# Circle of fifths rules

I'm trying to determine the correct algorithm for using a classical circle of fifths and create chord progressions please. I understand that we can navigate clockwise (5th) or counter clockwise (4th), starting from any point.

What are the do and don't for the cirlcle?

• How many steps can we 'jump' on the cicle? Must we always use the chord next to it?
• Can we navigate from the outer circle to the inner circle? Switching from Major to Minor? C seems to overlap Dm, Em and Am?
• There seems to be a third inner layer circle?

Any help on this would be apreciated.

Thanks

Have a good day

I cannot tell if you are a music student trying to understand Western music theory or a programmer trying to make a music app, given no actual knowledge about music. Either way your operating assumption are completely false.

The circle of 5ths (or 4ths) illustrates how keys are connected and this connection is related to the tetrachord, the structure of the major scale, and the natural harmonics of vibrating systems. By changing just one note of the major scale in any key you jump to a new key that is a 5th or 4th away. the classic example is the key of C, which has no accidentals. If you flatten the 7th degree, B, you will be in the key of F. If you raise the 4th, F, you will be key of G. As it turns out the lowest harmonics of the notes C, F, and G fill in the notes of the C major scale. These are referred to as "compatible" keys. However that does not relate in any way to building a chord progression in a single key.

Your assumption or question about how many jumps one cane take, or that one can just move in 5ths is not at all how chord progressions work in music. The fact is that if you keep moving in 4ths or 5ths you will leave your home key signature and not necessarily in a graceful way. The notes of the major scale are harmonized by the Major chords built on the 1st, 4th, and the 5th degrees (no surprise since these notes generated the harmonics that gave rise to the major scale in what is known as Just tuning). So, rather than just build a progression, one takes a melody and harmonizes it by choosing the chord from among the set {I, IV, V} that contains that note. This is the starting point for homophonic multi voice harmony.

There are other standard practices in music theory like ending a musical idea with a cadence like V7 --> I, etc. But these are just guidelines. There is no algorithm for making a progression. At the end of the day you just use the chords that sound nice. It is very rare that anyone just moves around the circle of 5th. In general that will never work and you will need 12 jumps to get back to the starting point (same as walking up the chromatic scale).

Rather than this, familiarize yourself with some of the most common progressions and how they are used.

Probably the most complete is the "circle" progression. It goes,

I --> IV --> vii0 --> iii --> vi --> ii --> V7 --> I

Note that this is NOT the circle of 4ths because of the 7th degree. Other small pieces of this are used,

ii --> V7 --> I (most common in Jazz)

I --> IV --> V (from Mozart to Rock)

I --> vi --> ii (or IV) --> V (Heart and Soul, or Rhythm changes)

There is the 12 bar blues and classic Rhythm changes in Jazz. Rhythm changes has a B section that does go through the circle of 4th but only to walk from the 3rd back to the I, III7 --> VI7 --> II7 --> V7 --> I.

And with that last example I would say that people use the ii-->V7 frequently to enhance movement form one chord to another, for example if you want to move from I to IV you can insert a I7 before the IV and that will sound cool (it will create a cadence to the IV and a true key modulation), you can also add the ii of the IV, I --> V --> v --> I7 --> IV.

The point is we don't just walk endlessly around the circle. We have way points in music that we can choose to move into using part of the circle (an arc if you will). This has been hammered to death by Max Reger in his work "Modulation". I'd suggest learning more about harmony and the reasons we choose certain chords before trying to distill the process into a "algorithm".

• Hi, thanks for the the anwser, yes I am familiar with basic chord notions. I'm still in the process of learning music, I will keep familiarizing myselft with chords and harmonies. – Orion Dec 20 '20 at 4:12

Quote

I understand that we can navigate clockwise (5th) or counter clockwise (4th), starting from any point.

That's not really correct. From C4 to G4 (i.e. up by 7 halftones) means going up by a perfect 5th. But if you go from C4 to G3 (i.e. down by 5 halftones), then you go down by a perfect 4th although you navigate clockwise through the circle.

Counter clockwise:
From C4 to F3 (i.e. down by 7 halftones) gives a perfect 5th.
From C4 to F4 (i.e. up by 6 halftones) gives a perfect 4th.

How many steps can we 'jump' on the circle?

As many as you like. You are the composer, you make the rules. Does it sound good? If it does: Jump!

Must we always use the chord next to it?

Same answer as before: You are the boss, you make the rules.

The outer (1st) ring contains major chords.

• C major contains the notes C-E-G. This is the I (1 major) chord.
• Its left neighbor is F major (F-A-C). F is the IV (4 major) chord of C.
• The right neighbor of C major is G major. G is the V (5 major) chord of C.

The 2nd ring contains minor chords that are related to the major chords standing nearby:

• E minor (Em) contains E-G-B, so, in relation to C Em ist the iii (3 minor) chord.
• D minor (Dm) is the ii (2 minor) chord of C. It consists of the notes D-F-A.
Dm is also the vi (6 minor) chord of F.
• The vi chord of C is Am (A-C-E).
It is also the ii chord of G.

The 3rd ring contains diminished chords that are related to the chords from ring 1:

• Bdim contains the notes B-D-F. It is the vii (7 diminished) chord of C.

Note, tha in all chords before the highest tone of each chors was 7 halftones above the lowest. But F is only 6 halftones above B. So B-F is not a perfect fifth but a diminished fifths, and this why the chord B-D-F is called "diminished".

• A major chord has these halftone steps: 4 (major third) - 3 (minor third), giving a total of 7 halftones (a perfect fifth)
• A minor chord has these halftone steps: 3 (minor third) + 4 (major third), giving a total of 7 halftones (a perfect fifth)
• A diminished chord has these halftone steps: 3 (minor third) + 3 (minor third), giving a total of 6 halftones (a diminished fifth)
• Thx for the anwser. – Orion Dec 20 '20 at 4:12

There are some different approaches to understand and apply the circle of fifths.

• the cadence I-IV-V-I: 3 neighboured chords are tonic subdominant and dominant (the middle one is the tonic).

Example 1: C-F-G-C .... F-C-G (C is the "tonal" center of the 3 chords)

• secondary dominants I -> V7/V7/V7 ....-> C.

Exemple 2: starting at C you can extend to F# and return B7-E7-A7-D7-G7 back home to C.

• ii7-V7 progressions: like the secondary dominants you can also use minor chords, by exchanging in example 2 some Dom7 chords by their minor parallel chord.

Example 3: C -> Bm7-E7-Am7-D7-Dm7-G7-C

• Tritonus substitution: you get a pattern that goes across the circle like and will be identical to chromatic scale down:

Example 4: C-F#-F-E-Eb-D-Db-C.

There are many other progressions that are represented in the circle like e.g. C-am-dm-G7. We can explain the as ii-V7 chain (going from C 3 chords (hours) ahead (clockwise) and step backward (counterclockwise) to C. But you can also say we go to the inner circle (minor chords) to the relative chord of C (am) and counterclockwise to the subdom relative (dm) and finally to V7-I (G7-C).

The secondary dominant chain is often paired with a chain of sequenced motives (fifth fall sequenc).

But there is also an ascending sequence in common use, like C-G-Dm-Am.

Example 5: Bach's Prelude in C#

Always mind that these progressions are related to a melody. Theoretically the fifth fall sequence has no end and you can play it round and round (like you can play a chromatic scale down. But in practice I've never seen a progression longer than 6 chords of secondary dominants following the circle.

• Thx for the anwser – Orion Dec 20 '20 at 4:12