In what respect does the wave pattern of a noise and music differ? Does the wave pattern of musical sounds contain only harmonics (other than the fundamental frequency) while noise contains random overtones (that are not harmonics)?
 A: Music is a sequence of sounds, carefully  chosen by several characteristics such as:

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*pitch/frequency

*length/duration

*intensity/loudness

*timber/quality

E.g., the choice of frequency is governed by tradition - heptatonic scale in Europe, but pentatonic in China, etc. (Although all of these traditions are more or less based on natural harmonics of strings, tubes, membranes and other similar objects.)
In noise (viewed by a physicist) any of these characteristics is random, although in casual life we would often call noise any sound that does not fit the narrow rules of traditional to us music harmony - such as the sound of a car motor or waves rolling onto a shore.
Note however that music, like any meaningful sound (such as human speech), is a random signal in the sense that the sounds the follow are not fully predetermined by the preceding ones, but they are nevertheless governed by strict probability rules (like the sounds of speech, wonderfully discussed in Shannon's seminal paper on Mathematical theory of communication).
As possible analogies one could give a printed text, vs. random ink spilled onto a page or paintings of classical masters vs. those of Jackson Pollock:

A: The majority of the energy in the musical tones "resides" in frequencies harmonic to the fundamental. Nevertheless, both mathematically and in practice, you cannot have energy concentrated in only one frequency unless your signal lasts for ever (from $-\infty$ to $+\infty$). This means that some energy will be "spilled" (apologies for the abuse of terms) into other frequencies too.
Nevertheless, the exact spectrum of the sound will strongly depend on the type (but not only) of the instrument/source. For example, flute, as well as other wind instruments exhibit significant noise-like characteristics due to the audibility of the "original sound source", which is the lips of the instrumentalist.
Furthermore, additional non-linear effects, such as vorticities (specifically in wind instruments, or the behaviour of plates and membranes in struck instruments) introduce more inharmonic frequencies in the spectrum. The actual phenomena are somewhat complex to be introduced in a generic context (such as this question) so I encourage you to look more into it. You could find much information in textbooks such as

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*"Acoustics of Musical Instruments" by Antoine Chaigne and Jean Kergomard.

*"The Physics of Musical Instruments" by Neville Fletcher and Thomas Rossing.

Please note that these references are just some of the available literature out there I happen to be aware of. By no means they constitute advertisement of the said textbooks and you should consult your own references, or those suggested by people you know and trust if that suites you best.
