There certainly are a lot of combinations, but I have some issues with the analysis here.
There’s a lot of redundancy in this counting, moving a pattern to an adjacent string or fret hardly qualifies as a “new” pattern.
The question then is what defines two movement patterns as “the same” or “different.” According the the textbooks on motor control and learning that I have read, movements are considered equivalent if certain invariant features are preserved.
At the most basic level, the invariants include
- Action sequence.
- Relative timing
- Relative force
The action sequence is the set of actions to be performed in the temporal order in which they are to be performed.
The relative timing refers to the time between actions in the action sequence as a proportion of the duration of the full sequence. The overall duration of the full sequence may be increased or decreased, resulting in slower or faster execution (respectively) and extending and contracting (respectively) the time between actions proportionally. However, the relative timing must remain (approximately) constant.
The relative force refers to the magnitude of the forces involved in the actions in the action sequence relative to each other. The overall force of the full sequence may be increased or decreased, with the relative forces of the sequential actions increasing or decreasing proportionally. However, the relative force must remain constant.
Many other features of movement are variant and can be varied quite significantly.
In a musical context, relative timing and relative force describe rhythm. Rhythm is invariant.
Suppose we start with the basic example of an ascending 6
|-------------|
|-------------|
|-------6-7-9-|
|-6-7-9-------|
|-------------|
|-------------|
1 2 4 1 2 4
Any pattern which shares the underlying movement invariants is considered equivalent. We have a lot of freedom in how we can alter the variants provided the invariants are preserved. I find it helpful to think of this as an “elastic deformation.” We need to preserve directions, but not distances.
The fret or string we begin on is variant, so we can move the ascending 6 to different locations on the fretboard. The half-whole pattern in variant, so we can change the specific intervals.
For example, we can have
|-------------|
|-------------|
|-------------|
|-------3-5-7-|
|-3-5-7-------|
|-------------|
1 2 4 1 2 4
Is still fundamentally the same movement pattern. More than that, we can vary the number of strings crossed, so something like
|-------------------|
|----------10-12-15-|
|-------------------|
|-10-12-15----------|
|-------------------|
|-------------------|
1 2 4 1 2 4
is also equivalent.
This is what I mean by a rudiment – A musically transferrable rhythmic coordination.
This is one of the main reasons I’m opposed to the classic “spider” permutation exercises. There are 24 possible permutations. Very few of them transfer to musically relevant shapes on the fretboard, and even then, the transfer is very limited.
Even if we ignore the fact that these exercises demand fretting postures which are suboptimal for actual playing, the movement patterns trained are fundamentally inequivalent those required in actual playing. It’s junk practice volume with almost no return on time invested.
It’s much more benefical to develop a vocabulary of rudiments that are naturally applicable to the types of fretboard figures that occur in music (2-note per string and 3 note per string scale shapes, arpeggios, triads and spread triads, etc) and which transfer broadly within those types.
If we restrict to patterns of length 4 with the first note accented (i.e., 16th note groups), three fingers on a single string, and assume a (1 2 4) finger combination, we find the following digital sequences.
Type 1
1214, 2141, 1412, 4121,
2124, 1242, 2421, 4212,
4142, 1424, 4241, 2414.
Type 2
1241, 2411, 4112, 1124,
2142, 1422, 4221, 2214,
4124, 1244, 2441, 4412.
As we can see above, Type 1 patterns do not involve the immediate reuse of a finger, while the Type 2 patterns all involve a reuse. In this way, Type 1 patterns naturally move across strings within a position, and the Type 2 patterns naturally shift across positions.
Some will notice that these each line of patterns involves the same sequence, but with an offset starting point. These patterns are not equivalent! Optimisation of these patterns involves different situational fretting mechanics (notably the reveal and the rock that I’ve described before), and more importantly, they’re not rhythmically equivalent because of the location of the accented note. The invariants are not preserved!
Also, depending on our anatomy, we can subsitute in a different combination relatively easily. We may be able to use (1 2 3) like Shawn Lane and Yngwie Malmsteen, or we may be able to use (1 3 4) like Paul Gilbert. You’ll know immediately which subsitution is naturally afforded to you.
So we’re left with 24 patterns which naturally apply to any 3 note per string figure on the guitar. We have no reduction in practice volume compared to the spider exercises, but every single one of the patterns described will transfer to a class of musically valuable fretboard figures, and will transfer broadly within that class.
If you absolutely must practice single string permutations, I think it makes much more sense to practice these patterns instead. I’m very comfortable with some, and not so comfortable with others. I’m not particularly interested in completing the set either, I’d rather spend my time working on other rudiments that I find more interesting, and making lines with them.
