The Circle of 5ths

Circle of 5ths The circle of fifths is a very elegant way of showing a number of things about music very concisely, but only if you understand what those things are. The chart below opens the circle into a square to show what those things are. It relates to two diatonic instruments that I play, the harmonica and mountain dulcimer, but it is actually generic music theory. This is not to say that it does not relate to chromatic instruments like the guitar, which I also play. People playing chromatic instruments usually think of modes a bit differently since they are not shackled by them, but also because the path to them are not as clearly defined. It shows modes and their relationship to the Major and minor scales as well as the what and why of sharps and flats. It also reveals the how and why of the nonhemitonic pentatonic scales.

Keys vs. Positions/Modes, C Harp & CGG Dulcimer Example
Mode Harp
Pos		 I   II   III IV   V   VI   VII Dulci
Fret
Ionian 1st C   D   E F   G   A   B 3
Mixolydian 2nd G   A   B C   D   E F # 0
Dorian 3rd D   E F # G   A   B C # 4
Aeolian 4th A   B C # D   E F # G # 1
Phrygian 5th E F # G # A   B C # D # 5
Locrian 6th B C # D # E F # G # A # 2
no name 7th F# G # A # B C # D # E # (F) 6+
no name 8th Db D b E F b G b A b B C 3+
no name 9th Ab A b B C b D b E F   G 0+
no name 10th Eb E F   G b A b B C   D 4+
no name 11th Bb B C   D b E F   G   A 1+
Lydian 12th F   G   A b B C   D   E 6

Many people know that as we move clockwise from C on the circle that we add one sharp at each step up to six at F#, and that moving counterclockwise from C on the circle adds one flat at each step, up to five at Db. It helps to understand why.

 
C D   E F   G   A   B C   D   E F  
I   II   III IV   V   VI   VII I   II   III IV  
IV   V   VI VIIb   I   II   III IV   V   VI VIIb  
C   D   E F   G   A   B C   D   E F  
C   D   E   F# G   A   B C   D   E   F#

The top two rows of the small chart above shows the 'C' Ionian Major interval and scale. It has no sharps or flats. When that scale is shifted to line up a new scale, 'G', (lines 3 & 4) so it starts at the 5th position of the 'C' scale, the F which is the 7th position of the 'G' scale does not line up. It is at a flattened 7th position. This change in interval is a change to the Mixolydian mode. To give it the same Ionian Major interval as the 'C' scale we must raise the F by a semitone to F# (bottom row).

Notice on the top chart that the Mixolydian row has a sharp sign (#) to the right of the note that was flattened. Each new row is movement to the next position on the circle of fifths. Each new mode flattens one more note, and the scale for the standard (Ionian mode) Major scale requires one more sharped note. The 7th through 11th harp positions do not have mode names since they start with sharp or flat notes they are out of mode. The 7th position, F#, is unique in that it is shown as having 6 sharps, but that is because the 7th is E# because F has already been named (F#) for the tonic note. The eighth position is Db and all of the altered notes are flattened so each letter in the scale is only used once. (If it were C# you'd have quite a dilemma for only using note letters once.) For the keys with flats it might be easier to see if you go counterclockwise on the circle (bottom up on the square chart). The 12th position, 'F' is the Lydian mode which has a raised 4th, so there is a flat to the left of it to tell us that the note must be flattened to make a Major scale interval.

The circle of fifths also shows us which notes are sharped. For 'G' Major, two positions back shows 'F', which is the note that gets the sharp sign. 'D' Major gets the F and C as sharps, etc. If you want to play 'D' Mixolydian, the chart shows that you would not raise the 7th to C#, so the 'D' Mixolydian scale is D E F# G A B C. This works everywhere on the circle.

Many people who play chromatic instruments are only vaguely aware of modes, but people who play diatonic instruments become aware of them quickly when they try to change keys. If all you have is a 'C' harp, and you wish to play in 'A' minor, it's not a problem since 'A' Aeolian minor has no sharps of flats, but if you want to play in 'D' minor the scale starting at 'D' is 3rd position (Dorian). Aeolian minor needs a flat 3rd, 6th, and 7th (see the chart), which means that you need a Bb that is not on the harp. There are three B notes on a 'C' harp. The lowest and highest are available with bends, but the middle one must be overblown which is a somewhat rare skill. For a fretted instrument, notes are bent up, and a 'C' tuned diatonic fretted instrument like the mountain dulcimer does have 'A' notes in spots that can be bent up to Bb. So for the player of diatonic instruments, bending is an essential skill, or having multiple instruments available (harps) of the ability to retune (dulcimer) is required to play in multiple keys. The circle of 5ths tells us which notes must be bent out of mode when playing in multiple keys. I hope that the squared circle helps you to see how the circle of fifths works and it's relationship to modes.

You can find an excellent, and very harmonica oriented, explanation of the circle of 5ths at www.angelfire.com/tx/myquill/CircleOfFifths.html that never mentions modes.

Pentatonics

The Major pentatonic is the interval that you get when you drop the semitones from the Mixolydian interval. The minor (Blues) pentatonic is the interval that you get when you drop the semitones from the Phrygian interval. These two are the most well known and used, certainly as far as harmonica players go.

There are three other anhemitonic (nonhemitonic, no half steps) pentatonic scales which are less common. The Chinese pentatonic is the interval that you get when you drop the semitones from the Dorian interval.

I don't know of any official or commonly used names for the remaining two. I just coined Appalachian for one of them because the only music that I can think of that use is are "Shady Grove" and "Barbry Ellen", which I think of as Appalachian. The other I'll call Fifthless since that is the most striking feature of the thing.

The Appalachian pentatonic is the interval that you get when you drop the semitones from the Aeolian interval. The Fifthless is the interval that you get when you drop the semitones from the Locrian interval.

Dropping the semitones from Ionian and Lydian makes no sense since they have a major seventh so you'd have to drop the tonic. Notice that there are three modes, or harmonica positions, that have the notes for each of the five anhemitonic pentatonic scales, but each of them can be easily remembered by the mode that you drop the semitones from to form them. And yes, pentatonics predates the church modes, but the mnemonic stands as useful, even if it does not describe the origin.

Notice that movement around the circle of 5th moves the pentatonics from major to neither major or minor to a minor 7th, to minor, to so minor that there is no 5th.

Pentatonics Keys vs. Positions/Modes, C Harp Example
Major
Pentatonic		 Harp
Pos		 I   II   III IV   V   VI bVII  
Lydian 12th F   G   A   B C   D   E
Ionian 1st C   D   E F   G   A   B
Mixolydian 2nd G   A   B C   D   E F  
Chinese
Pentatonic		 Harp
Pos		 I   II bIII   IV   V   VI bVII  
Ionian 1st C   D   E F   G   A   B
Mixolydian 2nd G   A   C C   D   E F  
Dorian 3rd D   E F   G   A   B C  
Appalachian
Pentatonic		 Harp
Pos		 I   II bIII   IV   V bVI   bVII  
Mixolydian 2nd G   A   C C   D   E F  
Dorian 3rd D   E F   G   A   B C  
Aeolian 4th A   B C   D   E F   G  
Blues minor
Pentatonic		 Harp
Pos		 I bII   bIII   IV   V bVI   bVII  
Dorian 3rd D   E F   G   A   B C  
Aeolian 4th A   B C   D   E F   G  
Phrygian 5th E F   G   A   B C   D  
Blues Scale 5th E F   G   A Bb B C   D  
Fifthless
Pentatonic		 Harp
Pos		 I bII   bIII   IV bV   bVI   bVII  
Aeolian 4th A   B C   D   E F   G  
Phrygian 5th E F   G   A   B C   D  
Locrian 6th B C   D   E F   G   A  

Thanks to Bing Futch for this. A great blues tuning for the mountain dulcimer. The 6+ fret gives the Locrian it's lost 5th back. Combined with it's flat 5th, and other minor notes, the blues scale is easy with a capo at fret #2.

Mountain Dulcimer Blues Tuning
Blues Interval   I     bIII   IV bV V     bVII  
Fret #   2     4   5 6 6+     8  

The Blue Third

Something that should be considered when playing a blues scale is that the blue third is actually somewhere between a major and minor third interval. Stringed instrument players often bend the minor third up slightly and harmonica players bend a major third down slightly. It is convenient to discuss it as a minor third, but we should not loose sight of the fact that it is actually not quite that, although it is often played as if it is.

Chords vs. Modes

One difficulty encountered with diatonic instruments is that they are essentially modal. Yes, you can bend (and other techniques) to get notes that are not naturally available, but in the case of the diatonic harmonica that only works for arpeggios for most players. In addition, on the Richter tuned harp, triads are not available for all chords, some only have two note intervals. The available modal chords are often not the chord that you want for non-modal music.

Second position does offer triads for the I-IV-v but since 2nd position is Mixolydian, the v chord is minor (see the chart below). The Melody Maker tuning is essentially a Lydian tuning so 2nd position is Ionian and the Major I-IV-V chord triads are all available. The Natural Minor tuning is essentially a Dorian tuning so 2nd position has the minor i-iv-v triads available. This is one of the primary benefits of special tunings - the triads that you want.

Modal Chords (U=Major, u=minor, uo=diminished)
Mode Harp
Pos		 I   II   III IV   V   VI   VII Dulci
Fret
Lydian 12th I   II   iii   ivo V   vi   vii 6
Ionian 1st I   ii   iii IV   V   vi   viio 3
Mixolydian 2nd I   ii   iiio IV   v   vi VII   0
Dorian 3rd i   ii III   IV   v   vio VII   4
Aeolian 4th i   iio III   iv   v VI   VII   1
Phrygian 5th i II   III   iv   vo VI   vii   5
Locrian 6th io II   iii   iv V   VI   vii   2

The chart below makes it easy to see the modal chords. You can see why some jazz players call the extended chords that they play by their mode names. It certainly is more concise. It also makes it easy for players of diatonic instruments to see what notes must be altered for chords. For example, playing the I7-IV7-V7 chords on a harmonica in second position (Mixolydian) needs the raise the 3 of the V chord (Dorian) to make it Major, and flatten the 7 on the IV chord (Ionian) to make it a natural 7 chord.

Modal Chords (U=normal placement for major scale, u=flatened (minor or diminished), U=raised (augmented)
Mode I   II   III IV   V   VI   VII I
Lydian I       III     V       VII  
Ionian I       III     V       VII  
Mixolydian I       III     V     vii    
Dorian i     iii       V     vii    
Aeolian i     iii       V     vii    
Phrygian i     iii       V     vii    
Locrian io     iii     v       vii    

Chord Progressions

Another interesting bit of information that the circle of fifths provides has to do with chord progressions.

When playing and instrument where you can play in any key like a guitar, chord progressions are not just a matter of a position on the instrument like with a harmonica. You need to keep track of the chord name. The circle of fifths helps here too.

It is generally known that with a I-IV-V progression the IV is CCW on the circle and the V is CW. Take a look at the circle while thinking of a I-iv-ii-V7 progression. In the key of C that would be C-Am-Dm-G7 which also has an easy to see and remember relationship to the circle of fifths. From the I jump CW to the relative minor and step back CCW.

If you are playing in a key that you don't normally play in; let's say that that is B. The I-iv-ii-V7 is B-G#m-C#m-F#7. The circle shows the enharmonics in this case; B-Abm-Db-F#7 which is the same thing.

The popular II-V7-I progression is also along the circle. Stepping CCW. II-V7-I in the key of Bb that would be C-F7-Bb.

Caveat For Harmonica Players

The relationship of the circle of 5ths, modes, sharps and flats, chords, and pentatonics, is general music theory. By adding information specific to a musical instrument there is room for confusion. The relationship to positions on a Richter tuned diatonic harmonica is with respect to available unbent notes. Harmonica players routinely bend notes to escape the shackles of modes and key change. While there is a relationship between modes and positions, they are not the same thing.

What Do I Need To Remember?

Circle of 5ths The idea of learning the circle of fifths is to make things easy. The stuff written above looks like way too much to remember. Once you see the relationships you don't need to remember it like that.

Learn the circle, the scale interval, the enharmonic names, and the relationship between the circle and the scale.

Scales: C = F C G D A E B. G = C G D A E B F#. D = G D A E B F# C# (Db). Etc...

Modes: C Ionian = F C G D A E B, D. C Mixolydian = Bb F C G D A E. C Dorian = Eb Bb F C G D A. Etc...

Pentatonics: Drop the semitone from the appropriate mode, or remember the scale degrees.

Chords: Big roman numberals are major, lowercase are flattened (minor)

Chord Progressions: Fall along the circle as discussed above.

Once you understand the why, seeing the what in the circle isn't too hard.