It has four pulses in each full stroke set. The sound is four equal length sounds (4 even 16th notes) (bum-pa-tit-ty. Or if hammer/pulloff is not done with left hand, the rhythm is long short-short (8th note plus 2 16ths) (bum__tit-ty) Below are each of the 4 parts of a single stroke set.
1) Back of middle finger nail stokes downward on a single sting
2) Left hand finger hammers down or pulls off for 2nd sound (or if tune doesn't demand a sound here, let 1) above ring thru this pulse.
3) Back finger nails of ring and small finger lightly brush all 4 (or the most convenient of the 4 ) full strings.
4) Thumb follows downward striking the short 5th string with the flesh of thumb
Suggest starting with 1)__3)4) and adding the hammers or pull offs after the fingers develop a smooth accurate stroke. The explanation is easy, which is why Pete covers it in a paragraph. Pete uses his index finger on 1) plucking a single string upward. The remaining three pulses of his style are identical to clawhammer style. I'd like to be able to do it too, but I had a lousy banjo with too much play in the strings. A good stiff string action is better. Learning to do it well is mostly a matter of getting control of the middle finger back nail downward stroke. Try playing notes or simple melodies with the middle back nail. When it seems to feel logical to your hand add a 3)brush-4)thumb after a note. Finally hammer or pull-off another note at 2). When any of this bungles your rhythm go back to the middle nail. Initially this can drive you crazy, but once you get it, you'll wonder why you couldn't do it immediately. Go back to Pete's book and read his explanation again. Honest, he told you all you needed to know. Good luck!
Basic Scruggs Stroke
There are three stroke types:
1. Index flesh plucks single string upward.
2. Middle flest plucks singlt string upward.
3. Thumb flesh plucks 5th string downward.
The above stokes can be used in any order and can be skipped at any time. Indeed, in order to clearly play just the basic melody or get the effect of clear single string work or chords, the bluegrass stroke is abandoned. However the basic bluegrass sound is a continuous string of fast 8th notes (8 of them in every 4 beat measure). You have three types of plucks: three of them played consecutively is a roll, two of them is a partial roll. In a 4 beat measure you can play two full rolls and one partial roll. Alternately you could play four partial rolls. However you could endlessly play full rolls and rarely coincide with a 4 beat bar length. Ie: your rolls roll over the beats. Partial rolls will coincide with the beat. Remember the sound is always 8 continuous 8th notes per bar, or 16 sounds per 2 bars or 32 sounds per 4 bars. So you start playing endless steady single 8th notes grouped as rolls and partial rolls. At first don't tap your foot because it will hinder your stroke pattern. Using 1,2,3 to stand for the three types of plucks, try the following:
12312313|12312323| Your finger group motion (not the speed or rhythm) will feel 123,123,13 | 123,123,23
Try your groups of 8 starting with thumb, then middle. Try different combinations of two fingers on the half roll. Make up all sorts of strokes and as you do it try to invent other new patterns without stopping, or simply let you fingers do what they prefer. The patterns are only for practice. When you can endlessly play out strings of 8th notes almost unconciously you can now add the beat in your foot.
In a measure your foot taps four times, once to each beat. There are two 8th notes to each beat. Try the easiest: play four partial rolls, four groups of two plucks. This coincides with your foot beat very nicely. Two even 8ths are sounded to each foot tap. This is cool but it's not bluegrass because it is steady, more like a simple march beat. There is no syncopation: which is places where the foot beat do not coordinate with the beginning of a roll. Let's go back to the first roll pattern we practiced:
12312313 = 123,123,13. Next we are going to indicate which notes coincide with the foot tap by bracketing the coinciding note. We'll also spread it out so it reads more easily:
 2 ,1  3,  3,
Notice you 2nd foot tap came before the first roll was completed and your second roll group starts before the 3rd foot tap. However, to your satisfaction the half roll final group coordinated with the 4th foot tap. You have been introduced to bluegrass syncopation and if you kept your eight 8th notes all steady, it had a jazzy rolled over rhythm where taps came without a tune emphasis and also where tune emphasises (roll group starts) occured when there was no tap (the off-beat) Here you will be happiest to just try this same pattern until your foot can tap smoothly and your fingers play evenly in rolls. Let the mistakes happen, but always put plenty of full rolls in your playing. Partial rolls just kick you down to simple unsyncopated steady music.
The partial roll can happen at the beginning 13,123,123, in the middle 123,13,123, twice 13,123,13,1|3,13,123,13|, never 123,123,12|3,123,123,1|23,123,123|, as little as you wish or as much as you wish. That you don't coordinate with each and every bar is not only not a problem, it is professional.
That is all there is to the basic stroke. Listen to some bluegrass and you'll notice that you distinctly hear tunes while all those endless 8th notes pour out. Indeed you may notice that full rolls and partial rolls are chosen to help sound those notes exactly or nearly where they belong in a tune. In other instances the player just simply plays the note louder (accents the note) which brings it out. However don't try melodies yet. Keep doing you old exercises and a listen for odd short tunes that you are creating while you are practicing. Change you left hand fingers and develop your odd tune. You'll be a bluegrass composer within the next half hour.
Do you want to play a tune? Choose an easy tune first. Play it noticing what left fingers have to fret and which right hand strings have to be plucked. If your tune is stead quarter notes (1 beat or foot tap per tune note), throw in a 5th string thumb on the off beat. (Remember you can play two 8ths to each beat) If the tune waits for a 2 beat (half note) note, you can throw in a full roll or three 8ths before you can continue. You are playing bluegrass again, but do it by starting with playing the tune and then start adding more notes to complete your full set of 8th notes. When you get moving, you will want to jog the tune around a bit so it accomodates your rolls. Sometimes you let the tune note hang beyond the time it should have sounded and then you'll catch it up by shortening some notes. Sometimes you'll drop an entire piece of the tune to show your bluegrass stuff and then suggest where the tune is toward its ending.
Again, Pete Seeger's book has a good introduction to bluegrass. Turn to the bluegrass section, you don't need to read the entire book first. There may be other books that do the same thing, but you would do well to tell yourself that bluegrass is one basic simplicity (8 notes grouped in 3's or 2's) which easily suggests tremendously complex musical sounds. Practice mastering the simplicity, your mistakes will produce the rest.