Major and Minor Scales for the Guitar in all Keys

Approach
Rather than starting with a theoretical explaination of the intervals that define the major and minor musical scales, we'll jump into a practical implementation of those intervals on the guitar neck. A common strategy, indeed common among many string instruments besides guitar, is to 'slice' scales into sets of intervals which ease fingering given a particular instrument. For guitar, there are a multitude of ways to slice the scales into fingering patterns. Some strategies focus on preserving the theoretical perspective of the scale. For instance, such strategies may favor patterns that begin and end on the key's root note. This may have some pedantical advantages. However, it usually requires a tradeoff in fingering. For example, some slicing strategies end up with a series of 3 whole steps on one string which requires expensive shifting or very large hands. Other strategies may produce a greater number of patterns and require more wrote memorization.

The approach provides here is a comprimise between economy of motion, memorization and theoretical pedentary. It requires the least amount of memorization out of any method I've studied. It has fair economy of motion but not the best. Other slicing methods that produce a greater number of patterns within the same physical guitar space require less shifting and therefore have greater economy of motion. Since easy fingering is to be favored over theoretical visualization, the start and end points of each pattern are in fairly arbitrary points on the scale. This slicing strategy yields some nice properties for fingering such as, a maximum of 1 whole step per string, 2 - 3 notes per string.


Assumptions
From this point on, I assume the reader is standard tuned to E and is playing a 6-string guitar.


Using the patterns
The 5 patterns below fully implement the C major and A minor scales (C major and A minor contain exactly the same notes but have different notes ending up consonant with the key). In each 5x6 table, the bottom row is the low E string and the top is the high E. Each table also contains a number denoting the fret in which the number rests. The dots are the notes that you play. Each pattern has some fingering recommendation and other notes of interest.


For economy of motion, try starting this pattern with your middle finger and hitting the second note with your pinky, third note with your index finger, fourth note with middle, fith with pinky and so forth. When you reach the b-string, shift so that you play the first note on that string with your index finger.
2
This pattern overlaps the previous pattern by 3 frets. That is, the last 3 frets of the previous pattern are the same as the first 3 frets of this pattern. The two patterns share 8 duplicate notes. Again, pay attention to your fingering with economy of motion in mind.
4
This pattern overlaps the previous pattern by 2 frets. The two patterns share 9 duplicate notes.
7
This pattern overlaps the previous pattern by 3 frets and shares 8 notes with the previous pattern.
9
The final pattern has 2 frets of overlap with the previous and shares 9 duplicate notes. Try playing this pattern through with your index finger always allong the 12th fret.
13


Transposition
The title of this document includes "for all keys" so let's address that now. I provided the fingering for A minor / C major. To get into any other major or minor key, we simply shift the entire set of patterns. The intervals between all the notes, and therefore the relative fingering, remains the same; just moved to a different place on the neck. There's an algorithm that simplifies shifting the patterns, at least in my mind, and it is as follows. For minor keys, shift the root note of the second pattern such that it rests on the root of the given key. For major keys, do the same thing but with the 2nd note of the 3rd pattern. For instance, if we want to be in D minor then move the 2nd pattern so that the 1st note starts on the 10th fret rather than the 5th fret. Then move all the other patterns by the same interval and behold you're now in D minor. If we want to be in D major then move the 3rd pattern such that the 2nd note is on the 10th fret rather than the 8th. Then move all other patterns by the same interval and you're in D major.

The transposition of these patterns is valid assuming you're in either a major or relative minor key. It does not work for modes, harmonic minor, melodic minor or other exotic scales as they have different intervals between notes. However, many exotic scales can be achieved by simply memorizing the deltas between these patterns and whatever is required for the new scale. Once the delta is integrated with the existing pattern, transposition can be used again. This is beyond the scope of discussion here.