First a bit of music theory!
American musical jargon (which we mainly use in the computer/sequencer field) derives from German nomenclature. So instead of using arbitrary names like crotchets and quavers we use the mathematical divisions of half- quarter- or sixteenth-notes, etc. This assumes the most common time signature of four beats in the bar/measure (trying to be transatlantic here), usually referred to as 4/4 ("four-four") time. Each beat is thus a quarter of the bar/measure and therefore known as a quarter note (crotchet in English). This nomenclature is retained even when there are a different number of beats in the bar/measure, e.g. 3/4. It is the speed at which quarter notes are played which is usually referred to as the BPM (Beats Per Minute) number, BPM=60 means 60 quarter notes per minute, or one beat per second.

When the beat is subdivided to get shorter notes we just use smaller fractions; two eighth notes (quavers) play in the same time as one quarter, four sixteenths (semiquavers) also fill one quarter beat and so on. To subdivide each beat into three, traditionally we don't invent another time value but speak of "triplets", meaning a group of three equal notes fitted into the time normally taken by two. Three eighth triplets or six sixteenth triplets fit into one quarter note beat, three sixteenth triplets fit into one regular eighth (half of a beat) and so on. Some software writers (e.g. Emagic) refer to eighth triplets as 1/12 notes and sixteenth triplets as 1/24 notes and I think this makes a lot of sense; there are, after all, twelve 1/12 notes in one bar/measure of 4/4.

Looking at the Redrum
Yes, it's about time we did that. The relevant parts are the STEPS and RESOLUTION selectors just above the step entry buttons (by the way, the pdf manual reference is pp. 90-91). STEPS selects how many equal time slots there are in the pattern, RESOLUTION sets how large or small those steps are. Patterns may have any number of steps up to 64 and the resolution of each of those steps may be as large as a half note (minim, two beats in normal time) or as small as a 1/128 note, each quarter note beat divided into 32 tiny segments!

Notice that the triplet subdivisions in ReDrum are given as:
1/8T, (same as 1/12) each quarter note beat divided into three, useful for jazzy/bluesy patterns, the traditional "swing" feel.
1/16T, (same as 1/24) each eighth divided into three, giving a more contemporary, "swung sixteenths" feel, typical of many hip hop tracks but could be used in a lot of styles.

Pay close attention to how STEPS and RESOLUTION are intimately linked. (For the purpose of these illustrations we are assuming that the music has a 4/4 meter, four beats to the bar/measure, those who want to explore further out time signatures will, presumably be able to adapt these figures.)

The number of steps required will depend on the musical style. A simple four beat rock drum pattern which only uses 1/8 notes will only require 8 steps. RESOLUTION should be set to 1/8 and only the leftmost eight step entry buttons will be any use (any hits from button 9 onwards will be ignored). Of course, you could still opt for 16 steps and program a two bar/measure phrase with the second half as a variation on the first. If you keep the 1/8 resolution and choose the full 64 steps then you can program an eight bar/measure phrase. Note that for any patterns longer than 16 steps you'll need to get fluent with the EDIT STEPS switch which allows you to see longer patterns in groups of 16. (I find it a little fiddly to use as it's easy to click just a little too high & select a different group from the one you want. It's probably easier to drag it.)

If you want to program a traditional jazz/blues feel you'll need twelve steps per bar/measure, each beat divided into three, so your STEPS value will need to be 12, 24 or 48, allowing for one, two or four bar/measure phrases. (If you're really masochistic you can write three or five bar phrases using 36 or 60 steps, but personally I wouldn't bother...) Note that the Propellorheads really didn't expect you to program in any kind of triplet feel as the 16 step entry buttons are still grouped in fours, even when you select 1/8T or 1/16T - a useful little revision, if you're listening, guys? So (just to drive it home) when you program patterns based on 1/8T (or 1/12s) be clear that the main beat comes every three buttons, i.e. the second bar/measure starts on button 13 and continues halfway into the next group of 16! Not exactly user friendly, I must say.

1/16 RESOLUTION is home territory & what ReDrum does (or displays) most graciously. Here each beat is divided into four so one row of step entry buttons equals one bar/measure and each of the four groups in EDIT STEPS represents a complete bar/measure. Set STEPS at 16 for one bar/measure, 32 for two or 64 for four. Let's just pause here a moment & compare what we've looked at. To hear a four-to-the-floor drum beat in 1/8 resolution (8 steps) you'd need to click buttons 1,3,5 & 7, buttons 2,4,6 & 8 being reserved for the offbeats. With a 1/8T resolution (12 steps) the drum will beat out the same pulse with buttons 1, 4, 7 & 10 clicked. Buttons 2 & 3 are used for the second and third parts of the triplet on the first beat and so on. With a 1/16 resolution (16 steps) click on buttons 1, 5, 9 & 13 to get exactly the same beat. Let me stress, each of these patterns will sound exactly the same, just the number of subdivisions available for offbeat notes increases. Note that in 1/16 resolution the 1/8 offbeats will be found on buttons 3, 7, 11 & 15. (You can't get even offbeat notes in 1/8T, it's not what it's designed for.)

Going up to 1/16T resolution means that each bar/measure is potentially divided into 24 time slots, or each beat can be divided in six parts, or each 1/8 note can be divided into three. With all this sub-dividability this resolution is obviously more suitable for moderate to slower tempos. The annoying thing is, given the limitations of ReDrum's display you can't even see one bar/measure at a time. A STEPS setting of 24 means that the 4/4 pulse mentioned above will occur on buttons 1, 7, 13 & 3 of the NEXT group of steps! (In a future re-write (ReWrite?) of ReDrum I hope the Props make the button numbering change when the edit group is changed.) Regular even offbeat 1/8s will occur on buttons 4, 10, 16 & 6 of the next group.

Rolls
In a roll, the individual hits blur together and are perceived almost as a sustained sound, rather than a rhythm, so to program rolls you need even higher resolutions and a correspondingly higher number of steps. The precise resolution will depend on the tempo. If we stick to a middle of the road tempo of 100 BPM then a resolution of 1/64 is quite enough to reach roll speed, 16 possible hits per beat. To program this into an intelligible phrase, say one bar/measure long, we need a step size of 64, ReDrum's maximum. This meant that each group of 16 will represent one 1/4 note beat so our four-to-the-floor pattern now becomes simply the first button of each edit group. Offbeat (1/8) hits will occur on the ninth button of each group.

Examples (in the accompanying Reason file "Patterns")
Most patterns sound good at around 100 BPM any use only snare & bass. A4 uses a bit of hi-hat as well & benefits from being played at a slightly slower tempo, say around 80.

A1 - a simple 2 bar/measure rock pattern using a 1/8 resolution, visible in it's entirety.

A2 - a two bar/measure jazzy phrase in 1/8T resolution, click up to edit steps 17-32 to see the ending.

A3 - a funky one bar/measure pattern using 1/16 resolution, 'nuff said. It uses the same number of steps as the two bar/measure rock pattern in A1.

A4 - a hip hoppish thing, one bar/measure long, using a 1/16T resolution so you'll need to go to the second edit group again to see the ending (uses the same number of steps as the jazzy phrase in A2).

A5 - a one measure pattern, all 64 steps long, using 1/64 resolution, which has a snare roll on the last beat. Like the other patterns it just uses bass and snare though I've used a second snare to give the roll a bit of build. Notice the "written in" flam for the snare in channel 2 visible as the last note in edit group one and the first note in edit group 2. (It more-or-less explains by itself what a flam is!) Notice also the build up in dynamics, soft to loud, in the snare roll. You'll need to switch to edit steps 49-64 and alternately select drum channels 2 & 5 to see it all.`