This tab illustrates intervals.
intervals are the distance between two notes.
intervals are important for several reasons:

1) they all have their own quality/function.
2) they are used to build chords and scales.
3) they are good for training your ears.
4) they are great for writting riffs/songs.
5) they cover all twelve tones in western music.

b = Flat
# = Sharp
8 = octave

We will use C as our root.
*Any note can be a root which means every note has all these intervals*

Layout:

(Interval)
(note)
(tab)
(timing)

Exercise 1 (C = Root/1)

 |1  b2   2  b3   3   4  #4   5   |#5  6  b7   7   8/1             |
 |C   Db  D   Eb  E   F   F#  G   |G#  A   Bb  B   C               |
G|————————————————————————————————|1———2———3———4———5———————————————|
D|————————————————2———3———4———5———|————————————————————————————————|
A|3———4———5———6———————————————————|————————————————————————————————|
E|————————————————————————————————|————————————————————————————————|
 |1 e + a 2 e + a 3 e + a 4 e + a |1 e + a 2 e + a 3 e + a 4 e + a |

Notice how all twelve notes are used. 
also notice that once you get to the octave,
it starts over.

here is each interval next to the root:

Exercise 2 (C = Root/1)

 |1 b2|1 2 |1 b3|1 3 |1 4 |1 b5|1 5 |1 b6|1 6 |1 b7|1 7 |1 8 |
 |C Db|C D |C Eb|C E |C F |C Gb|C G |C Ab|C A |C Bb|C B |C C |
G|————|————|————|————|————|————|————|————|——2—|——3—|——4—|——5—|
D|————|————|————|——2—|——3—|——4—|——5—|——6—|————|————|————|————|
A|3—4—|3—5—|3—6—|3———|3———|3———|3———|3———|3———|3———|3———|3———|
E|————|————|————|————|————|————|————|————|————|————|————|————|

Train your ear to recognize each of these intervals.
It's a great exercise for your ears.

A very important thing to know is that some intervals have other names.
they are:

b3 is also #2
#4 is also b5 
#5 is also b6
b7 is also #6 (#6 is not very common)

what decides the name is the context of the chord or scale.
example:

A diminished chord is: 1,b3,b5 not 1,#2,#4
The reason for this is that all basic three note chords are based around:
1, some kind of 3 and some kind of 5.
using altered 2s and 4s and 6s makes it more confussing to understand.

It's also important to keep in mind that when looking at a scale,
it's nice to have some kind of 1,2,3,4,5,6,7
it's wierd to look at a scale like this:
1,2,#2,4,5,6,#6 which is actually 1,2,b3,4,5,6,b7
notice how having one of each number makes the scale easier to read.
 
C is just the example for the past two exercises.
once you pick a note as a root,
all the intervals fall into place.
Let's use G as our root instead of C:

Exercise 3 (G = Root/1)

 |1  b2   2  b3   3   4  #4   5   |#5  6  b7   7   8/1             |
 |G   Ab  A   Bb  B   C   C#  D   |D#  E   F   F#  G               |
G|————————————————————————————————|————————————————————————————————|
D|————————————————————————————————|1———2———3———4———5———————————————|
A|————————————————2———3———4———5———|————————————————————————————————|
E|3———4———5———6———————————————————|————————————————————————————————|
 |1 e + a 2 e + a 3 e + a 4 e + a |1 e + a 2 e + a 3 e + a 4 e + a |

Notice how even though the notes have changed,
the intervals are the same.
Think of it as a grid.
once you pick a root,
you just layout all the intervals in order till you get to the octave.

here is each interval next to the root:

Exercise 4 (G = Root/1)

 |1 b2|1 2 |1 b3|1 3 |1 4 |1 b5|1 5 |1 b6|1 6 |1 b7|1 7 |1 8 |
 |G Ab|G A |G Bb|G B |G C |G Db|G D |G Eb|G E |G F |G F#|G G |
G|————|————|————|————|————|————|————|————|————|————|————|————|
D|————|————|————|————|————|————|————|————|——2—|——3—|——4—|——5—|
A|————|————|————|——2—|——3—|——4—|——5—|——6—|————|————|————|————|
E|3—4—|3—5—|3—6—|3———|3———|3———|3———|3———|3———|3———|3———|3———|

Also notice how the name of the interval is not dependent on the note name.

Example:

F# is not #7
F# is 7

The reason for that is because 7 is always a "half step" down from the Octave.
just because a note has a sharp or flat, doesn't mean the interval has a sharp or flat. 
a "half step" is one fret away.
Let's look at intervals from how many "half steps" up they are from the root.

b2    = 1  "half step"  up
2     = 2  "half steps" up
b3/#2 = 3  "half steps" up
3     = 4  "half steps" up
4     = 5  "half steps" up
#4/b5 = 6  "half steps" up
5     = 7  "half steps" up
#5/b6 = 8  "half steps" up
6     = 9  "half steps" up
b7/#6 = 10 "half steps" up
7     = 11 "half steps" up

I hope that this tab has been helpful.
please give me constructive criticism.
Thanks,

—Connor Larkin