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Basically, all you have to remember is that a major third is one semi-tone lower than a perfect fourth. Which means we need to move upwards one fret on the 2nd string to get the same intervals on the 2nd and 3rd strings. Let's do a quick example:
===3rds===
fig. 1
b-0--1--3--5--76--8--10-12-
g-0--2--4--5--7--9--10-12-
fig. 2
c----0--2--4--65--7--9--11-
g----2--4--5--7--9--10-12-
This allows you to always hold down both your middle and index fingers. You just add the ring finger for the major third.
===4ths and 5ths===
Now let's look at the 4th and 5th intervals:
fig. 4
Perfect 4th Perfect 5th Tritone |-|m| |-|-|-|p| |-|-|r| |i|-| |i|-|-|-| |i|-|-|
Again, the 2nd string is just one step higher; however, it certainly takes a while to get used to. It's easy to identify fingering patterns with sounds.
fig. 5
b-1--3--5--6--8--10-12-13-
g-0--2--4--5--7--9--10-12-
tt
fig. 6
b-3--5--6--8--10-12-13-15-
g-0--2--4--5--7--9--10-12-
tt
===Scales===
Now let's look at a scale. Let's play B to G on the 1st and 2nd strings:
fig. 57
e----------0--1--3-
b-0--1--3----------
And let's play those same exact notes on the 2nd and 3rd strings:
fig. 68
b----------5--6--8-
g-4--5--7----------
b c d e f g
We play a middle h/w pattern on both strings in both cases, but for when going from the 2nd and to 3rd stringsstring, we shift one fret upwards. '''My advice is to do a positional shift. ''' Let's take a look at this in a larger context:
fig. 79
e----------------------------------0--1--3--5-
b-------------------------0--1--3-------------
a b c d e f g a b c d e f g a
fig. 810
e-------------------------------------1--3--5-
b----------------------------1--3--5----------
a b c d e f g a b c d e f g a
Both examples play the exact same notes, except Figure 8 10 shifts from open to first position between the 3rd and 2nd strings. '''Notice how when performing the shift, we get 3 notes per string. ''' This is a concept we will revisit later, but many speed players prefer this because it creates more balance when moving up or down the scale through the 2nd and 3rd strings. It is also easier to derive scales this way - each string will be either a middlew/w, ringw/h, or stretch h/w pattern of 3 notes. Without the shift, we get 2 notes on either the 2nd or 3rd string, and 3 notes on the other. This disrupts the order of the patterns across strings. In the above examples, figure 8 10 has ring, ring, stretch, stretch, stretch patterns. In Figure 7 9 we have ring, ring, ?, middle, middle patterns, then a final stretch to the high A. And again, we may have 2 notes on the G string in this case, but in other cases it would have 3 notes and the B string has 2.
''Note: the figures above play an A minor scale. Notice that it's the same notes as C Major. We'll look more into this later on.''
== C Major notes on 3rd String ==
fig. 11
g-0--2--4--5--7--9--10-12-
G A B C D E F G