DontRunMeOver

Nobody's really answered your question yet though, have they? I'll put down a simpler answer now and add details, arguments and changes depending on other answers. Again, love the topic.

1. Why the traditional three piece is fine and shouldn't be messed with

The traditional three piece (and also four/five-pieces with extra guitars or synth/keys) is fine because each of the instruments fit together nicely in terms of pitch - with the drum kit unpitched, the bass on low frequencies, the rhythm guitar on mid-frequencies and the lead instrument (keys, guitar or singing) on higher notes. The bass/guitar/drums rhythm section combination also allows for detailed rhythmic interplay, due to the percussive nature of all of the instruments.

2. What they should replace the traditional three piece with

For the purposes of creating an energetic, passionate, instinctive style similar to current rock guitar band styles (that's the style I'm after, although it could be used for other guitar bands too), but using different sounds, I would say that we'd need to use other instruments which have similar rhythmic capabilities to the guitars and drum kit. To provide pure rhythm, another type of drum section could be used (as the kit is the cliche we're trying to move away from, not drums in general).

For pure energetic, sexy drive, I'd go for an african type drum section - three drummers, one on a big, bassy drum; one on a piercing mid-range drum and the other on little bongos. All of them miked up. I'd consider a samba section, but that'd involve too many drummers and would take up too much space in the mix.

For the bass notes, important for the 'groove' you need for my favourite rock,
I'd go for a dance-synth bass sound. A big, fat, raunchy noise. Like a randy elephant. You could use it to play around with the noise you get and its usually easy to get a decent pulse going when you only play one note.

And most importantly, I'd get rid of the guitars. Guitar music is great, but the six-string guitar must be the most over-used and over-played instrument of modern times. There aren't that many pitched percussive instruments and the piano (which is one) has also been over-used. How about a vibraphone, with effects pedals?

So my suggestion for a 5-piece set up, to take over the rock business, is:
3 drummers on a simplified african-style drum section.
1 bass-synth, with lots of dirty bass noises.
1 vibraphone player, with a selection of effect pedals at his/her feet.

3. Why it has survived this long

Partly for the reasons suggested in 1, that the set-up is a practical way to play a variety of music, particularly those styles requiring very rhythmic harmonic backing. The other reason is that guitars, basses and drum-kits are widely available, as is suitable amplification. Plus, the instruments are taught at a lot of schools. The overwhelming popularity of musical styles which use these instruments amongst young people perpetuates it. Big3, you made a very good point about the effort which has gone into the guitar-band setup, to develop it to the point it is at today. There must be many other contributing factors but I've run out of ideas for now...

4. and 5.

I'm going to leave these for now... Out of brain-power.

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