overtones (this one depends on the instrument used and is the "real" counterpart to #2)
- One element of a scale (e.g. a C, independent of frequency)
- Any concept of the above + information about length/duration
The terms which I've so far encountered in relationship with the concepts above are:
- Sound (corresponds to concept 1)
- Tone (although I'm not sure whether this is used in standalone form in English)
- Note (can correspond to concepts 2, 3, and 4, according to Wikipedia)
- Noise (sometimes used for concept 1, as in "I heard a noise")
- Pitch (according to Wikipedia, "Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale" and "may be quantified as a frequency")
- Timbre (according to Wikipedia, this refers to the collection of properties which distinguish two entities of concept #3 for the same fundamental frequency, i.e. harmonics and envelope)
- Amplitude and Loudness
There already exists a similar question and answer, but it distinguishes only pitch, note, timbre, and tone.
My background is mathematics, and hence I'm used to very precise definitions. I had expected that all these terms are defined more or less precisely, especially since music has strong ties to physics and mathematics. If this is not the case, how do musicians and music theorists usually resolve the resulting imprecision?