The blues scale formula

A scale formula shows how the notes relate to a major scale with the same root. The major scale is the constant to which you compare all other scales. The formula for a major scale is just 1 2 3 4 5 6 7. There are only 7 different notes in a major scale. The numbers in a scale formula are sometimes referred to as the scale functions. That just means that each note in a scale has a certain sound or role in relationship to the root of the scale. So a D note functions as the 2 in a C major scale.

C D E F G A B C - C major scale
1 2 3 4 5 6 7 1 - scale functions

Therefore if any note in a particular scale is different than the major scale with the same root, you will show how it is altered by a (sharp) or a (flat) symbol. A sharp raises the pitch of a note by a half step (1 fret), and flat lowers the pitch by a half step.

So the scale formula for a blues scale is 1 3 4 5 5 7. In a C blues scale there is an E, and in a C major scale there is an E. So you call the E a 3 since is is a half step lower than the 3rd note in a C major scale.

C E F G G B C - C blues scale
1 3 4 5 5 7 1 - scale functions

Here is the scale formula applied to the basic blues scale form. Understanding the function of each note helps you to train your ear to know what a particular note will sound like, before you play it.

|--1--|-----|-----|-3--| -1st string
|--5--|-----|-----|-7--|
|-3--|-----|--4--|-5--|
|-7--|-----|--1--|-----|
|--4--|-5--|--5--|-----|
|--1--|-----|-----|-3--| -6th string
   |
  8th fret

Page 1, Blues scale basics

Page 3, 5 positions of an A blues scale