Inverted Paradiddle

Question

I've been learning paradiddle variations and I've come across one called the "Inverted Paradiddle".

I'm not sure if this is a standard naming convention but what it means is instead of a normal single paradiddle.

Rlrr Lrll

We have this "Inverted" version.

Rllr Lrrl

My question is how is this an "Inversion"?

There are four different variations of the single paradiddle you can get by shifting where the accents are and by the resource I'm going from they are:

Single: Rlrr Lrll
Inverted: Rllr Lrrl
Reverse: Rrlr Llrl
Outward: Rlrl Lrlr

Reverse kind of makes sense since it's sort of played backwards.

Answer 1

Paradiddle
RLRR LRLL

The Inverted version, can be though of as:

• first shifting the starting position of the paradiddle pattern by one position to the right : LRRL RLLR

• but then, because we want to start with the right hand, we have to swap Lefts and Rights ("inverting"):
  RLLR LRRL

---

The Reverse is a shift of the original pattern by two position to the right. And the Outward is a shift by three.

Both the Reverse and Outward patterns don't need to swap Lefts and Rights compared to the original, because they already begin on a Right.

Answer 2

"Inversion" in music is sometimes closer to "rotation" ("chord inversions" in particular). The difference in the various paradiddles is the starting place, which is equivalent to changing the position of the accents.

RLRR LRLL
^ ^^  ^
| ||  |
Single|
  ||  |
  ||  Inverted
  ||
  Reverse
   |
   Outward

Or, put another way:

Single:   RLRR LRLL RLRR LRLL = RLRR LRLL
Inverted:       RLL RLRR L    = RLLR LRRL
Reverse:    RR LRLL RL        = RRLR LLRL
Outward:     R LRLL RLR       = RLRL LRLR

---

This begs the question of the remaining "inversions". Note first that all would start with the left hand.

LRRL RLLR = inverted, starting on second group
LRLL RLRR = single, starting on second group
LLRL RRLR = reverse, starting on second group
LRLR RLRL = outward, starting on second group

Answer 3

In my mind rudiment inversions are akin to chord inversions. For example, with a C Major 7 chord (for an equal number of notes to invert) you would have C-E-G-B. Hopefully the following table illustrates my way of thinking clearly:

C7 chord	Paradiddle	Inversion
CEGB	Rlrr Lrll	None
EGBC	Lrrl Rllr	1st Inv.
GBCE	Rrlr Llrl	2nd Inv.
BCEG	Rlrl Lrlr	3rd Inv.

At which point it wraps back around. The 1st, 2nd, 3rd, etc. inversion names aren't really used in my experience when it comes to rudiment terminology (i.e. I've never heard anyone refer to "Rrlr Llrl" as the 2nd inversion of a paradiddle), but hopefully that at least makes it clear where the terminology might have come from.