4th and 5th Intervals

Before I showed you a picture of the circle of fifths which is what you see below. Only now you'll learn that going in one direction around the circle gives you the circle of fifths and the opposite direction gives you the circle of fourths. This will help you to learn the 4th and 5th intervals.

Fourth Intervals:

A perfect 4th is 5 half steps.
E to A
Ab to Db

A diminished 4th is 4 half steps.
E to Ab
Gb to Bb

An augmented 4th is 6 half steps.
E to A#
Db to G


Fifth Intervals:

A perfect fifth is 7 half steps.
A to E
E to B

A diminished fifth is 6 half steps.
C to Gb
D to Ab

An augmented fifth is 8 half steps.
C to G#
Ab to E

Unison & Octave Intervals

The first thing to know about these two types of intervals is there are three kinds of each. These three kinds are: perfect, diminished, and augmented. When I took music theory nobody explained this to me and I was totally lost but there is no reason to fear these types of intervals. My teacher at the time was also partially deaf in one ear....and she tried telling me that I couldn't hear pitch right...lol. 

Anyway, perfect, diminished, and augmented will later be applied to 4th and 5th intervals.

For perfect unisons there are 0 half steps between the notes. In other words it is the exact same note.

For example, C = C

This is called a perfect unison.

Diminishing consists of lowering the note by half a step.

For example, A = Ab

This is called a diminished unison. 

Augmenting is the opposite and raises the note by half a step.

For example, D = D#

This is called an augmented unison.

A tip to remember the difference between augmented and diminished is to remember that 'diminish' means to lessen or to reduce. Then, you'll know that augmented is the opposite.

These modifiers to the notes are only applied to unisons, fourths, fifths, and octaves. 

Now on to octaves. 

A perfect octave is 12 half steps. 

G to G

F to F

A diminished octave is 11 half steps.

G to Gb

B to Bb

An augmented octave is 13 half steps. 

A to A#

C to C#

Chords & Arpeggios

A chord is multiple notes played together. Chords can be used to create an arpeggio. The basic chord is made up of three notes called a triad. You use notes 1, 3, and 5 of the given scale. I made a post about the intervals for each note. The intervals you use for triads are the same with major and minor scales.

For example, in D major

D E F# G A B C# D
1  2  3  4  5  6  7   1

Your triad is D F# A






Arpeggios are built the same way using intervals 1, 3, and 5. Although, you play chords and arpeggios differently. As the notes in a chord are played simultaneously, the notes for arpeggios are played individually.
Listed below are all the arpeggios for the major scales.

Chord:         Arpeggio:
   C               C, E, G
   G               G, B, D
   D               D, F#, A
   A               A, C#, E
   E                E, G#, B
   B                B, D#, F#
  F#               F#, A#, C#
  C#              C#, E#, G#
             
   F                F, A, C
   Bb             Bb, D, F
   Eb             Eb, G, Bb
   Ab             Ab, C, Eb
   Db             Db, F, Ab
   Gb             Gb, Bb, Db
   Cb             Cb, Eb, Gb

Circle of Fifths

The circle of fifths gives you a system that organizes the keys for you. The circle of fifths helps you to learn the corresponding key signatures from majors to minors and vice versa. It's called the circle of fifths because every note is a perfect fifth apart from the next. The outer ring of capital letter are the major scales. The ring on the insides of lower case letters are the minor scales. Minor scales are all represented as lower case letters. The middle ring is the number of flats or sharps each scale has.
For example, between C to G is five notes. C-D-E-F-G.
The circle of fifths is a life saver.