What is the scoring algorithm for Rock Band 2?
Here's some of the basics. It focuses on drums, but should apply to other instruments as well. Source has more details
Basic Scoring: Each note hit is worth 25 points, times your current multiplier (which ranges from 1-4).
For every ten notes hit in a row, your multiplier goes up until it maxes out at 4x. The multiplier takes effect on the 10th note of each streak. In other words:
Notes 1-9: 25 points
Notes 10-19: 50 points
Notes 20-29: 75 points
Notes 30+: 100 points For the multiplier, each note is counted sequentially, even if they occur at the same time. In other words, if the 9th and 10th note in a streak are in a "chord" (same time), you only get the 2x multiplier for one of those notes.
If you miss, your multiplier goes back down to 1x and your streak to zero after the "chord" you missed on. This means that you get your multiplier on all notes you hit in a "chord." For example, if three notes are in a "chord" and you only hit two of them, you get the multiplier for the two notes you hit, then lose your multiplier.
Playing in an overdrive fill gives you no points (except for squeezing, see section below). Big Rock Ending points are also covered below.
Overdrive: Each overdrive fill successfully hit gives you 1/4 bar of overdrive. You need 1/2 a bar of OD to activate. When activated, overdrive doubles your multiplier.
Big Rock Ending: Each drum hit is worth an initial value of 750 points, and afterwards the value "recharges" for 1.5 seconds until a hit is once again worth 750 points. Which note hit doesn't matter. The lights (for drums) do not reflect the recharge time.
As a result, rapidly hitting the drum board or just hitting a note every 1.5 seconds should net you the same amount of points. Another way of putting it is that you can get 500 points a second.
The score needed to get a certain number of stars is based on a base value for the song, multiplied by a different value for each star level. Source
Guitar/Drum/Vox: 1 star: 0.21 2 star: 0.46 3 star: 0.77 4 star: 1.86 5 star: 3.10 Gold star: 4.20
Bass: 1 star: 0.32 2 star: 0.69 3 star: 1.15 4 star: 2.76 5 star: 4.60 Gold star: 6.20
Edit: Vocal Scoring (source)
The vocal track is divided into phrases, visibly separated by bars on scrolling mode, or by each set of lyrics on static mode.
Whenever the arrow(aka your voice) matches the line on screen, the multiplier circle begins to fill. The higher it fills, the better a rating you'll get, such as Awesome, Strong, Messy, etc. The better the rating, the more points you get for that phrase. Awesome is the best, I think Messy is worse, and I don't think you get any points for a messy rating. To finish the song flawlessly, you actually don't have to hit every single note, you just have to make sure that you get an Awesome rating on all of the phrases.
Points for a phrase aren't variable over each song. Points are based off of the ratings. An Awesome score in any song will get you 1000 points; I haven't tested the other ratings but you get the idea.
As for Overdrive, since scoring is based on phrase rating, Overdrive will only score you the extra points if it lasts through the end of the phrase.
Another piece of info you might want to know is that the multiplier takes effect the next phrase, not the one it's created in. That is, on the first phrase if you score Awesome, you'll only get 1000 points. On the next phrase if you score Awesome again, you'll get 2000 points from the 2x mult even though you built up to the 3x.