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Let's say we're playing a melody, and all of a sudden the chord changes, like in the beginning of a bar or something. Is it safe to say that the melody note that is now played going to be a chord tone of the new chord we switched to? (I've noticed it usually is using sites like hooktheory, etc).
Edit: I meant a chord tone is one of the notes of the underlying chord. So in a triad of C major for example: C E G, then any of these 3 notes would be a chord 'tone'.
No, that's not a safe assumption.
For example, it's common for a melody note to be held while the harmony changes to a chord against which the melody note is a dissonance, and then for the melody note to be resolved to a chord tone later. See https://en.wikipedia.org/wiki/Nonchord_tone#Suspension
Trying to answer the question, not being too sure what is being asked!
I think you are looking for some sort of formula that will help in your playing, and possible composing. That formula doesn't really exist. Using your 'chord tone' idea, there are as many pieces which align with that as there are that don't. It's maybe not that easy to understand, but humans tend to pigeonhole stuff. Often to help those coming along later. So, it's a nice idea that yes, when the next chord comes along, the notes contained will be found in the melody at that time. It's nice and neat.
However, music isn't there to just be nice and neat. In fact, as often as not, it's just the opposite. For that to happen, there exists what we call tension and release. If every bar had just notes from the accompanying harmony, it would sound bland, and that's not what it's always about.
It would be very easy to make up a 'rule' (something we're 'good at'), and it could be said glibly that in a bar of C major, we need C, E and/or G, but where would that leave us?
Only in very simple harmony exercises! In real music there will be so many exceptions that we couldn't say 'most often'.
The way I understand you question is: when the chord changes in the accompaniment what does the melody commonly do? There is no 'rule' about what the melody should do, but it may be helpful to run through some of the possibilities.
This is just a simple outline, but you should see that there will be many possibilities. At the very least the next melody note will be either a chord tone or non-chord tone, and the chord tone could be a common tone found in both chords. If seventh or ninth chords are used it can become tricky what is considered a real chord tone. If that is confusing, try working with basic triads first and learn how to identify all the different non-chord tones.
Keep in mind this is just a overview of common practice harmony. Music isn't required to work this way. You could have a melody of all non-chord tones if you want. Try different things. Look at many examples and analyze them.
If the question means,'if there is a chord change, the melody note that occasioned the chord change must be included in the new chord',the answer would seem to be 'No', certainly in a practical sense. But how do we determine whether or not it was the melody note that caused the chord change? In jazz the chord progression can have its own logic and contain its own 'melody', so it could be the tail is wagging the dog
TL;DR: Theoretically, yes; applicably, no. What I'm going to say may be a little confusing depending on how you view chords. Classically, chords are built with maj/min 3rd intervals. You can construct a whole scale by following the pattern of switching between maj/min 3rd intervals. Say in C, the major would be C, E, G. CMaj7: C, E, G, B. CMaj9: C, E, G, B, D. CMaj11: C, E, G, B, D,(this is a little weird because it's a minor 3rd interval) F. CMaj13: C, E, G, B, D, F, A. If you were to condense a CMaj13 chord and play it in a linear fashion, it fully creates the CMaj scale. So, if the melody is inside the scale, which 99.99% of the time it is unless you're playing jazz or some impressionist piece, it will technically be in the chord. However, it's not safe to assume the melody will simply be in the CMaj triad simply because it the harmony. One way to really bring out specific sounds is to play a maj/min 3rd an octave apart. Play a C and G with your left hand, and an octave higher play E in your right. This really resonates the sound and makes it stand out more. This technique can be applied to any note of the scale, with any chord of the scale, really.
