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Difference between revisions of "Ref: Circle of Fifths"

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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:
 
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[[File:P5_CW_Circle_of_5ths.svg]]
 
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Revision as of 00:20, 24 August 2015

Clock Visualization

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

F C G
B♭ D
E♭ A
A♭ E
D♭ G♭ B

File:P5 CW Circle of 5ths.svg

Since the standard Western chromatic scale is composed of 12 notes, they match up to the 12 hours of an analog clock. Closely-related keys are adjacent, both clockwise and counter-clockwise, while the distantly-related keys are opposite (6 fifths (or "hours") apart).

Moving only clockwise and using strict naming for each P5, we require to start using sharps once we hit 6 o'clock. Notice that the sharp keys are enharmonic to the flat keys above. Here's the same visualization using sharp keys instead of flats:

E♯ C G
A♯ D
D♯ A
G♯ E
C♯ F♯ B

File:P5 CW Circle of 5ths.svg

If we kept going, B♯ would be the next P5 we reach at 12 o'clock, enharmonic to C. We could keep going around and start using double, then triple sharps, and so on. On the other hand, if we move strict P4's going clockwise, we get the following:

F C A16x16px
B♭ E16x16px
E♭ B16x16px
A♭ F♭
D♭ G♭ C♭

File:P4 CCW Circle of 5ths.svg

If we kept going, 12 o'clock would be D16x16px, and again, we'd be venturing into double and triple flats and beyond.

And if 12 o'clock is the root, the interval between root and each note is as follows:

P4 R P5
m7 M2
m3 M6
m6 M3
m2 tt M7

Notice the 2 intervals of equal distance from the root are inversions of each other (P4 - P5, m7 - M2, m3 - M6, m6 - M3, m2 - M7).

Top

Tables of fifths w/ scales

Major - C♭ to C♯

Key C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯
Flats/
Sharps		 7 ♭ 6 ♭ 5 ♭ 4 ♭ 3 ♭ 2 ♭ 1 ♭ 0 ♭/♯ 1 ♯ 2 ♯ 3 ♯ 4 ♯ 5 ♯ 6 ♯ 7 ♯
Uni 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♯

Notice the 4ths and 7ths - this is where the notes flatted/sharped when shifting keys up/down a fifth (or down/up a fourth).

Top

Natural Minor - A♭ to A♯

Key A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯
Flats/
Sharps		 7 ♭ 6 ♭ 5 ♭ 4 ♭ 3 ♭ 2 ♭ 1 ♭ 0 ♭/♯ 1 ♯ 2 ♯ 3 ♯ 4 ♯ 5 ♯ 6 ♯ 7 ♯
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 F♯ C♯ G♯
Oct A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯

Notice the 2nds and 6ths - this is where the notes flatted/sharped when shifting keys up/down a fifth (or down/up a fourth).

Top

Harmonic Minor - A♭ to A♯

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♯ F10x10px C10x10px G10x10px
Oct A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯
Top

Fifths and equivalents

All columns are equivalent pitches. Each cell is a perfect fifth above the cell to its left.

E16x16px16x16px B16x16px16x16px F16x16px♭ C16x16px♭ G16x16px♭ D16x16px♭ A16x16px♭ E16x16px♭ B16x16px♭ F16x16px C16x16px G16x16px D16x16px
D16x16px A16x16px E16x16px B16x16px F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C
C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯
B♯ F10x10px C10x10px G10x10px D10x10px A10x10px E10x10px B10x10px F10x10px♯ C10x10px♯ G10x10px♯ D10x10px♯ A10x10px♯
A10x10px♯ E10x10px♯ B10x10px♯ F10x10px10x10px C10x10px10x10px G10x10px10x10px D10x10px10x10px A10x10px10x10px E10x10px10x10px B10x10px10x10px F10x10px10x10px♯ C10x10px10x10px♯ G10x10px10x10px♯
Top

Rules and Guidelines

The 1.____ scale a perfect fifth 2.____ the current scale contains the same notes but the 3.___ in the current scale is 4.____ to become the 5.____ of the new scale.

1 2 3 4 5
major above P4 sharped M7
minor above m6 sharped M2
major below M7 flatted P4
minor below M2 flatted m6
Top

Equivalent Pitches for Scales Below/Above by Interval

Modulating from any major scale to a new major scale that is ___ interval above/below the original key has ___ same pitches and ♯/♭ per note:

Interval Above Root Uni m2 M2 m3 M3 P4 d5 P5 m6 M6 m7 M7
Interval Below Root Uni M7 m7 M6 m6 P5 d5 P4 M3 m3 M2 m2
Example Major Key vs C Major C C♯ D D♯ E F F♯ G G♯ A A♯ B
Number of Common Pitches 7 2 5 4 3 6 2 6 3 4 5 2

Which means the most harmonic key changes are:

Common Notes Diatonic Keys Non-Diatonic Keys
6 P4, P5
5 M2 m7
4 M6 m3
3 M3 m6
2 M7 m2, d5

* Note: All intervals in above table are above the root note

Top

Harmonic Minor

Key E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯
Notes in
common w/ Ahm 		4 3 4 4 3 4 7 4 3 4 4 3 4
Interval Above Root Uni m2 M2 m3 M3 P4 d5 P5 m6 M6 m7 M7
Interval Below Root Uni M7 m7 M6 m6 P5 d5 P4 M3 m3 M2 m2
Example Harm Minor Key vs A Harm Minor A A♯ B C C♯ D D♯ E F F♯ G G♯
Number of Common Pitches 7 3 3 4 4 4 4 4 4 4 3 3
Common Notes Diatonic Keys Non-Diatonic Keys
4 m3, P4, P5, m6 M3, d5, M6
3 M2, M7 m2, m7
Top

Harmony between Keys

From Major

to Major

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

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
Top

to Harmonic Minor

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

From 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
Top

to Minor

Common Notes Diatonic Keys Non-Diatonic Keys Example
6 P4, P5 Am -> Em
5 M2, m7 Am -> Bm
4 m3 M6 Am -> Cm
3 m6 M3 Am -> Fm
2 m2, d5, M7 Am -> E♭m
Top

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
Top

From 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
Top

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
Top

to Harmonic Minor

Common Notes Diatonic Keys Non-Diatonic Keys Example
4 m3, P4, P5, m6 M3, d5, M6 Ahm -> Chm
3 M2, M7 m2, m7 Ahm -> Bhm
Top


Common Notes Table

Ordered by Half-Steps
Key 2 Type
Key 1 Type Key 2 Root's
relation to
Key 1 Root 		Major Minor Harmonic
Minor
Major
U 7 4 5
m2 2 3 3
M2 5 6 5
m3 4 2 3
M3 3 6 5
P4 6 3 3
tt 2 4 4
P5 6 5 3
m6 3 2 3
M6 4 7 6
m7 5 2 4
M7 2 5 4
Minor
U 4 7 6
m2 5 2 4
M2 2 5 4
m3 7 4 5
M3 2 3 3
P4 5 6 5
tt 4 2 3
P5 3 6 5
m6 6 3 3
M6 2 4 4
m7 6 5 3
M7 3 2 3
Harmonic Minor
U 4 6 7
m2 4 3 3
M2 4 3 3
m3 6 4 4
M3 3 3 4
P4 3 5 4
tt 4 3 4
P5 3 5 4
m6 5 3 4
M6 3 4 4
m7 5 4 3
M7 3 3 3
Ordered by 5ths
Key 2 Type
Key 1 Type Key 2 Root's
relation to
Key 1 Root 		Major Minor Harmonic
Minor
Major
U 7 4 5
P5 6 5 3
M2 5 6 5
M6 4 7 6
M3 3 6 5
M7 2 5 4
tt 2 4 4
m2 2 3 3
m6 3 2 3
m3 4 2 3
m7 5 2 4
P4 6 3 3
Minor
U 4 7 6
P5 3 6 5
M2 2 5 4
M6 2 4 4
M3 2 3 3
M7 3 2 3
tt 4 2 3
m2 5 2 4
m6 6 3 3
m3 7 4 5
m7 6 5 3
P4 5 6 5
Harmonic Minor
U 4 6 7
P5 3 5 4
M2 4 3 3
M6 3 4 4
M3 3 3 4
M7 3 3 3
tt 4 3 4
m2 4 3 3
m6 5 3 4
m3 6 4 4
m7 5 4 3
P4 3 5 4
Top
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