Jump to: navigation, search

Difference between revisions of "Circle of Fifths"

m (→‎Harmonic Minor)
m (→‎Full Circle)
 
(35 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
The circle of fifths lays out the 12 tones in a circle, moving clockwise in fifths.  If C is 12 o'clock, its fifth, G, is 1 o'clock.  G's fifth, D, is two o'clock.  And so on.
+
{{Top-Level Crumbs|1}}
 +
{{Lesson Crumbs|2}}
 +
{{Intermediate Lesson Crumbs|8}}
 +
 
 +
The '''circle of fifths''' lays out the 12 tones in a circle, just like the 12 hours on an analog clock face, moving clockwise in perfect fifths (or counter-clockwise in perfect 4ths which are inverted perfect 5ths).  If C is 12 o'clock, its fifth, G, is 1 o'clock.  G's fifth, D, is two o'clock.  And so on.
 +
 
 +
::{|
 +
| || F || C || G ||
 +
|-
 +
| B{{f}} || || || || D
 +
|-
 +
| E{{f}} || || || || A
 +
|-
 +
| A{{f}} || || || || E
 +
|-
 +
| || D{{f}} || G{{f}} || B ||
 +
|}
  
 
==Inter-relation of Keys==
 
==Inter-relation of Keys==
 +
{{Crumbs|blue|1
 +
|Circle of Fifths#Inter-relation of Keys|Inter-relation of Keys
 +
|Circle of Fifths#Full Circle|Full Circle
 +
|Circle of Fifths#Modulation|Modulation
 +
|Circle of Fifths#Minor Keys|Minor Keys
 +
|Circle of Fifths#Modulating Between Types of Scales|Between Scale Types
 +
}}
 +
 
So far we've really only talked about C Major and A minor, which are composed of the 7 white keys per octave on the piano.  But scales can be built upon any of the 12 tones in the chromatic scale.  We know the whole-half patterns of the major and minor scales, so we can figure out what notes any scale has, but what about the interrelation between scales?  This is where the circle of fifths helps to keep things in perspective.
 
So far we've really only talked about C Major and A minor, which are composed of the 7 white keys per octave on the piano.  But scales can be built upon any of the 12 tones in the chromatic scale.  We know the whole-half patterns of the major and minor scales, so we can figure out what notes any scale has, but what about the interrelation between scales?  This is where the circle of fifths helps to keep things in perspective.
  
Line 10: Line 34:
 
  G  - A  - B  - C  - D  - E  - F# - G
 
  G  - A  - B  - C  - D  - E  - F# - G
  
−
F and C Major differ by only one note (C Major has a B while F Major has a Bb).  Similarly, C and G also differ by one note (F vs. F#).  Let's look at the whole-half patterns:
+
F and C Major differ by only one note (C Major has a B while F Major has a B{{b}}).  Similarly, C and G also differ by one note (F vs. F{{s}}).  Let's look at the whole-half patterns:
  
 
                   w    w    h    w    w    w    h
 
                   w    w    h    w    w    w    h
 
                 F  - G  - A  - Bb - C  - D  - E  - F
 
                 F  - G  - A  - Bb - C  - D  - E  - F
 
   
 
   
−
     w    w    h    w    w    w    h    w    w    h    w    w    w    h            
+
     w    w    h    w    w    w    h    w    w    h    w    w    w    h
 
  C  - D  - E  - F  - G  - A  - B  - C  - D  - E  - F  - G  - A  - B  - C
 
  C  - D  - E  - F  - G  - A  - B  - C  - D  - E  - F  - G  - A  - B  - C
 
   
 
   
Line 21: Line 45:
 
                     G  - A  - B  - C  - D  - E  - F# - G
 
                     G  - A  - B  - C  - D  - E  - F# - G
  
−
The whole-half pattern from F to F in the key of C Major is w-w-w-h-w-w-h.  If we flatten the 4th note, the B, we get w-w-h-w-w-w-h - the major scale pattern.
+
The whole-half pattern from F to F in the key of C Major is w-w-w-h-w-w-h.  If we flat the 4th note, the B, we get w-w-h-w-w-w-h - the major scale pattern.
  
 
The whole-half pattern from G to G in the key of C Major is w-w-h-w-w-h-w.  If we sharp the 7th note, the F, we get w-w-h-w-w-w-h - the major scale pattern.
 
The whole-half pattern from G to G in the key of C Major is w-w-h-w-w-h-w.  If we sharp the 7th note, the F, we get w-w-h-w-w-w-h - the major scale pattern.
  
−
Remember that F is a fifth below C and G is a fifth above.  We notice that if we change the key by moving in fifths, only one note changes.  While no two major scales will have different tonic notes but identical sets of notes, some scales are more ''inter-related'' or harmonic than others.
+
Remember that F is a fifth below C and G is a fifth above.  We notice that if we change the key by moving the root note by perfect fifths, only one note changes.  While no two major scales will have different tonic notes but identical sets of notes, some scales are more ''inter-related'' or relatively harmonic than others.
  
−
The circle of fifths lists keys in 5ths, which is useful to determine how interrelated any two keys are.
+
The circle of fifths lists keys in 5ths, which is useful to determine how interrelated any two keys are.  The points opposite each other (12:00 vs. 6:00, 3:00 vs. 9:00, 11:00 vs. 5:00, etc.) are the least related, while the points nearest each other (12:00 and 1:00, 1:00 and 2:00, etc.) are most related.  As we go right or clockwise, we sharp the 4th of the current key to get the next key.  For example in C Major, sharping the 4th (F) gives us the scale of G Major.  As we move left or counter-clockwise, we flatten the 7th of the current key to get the next key.  For C Major, we flat the B to get F Major.
  
−
The full circle only consists of the 12 tones, which can be arranged like the hours on an analog clock.  The points opposite each other (12 vs. 6, 3 vs. 9, 11 vs. 5, etc.) are the least related, while the points nearest each other (12 and 1, 1 and 2, etc.) are most related.  As we go right or clockwise, we sharp the 4th of the current key to get the next key.  For example in C Major, sharping the 4th (F) gives us the scale of G Major.  As we left or counter-clockwise, we flatten the 7th of the current key to get the next key.  For C Major, we flat the B to get F Major.
+
So each movement is a single note difference, always adjusting the leading tone of the key on the clockwise side of the pair.  Note that the major scale has two half-steps, which means two notes right next to each other.  Every other major or natural minor scale has to contain at least one of these notes, since the largest movement between neighboring notes is a whole step.  So the least related scales will share 2 notes.  For example, C and C{{s}} don't share any notes by name - every note in C is the same note in C{{s}} but sharped.  However, E{{s}} = F and B{{s}} = C in terms of pitch; so they still have two ''enharmonic'' notes in common.
  
−
So each movement is a single note difference.  Note that the major scale has two half-steps, which means two notes right next to each other.  Every other major or natural minor scale has to contain at least one of these notes, since the largest movement between neighboring notes is a whole step.  So the least related scales will share 2 notes.  For example, C and C# don't share any notes by name - every note in C is the same note in C# but sharped.  However, E# = F and B# = C; so they still have two notes in common.
+
{{top}}
  
 
== Full Circle ==
 
== Full Circle ==
 +
{{Crumbs|blue|2
 +
|Circle of Fifths#Inter-relation of Keys|Inter-relation of Keys
 +
|Circle of Fifths#Full Circle|Full Circle
 +
|Circle of Fifths#Modulation|Modulation
 +
|Circle of Fifths#Minor Keys|Minor Keys
 +
|Circle of Fifths#Modulating Between Types of Scales|Between Scale Types
 +
}}
 +
 
Let's find all 12 tones in order of fifths, going both ways from C:
 
Let's find all 12 tones in order of fifths, going both ways from C:
 
                               C
 
                               C
Line 42: Line 74:
 
       Db - Ab - Eb - Bb - F - C - G - D - A - E - B
 
       Db - Ab - Eb - Bb - F - C - G - D - A - E - B
 
  Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F#
 
  Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F#
−
F# is the same pitch as Gb, which means we've completed the circle.  If we keep going, we still get unique key names, but the pitches will match other keys already in the circle.  For example, continuing left (counter-clockwise), we reach Cb, which is the same as B.  Going right (clockwise), we reach C#, which is the same as Db.
+
 
 +
F{{s}} is the same pitch as G{{b}}, which means we've completed the circle.  If we keep going, we still get unique key names, but the pitches will match other keys already in the circle.  For example, continuing left (counter-clockwise), we reach C{{b}}, which is the same as B.  Going right (clockwise), we reach C{{s}}, which is the same as D{{b}}.
  
 
So assuming C is "12 o'Clock", our circle of fifths looks like this:
 
So assuming C is "12 o'Clock", our circle of fifths looks like this:
−
{|
+
:{|
 +
|-
 +
!align="center"| Least {{s}}/{{b}} !! Clockwise !! Counter-Clockwise
 +
|-
 +
|
 +
:{|
 
| || F || C || G ||  
 
| || F || C || G ||  
 
|-
 
|-
Line 54: Line 92:
 
| A{{f}} || || || || E
 
| A{{f}} || || || || E
 
|-
 
|-
−
| || D{{f}} || F{{s}} || B ||  
+
| || D{{f}} || G{{f}} || B ||
 +
|}
 +
|
 +
:{|
 +
| || E{{s}} || C || G ||
 +
|-
 +
| A{{s}} || || || || D
 +
|-
 +
| D{{s}} || || || || A
 +
|-
 +
| G{{s}} || || || || E
 +
|-
 +
| || C{{s}} || F{{s}} || B ||  
 +
|}
 +
|
 +
:{|
 +
| || F || C || A{{db}} ||
 +
|-
 +
| B{{f}} || || || || E{{db}}
 +
|-
 +
| E{{f}} || || || || B{{db}}
 +
|-
 +
| A{{f}} || || || || F{{b}}
 +
|-
 +
| || D{{f}} || G{{f}} || C{{b}} ||
 +
|}
 
|}
 
|}
  
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
−
! Key !!Cb !! Gb !! Db !! Ab !! Eb !! Bb !! F !! C !! G !! D !! A !! E !! B !! F# !! C#
+
! Key !!C{{b}} !! G{{b}} !! D{{b}} !! A{{b}} !! E{{b}} !! B{{b}} !! F !! C !! G !! D !! A !! E !! B !! F{{s}} !! C{{s}}
 
|-
 
|-
−
| Flats/Sharps||7 b's||6 b's || 5 b's || 4 b's || 3 b's || 2 b's || 1 b's || 0 b/#'s || 1 #'s || 2 #'s || 3 #'s || 4 #'s || 5 #'s || 6 #'s || 7 #'s
+
| Flats/Sharps||7 {{b}}'s||6 {{b}}'s || 5 {{b}}'s || 4 {{b}}'s || 3 {{b}}'s || 2 {{b}}'s || 1 {{b}}'s || 0 {{b}}/{{s}}'s || 1 {{s}}'s || 2 {{s}}'s || 3 {{s}}'s || 4 {{s}}'s || 5 {{s}}'s || 6 {{s}}'s || 7 {{s}}'s
 
|-
 
|-
−
! Unison ||Cb || Gb || Db || Ab || Eb || Bb || F || C || G || D || A || E || B || F# || C#
+
! Unison ||C{{b}} || G{{b}} || D{{b}} || A{{b}} || E{{b}} || B{{b}} || F || C || G || D || A || E || B || F{{s}} || C{{s}}
 
|-
 
|-
−
| 2nd ||Db || Ab|| Eb || Bb || F || C || G || D || A || E|| B || F#|| C# || G# || D#
+
| 2nd ||D{{b}} || A{{b}}|| E{{b}} || B{{b}} || F || C || G || D || A || E|| B || F{{s}}|| C{{s}} || G{{s}} || D{{s}}
 
|-
 
|-
−
| 3rd ||Eb || Bb || F || C || G || D || A || E || B || F# || C# || G#|| D# || A# || E#
+
| 3rd ||E{{b}} || B{{b}} || F || C || G || D || A || E || B || F{{s}} || C{{s}} || G{{s}}|| D{{s}} || A{{s}} || E{{s}}
 
|-
 
|-
−
! 4th ||Fb || Cb || Gb || Db || Ab || Eb || Bb || F || C || G || D || A|| E || B || F#
+
! 4th ||F{{b}} || C{{b}} || G{{b}} || D{{b}} || A{{b}} || E{{b}} || B{{b}} || F || C || G || D || A|| E || B || F{{s}}
 
|-
 
|-
−
| 5th ||Gb || Db || Ab || Eb || Bb || F || C || G || D || A || E|| B|| F# || C# || G#
+
| 5th ||G{{b}} || D{{b}} || A{{b}} || E{{b}} || B{{b}} || F || C || G || D || A || E|| B || F{{s}} || C{{s}} || G{{s}}
 
|-
 
|-
−
| 6th ||Ab || Eb || Bb || F || C || G || D || A || E || B || F#|| C#|| G# || D# || A#
+
| 6th ||A{{b}} || E{{b}} || B{{b}} || F || C || G || D || A || E || B || F{{s}}|| C{{s}}|| G{{s}} || D{{s}} || A{{s}}
 
|-
 
|-
−
! 7th ||Bb || F || C || G || D || A || E || B || F# || C# || G#|| D#|| A# || E# || B#
+
! 7th ||B{{b}} || F || C || G || D || A || E || B || F{{s}} || C{{s}} || G{{s}}|| D{{s}}|| A{{s}} || E{{s}} || B{{s}}
 
|-
 
|-
−
| Oct ||Cb || Gb || Db || Ab || Eb || Bb || F || C || G || D || A|| E|| B || F# || C#
+
| Oct ||C{{b}} || G{{b}} || D{{b}} || A{{b}} || E{{b}} || B{{b}} || F || C || G || D || A|| E|| B || F{{s}} || C{{s}}
 
|}
 
|}
  
−
Above is the list of the keys from Cb to C#.  Note that this is actually 15 tones.  Since C# = Db, Cb = B, and F# = Gb, we can eliminate them, leaving with only the 12 distinct tones on the circle of fifths.
+
Above is the list of the keys from C{{b}} to C{{s}}.  Note that this is actually 15 tones.  Since C{{s}} = D{{b}}, C{{b}} = B, and F{{s}} = G{{b}}, we can eliminate them, leaving with only the 12 distinct tones on the circle of fifths.
 +
 
 +
{{top}}
  
 
== Modulation ==
 
== Modulation ==
−
''Modulation'' is the practice of changing keys.  The source and destination keys are important.  Many composers only modulate into destination keys based on the 4th or 5th of the source key, as these are the most harmonic keys.
+
{{Crumbs|blue|3
 +
|Circle of Fifths#Inter-relation of Keys|Inter-relation of Keys
 +
|Circle of Fifths#Full Circle|Full Circle
 +
|Circle of Fifths#Modulation|Modulation
 +
|Circle of Fifths#Minor Keys|Minor Keys
 +
|Circle of Fifths#Modulating Between Types of Scales|Between Scale Types
 +
}}
 +
 
 +
'''Modulation''' is the practice of changing keys.  The source and destination keys are important.  Many composers only modulate into destination keys based on the 4th or 5th of the source key, as these are the most harmonic keys.
  
 
Below is a table to show the most interrelated keys.  It says how many notes the two keys will have in common, modulating to the key of the named interval above the current key.  For example, the key of C Major will only have 2 notes in common with the major keys a M7, m2, or d5 above C (C{{f}} or B Major, C{{s}} or D{{f}} Major, and G{{f}} or F{{s}} Major).
 
Below is a table to show the most interrelated keys.  It says how many notes the two keys will have in common, modulating to the key of the named interval above the current key.  For example, the key of C Major will only have 2 notes in common with the major keys a M7, m2, or d5 above C (C{{f}} or B Major, C{{s}} or D{{f}} Major, and G{{f}} or F{{s}} Major).
Line 108: Line 181:
  
 
== Minor Keys ==
 
== Minor Keys ==
 +
{{Crumbs|blue|4
 +
|Circle of Fifths#Inter-relation of Keys|Inter-relation of Keys
 +
|Circle of Fifths#Full Circle|Full Circle
 +
|Circle of Fifths#Modulation|Modulation
 +
|Circle of Fifths#Minor Keys|Minor Keys
 +
|Circle of Fifths#Modulating Between Types of Scales|Between Scale Types
 +
}}
 +
 
=== Natural Minor ===
 
=== Natural Minor ===
 
So far I have always discussed the circle of fifth in terms of major keys.  Since natural minor keys have the same notes as their relative major, the same rules apply.  Other natural minor keys based on the 4th or 5th of the current natural minor key will have one note difference, and the 3 keys opposite the current key are the last related with 5 notes different.
 
So far I have always discussed the circle of fifth in terms of major keys.  Since natural minor keys have the same notes as their relative major, the same rules apply.  Other natural minor keys based on the 4th or 5th of the current natural minor key will have one note difference, and the 3 keys opposite the current key are the last related with 5 notes different.
Line 114: Line 195:
 
Harmonic minor is a bit different.  The M7 does not carry over to the next key in sequence.  For example, in A Harmonic Minor, there is a G{{s}}.  But in the key a fifth above, E Harmonic Minor, there is a G.  Similarly, a fifth below A is D.  D Harmonic minor has a G as well.
 
Harmonic minor is a bit different.  The M7 does not carry over to the next key in sequence.  For example, in A Harmonic Minor, there is a G{{s}}.  But in the key a fifth above, E Harmonic Minor, there is a G.  Similarly, a fifth below A is D.  D Harmonic minor has a G as well.
  
−
{| class="wikita{{f}}le"
+
{| class="wikitable"
 
|-
 
|-
 
! Key !!A{{f}} !! E{{f}} !! B{{f}} !! F !! C !! G !! D !! A !! E !! B !! F{{s}} !! C{{s}} !! G{{s}} !! D{{s}} !! A{{s}}
 
! Key !!A{{f}} !! E{{f}} !! B{{f}} !! F !! C !! G !! D !! A !! E !! B !! F{{s}} !! C{{s}} !! G{{s}} !! D{{s}} !! A{{s}}
Line 130: Line 211:
 
! 6th ||F{{f}} || C{{f}} || G{{f}} || D{{f}} || A{{f}} || E{{f}} || B{{f}} || F || C || G || D || A|| E || B || F{{s}}
 
! 6th ||F{{f}} || C{{f}} || G{{f}} || D{{f}} || A{{f}} || E{{f}} || B{{f}} || F || C || G || D || A|| E || B || F{{s}}
 
|-
 
|-
−
! 7th ||G  || D  || A  || E  || B  || F{{s}} || C{{s}} || G{{s}} || D{{s}} || A{{s}} || E{{s}}|| B{{s}}|| F{{s}}{{s}} || C{{s}}{{s}} || G{{s}}{{s}}
+
! 7th ||G  || D  || A  || E  || B  || F{{s}} || C{{s}} || G{{s}} || D{{s}} || A{{s}} || E{{s}}|| B{{s}}|| F{{ds}} || C{{ds}} || G{{ds}}
 
|-
 
|-
 
| Oct ||A{{f}} || E{{f}} || B{{f}} || F || C || G || D || A || E || B || F{{s}}|| C{{s}}|| G{{s}} || D{{s}} || A{{s}}
 
| Oct ||A{{f}} || E{{f}} || B{{f}} || F || C || G || D || A || E || B || F{{s}}|| C{{s}}|| G{{s}} || D{{s}} || A{{s}}
Line 157: Line 238:
  
 
== Modulating Between Types of Scales ==
 
== Modulating Between Types of Scales ==
 +
{{Crumbs|blue|5
 +
|Circle of Fifths#Inter-relation of Keys|Inter-relation of Keys
 +
|Circle of Fifths#Full Circle|Full Circle
 +
|Circle of Fifths#Modulation|Modulation
 +
|Circle of Fifths#Minor Keys|Minor Keys
 +
|Circle of Fifths#Modulating Between Types of Scales|Between Scale Types
 +
}}
 +
 
Often a modulation desires to move from a major to minor or harmonic minor tonality, or vice versa.  This changes which keys will be most and least harmonic.
 
Often a modulation desires to move from a major to minor or harmonic minor tonality, or vice versa.  This changes which keys will be most and least harmonic.
  
 
=== Major to Minor ===
 
=== Major to Minor ===
 +
{{Crumbs|blue2|1
 +
|Circle of Fifths#Major to Minor|Major to Minor
 +
|Circle of Fifths#Major to Harmonic Minor|Major to Harmonic Minor
 +
|Circle of Fifths#Minor to Major|Minor to Major
 +
|Circle of Fifths#Minor to Harmonic Minor|Minor to Harmonic Minor
 +
|Circle of Fifths#Harmonic Minor to Major|Harmonic Minor to Major
 +
|Circle of Fifths#Harmonic Minor to Minor|Harmonic Minor to Minor
 +
}}
 +
 
{| class = "wikitable"
 
{| class = "wikitable"
 
|-  
 
|-  
Line 180: Line 278:
 
|-
 
|-
 
!2  
 
!2  
−
|  || m6, m7, m3 || C -> Abm
+
|  || m6, m7, m3 || C -> A{{f}}m
 +
|}
 +
 
 +
=== Major to Harmonic Minor ===
 +
{{Crumbs|blue2|2
 +
|Circle of Fifths#Major to Minor|Major to Minor
 +
|Circle of Fifths#Major to Harmonic Minor|Major to Harmonic Minor
 +
|Circle of Fifths#Minor to Major|Minor to Major
 +
|Circle of Fifths#Minor to Harmonic Minor|Minor to Harmonic Minor
 +
|Circle of Fifths#Harmonic Minor to Major|Harmonic Minor to Major
 +
|Circle of Fifths#Harmonic Minor to Minor|Harmonic Minor to Minor
 +
}}
 +
 
 +
{| class = "wikitable"
 +
|-
 +
!Common<br>Notes !! Diatonic<br>Keys !! Non-Diatonic<br>Keys !! Example
 +
|-
 +
!6
 +
| M6 || || C -> Ahm
 +
|-
 +
!5
 +
| M2, M3 || || C -> Dhm
 +
|-
 +
!4
 +
| U, M7 || d5, m7 || C -> Chm
 +
|-
 +
!3
 +
| P4, P5 || m2, m3, m6 || C -> Ghm
 
|}
 
|}
  
 
=== Minor to Major ===
 
=== Minor to Major ===
 +
{{Crumbs|blue2|3
 +
|Circle of Fifths#Major to Minor|Major to Minor
 +
|Circle of Fifths#Major to Harmonic Minor|Major to Harmonic Minor
 +
|Circle of Fifths#Minor to Major|Minor to Major
 +
|Circle of Fifths#Minor to Harmonic Minor|Minor to Harmonic Minor
 +
|Circle of Fifths#Harmonic Minor to Major|Harmonic Minor to Major
 +
|Circle of Fifths#Harmonic Minor to Minor|Harmonic Minor to Minor
 +
}}
 +
 
{| class = "wikitable"
 
{| class = "wikitable"
 
|-  
 
|-  
Line 207: Line 341:
 
|}
 
|}
  
−
=== Major to Harmonic Minor ===
+
=== Minor to Harmonic Minor ===
−
{| class = "wikitable"
+
{{Crumbs|blue2|4
−
|-
+
|Circle of Fifths#Major to Minor|Major to Minor
−
!Common<br>Notes !! Diatonic<br>Keys !! Non-Diatonic<br>Keys !! Example
+
|Circle of Fifths#Major to Harmonic Minor|Major to Harmonic Minor
−
|-
+
|Circle of Fifths#Minor to Major|Minor to Major
−
!6
+
|Circle of Fifths#Minor to Harmonic Minor|Minor to Harmonic Minor
−
| M6 || || C -> Ahm
+
|Circle of Fifths#Harmonic Minor to Major|Harmonic Minor to Major
−
|-
+
|Circle of Fifths#Harmonic Minor to Minor|Harmonic Minor to Minor
−
!5
+
}}
−
| M2, M3 || || C -> Dhm
 
−
|-
 
−
!4
 
−
| U, M7 || d5, m7 || C -> Chm
 
−
|-
 
−
!3
 
−
| P4, P5 || m2, m3, m6 || C -> Ghm
 
−
|}
 
  
−
=== Minor to Harmonic Minor ===
 
 
{| class = "wikitable"
 
{| class = "wikitable"
 
|-  
 
|-  
Line 244: Line 369:
  
 
=== Harmonic Minor to Major ===
 
=== Harmonic Minor to Major ===
 +
{{Crumbs|blue2|5
 +
|Circle of Fifths#Major to Minor|Major to Minor
 +
|Circle of Fifths#Major to Harmonic Minor|Major to Harmonic Minor
 +
|Circle of Fifths#Minor to Major|Minor to Major
 +
|Circle of Fifths#Minor to Harmonic Minor|Minor to Harmonic Minor
 +
|Circle of Fifths#Harmonic Minor to Major|Harmonic Minor to Major
 +
|Circle of Fifths#Harmonic Minor to Minor|Harmonic Minor to Minor
 +
}}
 +
 
{| class = "wikitable"
 
{| class = "wikitable"
 
|-  
 
|-  
Line 262: Line 396:
  
 
=== Harmonic Minor to Minor ===
 
=== Harmonic Minor to Minor ===
 +
{{Crumbs|blue2|6
 +
|Circle of Fifths#Major to Minor|Major to Minor
 +
|Circle of Fifths#Major to Harmonic Minor|Major to Harmonic Minor
 +
|Circle of Fifths#Minor to Major|Minor to Major
 +
|Circle of Fifths#Minor to Harmonic Minor|Minor to Harmonic Minor
 +
|Circle of Fifths#Harmonic Minor to Major|Harmonic Minor to Major
 +
|Circle of Fifths#Harmonic Minor to Minor|Harmonic Minor to Minor
 +
}}
 +
 
{| class = "wikitable"
 
{| class = "wikitable"
 
|-  
 
|-  
Line 280: Line 423:
  
 
== Homework ==
 
== Homework ==
 +
* Memorize traversing the entire circle of fifths, moving both clockwise and counter-clockwise.
 +
* Understand the concept of modulation.
 +
* Understand that the circle of fifths demonstrates how inter-related any two keys are by their proximity on the circle.
 +
* Know how inter-related keys are when switching from minor to major, or vice versa.
  
 
== Q & A ==
 
== Q & A ==
  
 
== Related Lessons ==
 
== Related Lessons ==
−
* [[Applying Rhythm to Chords|Prev: Applying Rhythm to Chords]]
+
* [[Music Theory Basics]]
−
* [[G Major and E Minor|Next: G Major and E Minor]]
+
* [[Modulation]]
 +
* [[Equal Temperament and Alternate Tunings]]
 +
 
 +
{{top}}
 +
 
 +
{{Intermediate Lesson Crumbs|8}}
  
 
[[Category:Guitar]]
 
[[Category:Guitar]]

Latest revision as of 13:44, 10 August 2015

The circle of fifths lays out the 12 tones in a circle, just like the 12 hours on an analog clock face, moving clockwise in perfect fifths (or counter-clockwise in perfect 4ths which are inverted perfect 5ths). If C is 12 o'clock, its fifth, G, is 1 o'clock. G's fifth, D, is two o'clock. And so on.

F C G
B♭ D
E♭ A
A♭ E
D♭ G♭ B

Inter-relation of Keys

So far we've really only talked about C Major and A minor, which are composed of the 7 white keys per octave on the piano. But scales can be built upon any of the 12 tones in the chromatic scale. We know the whole-half patterns of the major and minor scales, so we can figure out what notes any scale has, but what about the interrelation between scales? This is where the circle of fifths helps to keep things in perspective.

Let's look at the scales of F Major, C Major, and G Major: 

F  - G  - A  - Bb - C  - D  - E  - F
C  - D  - E  - F  - G  - A  - B  - C
G  - A  - B  - C  - D  - E  - F# - G

F and C Major differ by only one note (C Major has a B while F Major has a B♭). Similarly, C and G also differ by one note (F vs. F♯). Let's look at the whole-half patterns: 

                  w    w    h    w    w    w    h
               F  - G  - A  - Bb - C  - D  - E  - F

   w    w    h    w    w    w    h    w    w    h    w    w    w    h
C  - D  - E  - F  - G  - A  - B  - C  - D  - E  - F  - G  - A  - B  - C

                       w    w    h    w    w    w    h
                    G  - A  - B  - C  - D  - E  - F# - G

The whole-half pattern from F to F in the key of C Major is w-w-w-h-w-w-h. If we flat the 4th note, the B, we get w-w-h-w-w-w-h - the major scale pattern.

The whole-half pattern from G to G in the key of C Major is w-w-h-w-w-h-w. If we sharp the 7th note, the F, we get w-w-h-w-w-w-h - the major scale pattern.

Remember that F is a fifth below C and G is a fifth above. We notice that if we change the key by moving the root note by perfect fifths, only one note changes. While no two major scales will have different tonic notes but identical sets of notes, some scales are more inter-related or relatively harmonic than others.

The circle of fifths lists keys in 5ths, which is useful to determine how interrelated any two keys are. The points opposite each other (12:00 vs. 6:00, 3:00 vs. 9:00, 11:00 vs. 5:00, etc.) are the least related, while the points nearest each other (12:00 and 1:00, 1:00 and 2:00, etc.) are most related. As we go right or clockwise, we sharp the 4th of the current key to get the next key. For example in C Major, sharping the 4th (F) gives us the scale of G Major. As we move left or counter-clockwise, we flatten the 7th of the current key to get the next key. For C Major, we flat the B to get F Major.

So each movement is a single note difference, always adjusting the leading tone of the key on the clockwise side of the pair. Note that the major scale has two half-steps, which means two notes right next to each other. Every other major or natural minor scale has to contain at least one of these notes, since the largest movement between neighboring notes is a whole step. So the least related scales will share 2 notes. For example, C and C♯ don't share any notes by name - every note in C is the same note in C♯ but sharped. However, E♯ = F and B♯ = C in terms of pitch; so they still have two enharmonic notes in common.

Top

Full Circle

Let's find all 12 tones in order of fifths, going both ways from C: 

                             C
                         F - C - G
                    Bb - F - C - G - D
               Eb - Bb - F - C - G - D - A
          Ab - Eb - Bb - F - C - G - D - A - E 
     Db - Ab - Eb - Bb - F - C - G - D - A - E - B
Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F#

F♯ is the same pitch as G♭, which means we've completed the circle. If we keep going, we still get unique key names, but the pitches will match other keys already in the circle. For example, continuing left (counter-clockwise), we reach C♭, which is the same as B. Going right (clockwise), we reach C♯, which is the same as D♭.

So assuming C is "12 o'Clock", our circle of fifths looks like this:

Least ♯/♭ Clockwise Counter-Clockwise
F C G
B♭ D
E♭ A
A♭ E
D♭ G♭ B
E♯ C G
A♯ D
D♯ A
G♯ E
C♯ F♯ B
F C ADoubleflat.svg
B♭ EDoubleflat.svg
E♭ BDoubleflat.svg
A♭ F♭
D♭ G♭ C♭
Key C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯
Flats/Sharps 7 ♭'s 6 ♭'s 5 ♭'s 4 ♭'s 3 ♭'s 2 ♭'s 1 ♭'s 0 ♭/♯'s 1 ♯'s 2 ♯'s 3 ♯'s 4 ♯'s 5 ♯'s 6 ♯'s 7 ♯'s
Unison C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯
2nd D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯
3rd E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯
4th F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯
5th G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯
6th A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯
7th B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯
Oct C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯

Above is the list of the keys from C♭ to C♯. Note that this is actually 15 tones. Since C♯ = D♭, C♭ = B, and F♯ = G♭, we can eliminate them, leaving with only the 12 distinct tones on the circle of fifths.

Top

Modulation

Modulation is the practice of changing keys. The source and destination keys are important. Many composers only modulate into destination keys based on the 4th or 5th of the source key, as these are the most harmonic keys.

Below is a table to show the most interrelated keys. It says how many notes the two keys will have in common, modulating to the key of the named interval above the current key. For example, the key of C Major will only have 2 notes in common with the major keys a M7, m2, or d5 above C (C♭ or B Major, C♯ or D♭ Major, and G♭ or F♯ Major).

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys
6 P4, P5
5 M2 D7
4 M6 m3
3 M3 m6
2 M7 m2, d5

Minor Keys

Natural Minor

So far I have always discussed the circle of fifth in terms of major keys. Since natural minor keys have the same notes as their relative major, the same rules apply. Other natural minor keys based on the 4th or 5th of the current natural minor key will have one note difference, and the 3 keys opposite the current key are the last related with 5 notes different.

Harmonic Minor

Harmonic minor is a bit different. The M7 does not carry over to the next key in sequence. For example, in A Harmonic Minor, there is a G♯. But in the key a fifth above, E Harmonic Minor, there is a G. Similarly, a fifth below A is D. D Harmonic minor has a G as well.

Key A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯
Uni A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯
2nd B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯
3rd C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯
4nd D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯
5rd E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯
6th F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯
7th G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯ FDoubleSharp.svg CDoubleSharp.svg GDoubleSharp.svg
Oct A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯

Because of the raised 7th, this throws the normal progression of the circle of fifths off a bit. It causes most keys to have a similar number of common tones to any other harmonic minor key, with no relevance to their order on the circle of fifths:

Key E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯
Notes in
common w/ A 		4 3 4 4 3 4 7 4 3 4 4 3 4
Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys
4 m3, P4, P5, m6 M3, d5, M6
3 M2, M7 m2, m7

Modulating Between Types of Scales

Often a modulation desires to move from a major to minor or harmonic minor tonality, or vice versa. This changes which keys will be most and least harmonic.

Major to Minor

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys 		Example
7 M6 C -> Am
6 M2, M3 C -> Dm
5 P5, M7 C -> Gm
4 U d5 C -> Cm
3 P4 m2 C -> Fm
2 m6, m7, m3 C -> A♭m

Major to Harmonic Minor

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys 		Example
6 M6 C -> Ahm
5 M2, M3 C -> Dhm
4 U, M7 d5, m7 C -> Chm
3 P4, P5 m2, m3, m6 C -> Ghm

Minor to Major

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys 		Example
7 m3 Am -> C
6 m7, m6 Am -> G
5 P4 m2 Am -> D
4 U d5 Am -> A
3 P5 M7 Am -> E
2 M2 M3, M6 Am -> B

Minor to Harmonic Minor

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys 		Example
6 U Am -> Ahm
5 P4, P5 Am -> Dhm
4 m3, M2 M6, m2 Am -> Chm
3 m6, m7 M3, d5, M7 Am -> Fhm

Harmonic Minor to Major

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys 		Example
6 m3 Ahm -> C
5 m6 m7 Ahm -> F
4 U, M2 m2, d5 Ahm -> A
3 P4, P5, M7 M6, M3 Ahm -> D

Harmonic Minor to Minor

Common
Notes 		Diatonic
Keys 		Non-Diatonic
Keys 		Example
6 U Ahm -> Am
5 P4, P5 Ahm -> Dm
4 m3 M6, m7, m2 Ahm -> Cm
3 m6, M2 M3, d5, m2 Ahm -> Fm

Homework

  • Memorize traversing the entire circle of fifths, moving both clockwise and counter-clockwise.
  • Understand the concept of modulation.
  • Understand that the circle of fifths demonstrates how inter-related any two keys are by their proximity on the circle.
  • Know how inter-related keys are when switching from minor to major, or vice versa.

Q & A

Related Lessons

Top
Retrieved from "http://foobazaar.com/wiki/index.php?title=Circle_of_Fifths&oldid=7514"