For centuries the drum and percussion community has been plagued by the ultimately irrelevant but persistent question: How many rudiments ought there be? The easy answer is that it doesn’t matter, but argumentative drummers have difficulty letting go sometimes. Myself included. I come down heavily on the side of learning as many rudiments as possible, as evidenced by my Encyclopedia Rudimentia with its 850+ patterns and variations. Some drummers are diametrically opposed to this and would rather learn the minimum number possible to function, perhaps 3 or 5 at the most. I have addressed the differences between the NARD 26 and the PAS 40 already in another piece on the website, but generally these are the most commonly argued numbers. Either 26 is enough and 40 is too many, or 40 is enough and 26 is too few. Rather than argue philosophically or abstractly about which sheet is best or how many rudiments one ultimately needs, I thought I would take a different approach here and think about how many actually get published in Anglo-American sources.
For this exploration I tallied up the number of rudiments that appear in 34 different British and American rudimental publications from 1778 up through 1984. Included in the list are the PAS and NARD sheets, Ashworth, Bruce and Emmett, Strube, Moeller, Sousa, and many other legendary names. Over the 224 years span, the rudiment lists range from a mere 8 rudimental entries to the familiar 40 rudiments at the high end. Both the modern PAS sheet and Colonel Hart’s 1862 book reach this figure. Despite the high end of the American lists being 40, there are some common rudiments that American still use that are not on the PAS sheet, the 3 stroke ruff is a good example, but not many more than 40. It seems that the “right amount” is probably lower than 40 and more than 8 — but how many?
Both the mean and geometric mean number of rudiments listed in across the centuries happen to be 23. The median is 24. Since these numbers are all extremely similar, I think it is safe to say that most British and American rudimental authors over a 224 year span would agree, on average, to a list featuring about 23 rudimental selections. This is interestingly close to the NARD 26, but still fewer. Of course, I’m not going to try to decree which of the hallowed 26 are superfluous, just that most drum publications seem to get away with about 3 fewer on average.
Mathematically, 23 sounds cut and dry. Done and done. Unfortunately, the flaw in this math is that the total number of American and British rudiments, by my count, is 81. Even though 40 seems excessively high, compared to the average above, any set of 40 is only about 50% of the total number of rudiments that appear in Anglo-American sources over the 224 year span. Our perfect calculated average of 23 rudiments then only represents a conservative 28% of the total pool of rudiments used in Britain and America. What sounded reasonable by the math looks a bit anemic in this context.
Another flaw in the logic is that America and Britain are not the only rudimental cultures on earth. Perhaps the Anglo-American rudimental philosophy isn’t typical. To get a better handle on what’s reasonable in a global sense, let’s try another exercise. Instead of looking at individual publications, we can compare entire regional or national traditions. For this exploration I tallied the total number of rudiments in each of 19 distinct rudimental systems from Europe and the Americas over the entire span of their publication history, up to 700 years, or at least as much of it as I could find. The numbers ranged from a tiny 6 named rudiments in the Bavarian system to a whopping 76 in the American system (I split American from British in this calculation). The mean number of rudiments used in any given rudimental system is about 25 while the median number of listed rudiments is only 13. The geometric mean comes in around 17 and the mode (which I’ve never used for anything since about 5th grade math class) is 11. The discrepancy in different mathematical averages stems from the fact that just a few big systems use about 10 times more named rudiments over their history than the smallest systems. There are 12 distinct traditions that feature 15 rudiments or fewer in the entirety of their rudimental playing over time. There are just 3 that use more than 70: Scotland, France, and America.
Intriguingly, the mean for entire systems, 25, and our previous perfect average for individual Anglo-American publications, 23, are very similar. Results appear to be confirmed. Problem solved. It is common, in fact, to have an entire drumming tradition based on fewer than 24 rudiments, but the 6 of Bavaria is misleadingly low. Bavarian music uses more than 6 popular rudimental patterns, they just don’t name some of them. It is also the case that no system ever uses more than about 50 rudiments at any one point in history. As noted above, 11 is actually the most common repeated number of rudiments across many systems. To sum it up, mathematically, the NARD 26 appears to be pretty close to the historical and international sweet spot in terms of pure average number of patterns. Well done, NARD founders.
The next question, however, is which rudiments are the perfect set of 23 or 25? Most drummers will likely argue the NARD set is already perfect, and thus I’ll leave the argument there — for now. I will reiterate that I am a proponent of learning as much as possible and not limiting knowledge or skills to a canonical set of any rudiments. This has just been a fun, and mostly meaningless, exercise in low-level, unrigorous statistics. The important thing is to remember to have fun and play actual music.