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As an example, first one off the top of my head: Ramblin' Man (Allman Bros)
There are lots of major thirds in rock. In a lot of songs a guitarist might be playing a minor pentatonic scale as a solo over a major chord, in which case the bass player usually avoids the major third. And as a passing tone, they are very frequent. Seems like modern pop doesn't have a lot of major thirds in the bass-- in fact, often not a lot going on in the bass in modern pop. looking at soul, old R&B, blues, reggae, and so on, there's a lot of maj 3rds.
There are lots of major thirds in rock. In a lot of songs a guitarist might be playing a minor pentatonic scale as a solo over a major chord, in which case the bass player usually avoids the major third. And as a passing tone, they are very frequent. Seems like modern pop doesn't have a lot of major thirds in the bass-- in fact, often not a lot going on in the bass in modern pop. looking at soul, old R&B, blues, reggae, and so on, there's a lot of maj 3rds.
My only gig is church band music and while it is extremely rare to have a written out part and even rarer to have a written out part that sounds like anything you'd want to play, the chord notations that we fake off of will often indicate what note the writer wanted emphasized in the bass. My favorite is when I'm asked to pedal on the same note for three or four pages but I digress.... With fair frequency the indicated note is a major 3rd. So it is a common enough note in this type of music but of course that proves nothing and answers no questions about its usage in "rock" music. I can tell you this however, sometimes when I'm asked to emphasize a major third it sounds fine, sometimes it sounds awful. I mean double check the chart and your fingers to make sure you are on the right note awful.
I'm not entirely sure why that is but I think it must be related to the fact that thirds are quite out of tune in the even tempered scale. If I were a skilled fretless player I could try tuning them when I play them but I don't even own a fretless at the moment to give that experiment a try. My theory is that sometimes I am the only one in the band sitting on a third for any length of time and so I can hear its error quite well, especially if a singer (who like a fretless player can tune their thirds correctly) happens to be singing a third along with me. When other instruments are also playing the third I just blend in and I don't hear a problem with that. That's my theory and while I won't stick to it if confronted with a better one, it's all I have right now!
So it could be that rock musicians, for some reason, are more in tune with how out of tune major thirds are and they just avoid them as a result. Now minor thirds are just as out of tune but minor thirds have an out of tune feel to them to begin with, it's kind of the reason for their existence, so perhaps their errors do not detract from and may even enhance their usefulness. Major thirds are sharp, minor thirds are flat. I also sing in the choir and pretty much all choral directors everywhere just detest it when you are flat and almost encourage you to be a little sharp. That fact would counter argue that we should prefer even tempered major thirds over minor thirds but perhaps we react differently to the errors in instrumental versus vocal music. Or maybe it is as simple as the fact that my minor thirds make the singers sound sharp by comparison while the major thirds make them sound flat?!?
I'm not entirely sure why that is but I think it must be related to the fact that thirds are quite out of tune in the even tempered scale. If I were a skilled fretless player I could try tuning them when I play them but I don't even own a fretless at the moment to give that experiment a try. My theory is that sometimes I am the only one in the band sitting on a third for any length of time and so I can hear its error quite well, especially if a singer (who like a fretless player can tune their thirds correctly) happens to be singing a third along with me. When other instruments are also playing the third I just blend in and I don't hear a problem with that. That's my theory and while I won't stick to it if confronted with a better one, it's all I have right now!
So it could be that rock musicians, for some reason, are more in tune with how out of tune major thirds are and they just avoid them as a result. Now minor thirds are just as out of tune but minor thirds have an out of tune feel to them to begin with, it's kind of the reason for their existence, so perhaps their errors do not detract from and may even enhance their usefulness. Major thirds are sharp, minor thirds are flat. I also sing in the choir and pretty much all choral directors everywhere just detest it when you are flat and almost encourage you to be a little sharp. That fact would counter argue that we should prefer even tempered major thirds over minor thirds but perhaps we react differently to the errors in instrumental versus vocal music. Or maybe it is as simple as the fact that my minor thirds make the singers sound sharp by comparison while the major thirds make them sound flat?!?
As said before a lot of rock music is based in minor keys so riffs and fills are abundant with the minor third (1-flat 3-5). A lot of fills I remember years ago for major based songs the bass fills were more in the 1-4-5-7-8 box patterns. This isn't always the case but I noticed this too. The more songs I learned the less it seemed so. But I think in many rock songs when in a major key they tend to use these box patterns. Almost to keep it minor-ish in sounding? 
Of course music is about being inventive as well. A good example is Number of the Beast by Iron Maiden. Major 3rd in the opening riff and carries the song through out.
Of course music is about being inventive as well. A good example is Number of the Beast by Iron Maiden. Major 3rd in the opening riff and carries the song through out.
I was just about to mention Eyes of the World... Also... Brown Eyed Women, Mississippi Half Step, Estimated Prophet, Deal, Scarlet Begonias, Let It Grow, and many others. So many in fact, that I've learned to position my middle finger on the root for just about every song to make it easier to play the maj3 (some songs it's also easier with the pinky on the root, which has the same effect)
Here is my take on this.
Some people play power chords. No 3 in a power chord. Would it hurt the song to add the 3? Probably not. Would it hurt the song to just use power chords? Probably not.
The major 3 is implied. Now the minor b3 is necessary for the minor sound to develop IMO.
That and $1.58 will get you a cup of coffee at most East Texas eating places.
Some people play power chords. No 3 in a power chord. Would it hurt the song to add the 3? Probably not. Would it hurt the song to just use power chords? Probably not.
The major 3 is implied. Now the minor b3 is necessary for the minor sound to develop IMO.
That and $1.58 will get you a cup of coffee at most East Texas eating places.
Disclaimer: haven't read all the reply's so I'm sure it's been said and conversation has deteriorated into something else but....
A good reason is that a major third implies a strong pull toward the relative IV chord of whatever chord you're currently on. Roots and 5ths don't imply as much direction. So it's not that you can't use them, it just requires a little more planning. I use them if it's diatonic and I'm moving up a fourth, or sometimes along with the 5th to arpeggiate the chord.
A good reason is that a major third implies a strong pull toward the relative IV chord of whatever chord you're currently on. Roots and 5ths don't imply as much direction. So it's not that you can't use them, it just requires a little more planning. I use them if it's diatonic and I'm moving up a fourth, or sometimes along with the 5th to arpeggiate the chord.
Due to the minor flavor of popular rock tunes, not to mention the bluesy tendency of many guitarists to favor bent strings that all too often are somewhere in between major and minor thirds, the root or fifth in the bass creates a firm foundation rather than dissonance. That, plus the apparent inability of some rock songwriters to create memorable contrapuntal bass lines leads to the simplification of our role. By using your imagination and learning some theory, you'll have the tools required to incorporate thirds, sixths and sevenths in your playing without sounding weird or wrong.
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I think you are finding the exceptions to the rule in certain rock songs that focus on root-fifth only. Major thirds are common all over. Rock is a small subset of that.
With in rock, we can estimate from the following.
1 - Power chords are common, so in that case the 3rds are avoided.
2 - voicing out the chord from the entire band, roots and fifths sound better at the bottom, thirds, sevenths, and extensions sound better in higher registers. So the bass plays roots + fifths, the guitar, piano or vocals perform the 3rds and others. Go the the piano and play out the chords. 3rds sound better on top, not too low to avoid being muddy, UNLESS it is the actual bass note. Then the voicing is 3rd on bottom, and root and fifth up on top. Plenty of songs with 1st inversion chords in rock. Usually 1st inversion V (in between I and vi,) or I chords (leading up to IV).
Uh, I've covered a lot of Stones material over the years, and Bill Wyman didn't exactly shy away from them. As was mentioned, a lot of rock is based in minor keys, which requires minor modal scales to be in good taste.
Most musical compositions of late do not use bass scales much for chordal movement, and for the most part, we've been relegated to mostly quarters and 8ths on the root which may be why it's sounding odd to you. I'll wager dollars to donuts, if you play a song performed before 1970 in a major key, you are likely to find a bassist playing the major third.
My Carvin bass has no major 3rd's. They were a $120 upgrade on the "build-your-bass" page so I passed.
Riis
Riis
Surely this is just a result of the rock genre not needing them - as the bass frequently drives the song along, and isn't there to be clever. In rock and roll, the 3rd leads the way to the next chord, and in pop, it's there to give colour, not support. Rock with the usual distorted guitars doesn't respond very well to not having root or 5th as the driver. Those that make a thing about not being either Major or minor can't really use a 3rd because it gives the game away and takes away the body - and being low, tends to clash with the guitars above. Loads of musical styles just don't explore music in a expanded way. I can't think of a punk song, or an Irish jig that features a Major 3rd in the bass. Elton John of course made it a kind of signature - in so many of his songs in a VERY obvious way. Isn't this like asking why rock songs don't seem to have diminished or Major 7 chords either?
Because science. Yes, that's right. Psychological science says you are looking for a problem that doesn't exist. Perhaps YOU have found exceptions to the rule that a major 3rd DOES sound good on a major chord and you are focusing on some songs where it doesn't work due to melody or your 3rd clashing with the recorded bass line.
Well there is most definitely *not* a minor 3rd in Althea, except of course over the minor chord (Bm). I am pretty sure there are plenty of major 3rds on the E and A. And the chorus starts on A and goes to C#m, which is kind of like playing a major 3rd over the A in the chorus.
