Here are some alternate riffs i made of Tool songs along with the originals.

All riffs in Drop D.
. = palm mute

The Grudge opening riff Original
|---------------------------------------------------|
|---------------------------------------------------|
|---------------------5--------------------------5--|
|------7-------5-------------7-----7------5---------|
|-5h6p5--5h6p5---5h6p5--5h6p5-5h6p5--5h6p5--5h6p5---|
|---------------------------------------------------|

Alternate #1(Octave lower)
|---------------------------------------------------|
|---------------------------------------------------|
|---------------------------------------------------|
|---------------------------------------------------|
|------0-------------3------0------0-------------3--|
|-0h1p0--0h1p05-0h1p0--0h1p0--0h1p0--0h1p05-0h1p0---|

Alternate #2 
|----------------------------------------|
|----------------------------------------|
|------------------------------------5---|
|------7------5-----------7------5----7--|
|-5h6p5--5h6p5-5555555h6p5--5h6p5-5h6----|
|----------------------------------------|

Schism opening riff Original
|-----------------------------------|
|-----------------------------------|
|-7---5---7---7------7---5---7------|
|-8---7---5---8------8---7---5---7--|
|-5---8--------------5---8-------5--|
|-----------------------------------|

Alternate #1
|--------------------------------|
|--------------------------------|
|-7775557777------777555777777---|
|-8887775558------8887775555557--|
|-555888----------555888------5--|
|--------------------------------|
   .  .  ..        .  .  .....