Are the primary chords of the major scale (I IV V) enough to make any major scale melody sound good? These chords together seem to encompass all 7 notes of the key.
I ask this because as I'm learning songs I know in different keys I'd rather just focus on these three chords for now. I'm just playing by ear, and so far I find this to be true. But I want to check with other musicians.
I'm talking about the major scale as I found minor to be a bit different.
A melody diatonic to the key can be accompanied with just I, IV and V chords, but this will give a less rich harmonization than using a wider variety of chords. But based on your question, you want to keep things simple.
That being said, do not feel you must match one of these chords to every single note of the melody. Using a reasonable harmonic rhythm, some of the melody notes, even though they belong to the key, will create a dissonance with the harmonizing chord. Listen carefully so you can harmonize in such a way to resolve these dissonances and make them pleasing.
Short answer. The short answer is yes: because all 7 scale degrees are represented by one of the chords, it is possible to make a harmonisation that only uses I, IV, and V. This is pretty close to how a typical treatise of music theory starts: start with these harmonies, and add more as need be.
Long answer. The longer answer is no. Although you can string together a progression of I's, IV's, and V's to accompany any melody, this does not necessarily mean that the accompaniment sounds good. This has to do with structural functions that each of the harmonies imply.
Concretely, a typical musical phrase will develop (on the large scale) as I IV V I or a variant thereof (e.g. I ii V I or simply I V I). There might be some other chords in between, but most likely all earlier incarnations of IV and V are in some inversion or otherwise have a weaker structural function. If you arrive on a V, in a lot of situations the only way out is to go to a I afterwards. Similarly, the strongest tendency for IV is to go to V (although back to I is also ok).
This is where other chords start coming in handy: if you move to IV or V too early, your melody is over and has to resolve. But sometimes you want to stretch it a bit longer, and then chords like vii˚, vi, iii, ii, and inversions of all triads become more important.
So what now? The harmonies I, IV, and V are certainly enough to get you started. But as you practise, you will start to notice that you want to do more, and that is probably the right time to add other harmonies to your repertoire.
The I, IV, and V chords will certainly be enough to make a progression that subjectively sounds like it 'works', by most normal people's standards, under any melody that genuinely restricts itself to the major scale. As you say, you have all 7 notes of the key contained within your chord options (which allows any note in the melody to be a chord tone if you wish) and the transitions between all of those chords will sound very standard and subjectively acceptable to most.
As to whether it's possible to always make something that sounds good is more subjective - you might always be able to make something someone would like - but I think you might be in danger of boring yourself by using such a restricted palette of harmony.
I ask this because as I'm learning songs I know in different keys
It sounds a bit strange to be asking about which chords to use if you're learning songs you know. If you're learning songs you know, you (IMO) need to use the chords from the songs, or they won't sound right! You could restrict yourself to songs that do only use I, IV, V chords and play them in different keys though, if that's what you mean - in fact that sounds like a great exercise to me.
You could accompany a diatonic melody with just I. Bagpipes and hurdy-gurdys do it all the time. Going up a notch, yes the 'three chord trick' will enable an accompaniment to a diatonic melody that doesn't sound painful. But beware. Many simple songs are not diatonic in one key. And do you really want to merely avoid sounding dissonant, or do you want the RIGHT chords? I strongly suggest you move your goal from being able to play ALL songs with just a few chords to learning THIS particular song with the right ones. Then another...
In theory absolutely. This is basic harmonization theory 100. However, You have injected a bit of opinion into this question making it a little unfair. You ask if the harmonization will "sound good". That's a bit subjective. The I IV and V are enough to harmonize anything and you do have the inversions each of which have a different harmonic character.
But if you ask me it won't sound "good" until you start putting tri-tone substitutes in there, I IV V, bV, etc.
