Lots of fields have some device that is used to illustrate concepts
which would be difficult to understand without it. A case in point is
the Moebius strip for mathematicians. This Moebius strip has only one
side and one edge despite being a 3-dimensional figure. It
illustrates some of the central concepts of Topology, a field of
mathematics that studies properties of physical shapes. Other fields
have similar symbols. Shipboard navigators had their sextants for
sighting stars, and engineers their sliderules.
In music, the Circle of Fifths plays a similar role. The Free Hands
uniform 4ths/5ths tuning makes good use of many of the relationships
that the Circle of Fifths illustrates, so it is especially important
and relevant to it's methodology.
The entire name of the Circle is "The Circle of Fifths and Fourths".
This is normally abbreviated to just The Circle of Fifths which
looks like this:
As you go clockwise each successive note on the outer ring is a
fifth above the previous note. As you go counter-clockwise each
note is a fifth below the previous note. So where do fourths come
into it? It is also true that as you go clockwise each note is a
fourth down from the previous note, and as you go counter-clockwise
each note is a fourth above the previous note.
The internal relationship that makes this possible is the fact that
going up a fifth and down a fourth brings you to the same letter note
(though in a different octave). For instance going up a fifth from C
brings you to a G and going down a fourth from the same C brings you
also to G, but an octave down.
This particular trick is the basis of many of the interesting
properties of the tuning system of the Stick. The treble strings are
in fourths while the bass strings are in fifths and in reverse order.
This allows the same chord shapes to be played on both sides, though
they will result in different inversions.
The circle of fifths can also be used as a guide to figuring out how
many flats or sharps a particular key has. If you start at C and move
counterclockwise, each successive key has one more flat in its key
signature than the previous one. If you start at C and move
clockwise, each successive key has one more sharp than the previous
one. This is what is shown in the inner ring of the circle diagram.
As you can see the key of A has 3 sharps, and the key of Db has 5
flats. But which notes are the flats and sharps? If you start at Bb
and move counterclockwise you will get the flats in order. For
instance in the key of Db the flats in the key signature are Bb, Eb,
Ab, Db, and Gb. If you start at F (which is right next to Bb, the
starting point for the flats) and move clockwise you will get the
sharps in order. For instance the sharps in the key of A are F#, C#,
and G#.
The order of the flats and sharps for the minor keys (shown underneath their relative major keys on the outer ring) is done exactly like the major keys.
Mode | Number of steps | Direction |
---|---|---|
Ionian | 0 | ![]() |
Dorian | 2 | Counter-clockwise |
Phrygian | 4 | Counter-clockwise |
Lydian | 1 | Clockwise |
Mixolydian | 1 | Counter-clockwise |
Aeolian | 3 | Counter-clockwise |
Locrian | 5 | Counter-clockwise |
Looking at the circle as representing chords, it is no accident that
the I, IV, and V chords of any key are adjacent (for instance C, F,
and G in the key of C) because these chords provide very consonant
progressions. On the other hand, moving 6 positions in either
direction provides a jump of a tritone (diminished fifth) which is the
most dissonant interval, key change, or chord change.
As you can see from this circle, very consonant songs like "Heart and
Soul" (C-Am-F-G) use a limited area of the circle (three positions)
while slightly more adventurous progressions like the Who's "I'm Free"
(C-F-G-D-G-A) use more area (five positions).
The proximity on the circle can also be used in a simplistic chord
substitution strategy. If you want a substitute chord for C in a
progression, the ones close to it on the circle will make reasonable
substitutes. Jazz theory teaches more involved chord substitution
approaches involving analysis of the progression, but this method can
get you started with it.
So far we have spread the points around a circle, but it is not clear
why it should be a circle. One reason is that in a chromatic scale
there are only 12 possible notes (ignoring octaves). This implies
that if we make the circle a line, it will have to repeat itself a lot
as it streches toward infinity. On the other hand, there are almost
an unlimited number of ways to "spell" a particular note. For
instance C can be written as C, Dbb, Ebbbb, B#, A###, etc. Other
notes are commonly spelled two different ways (such as G# which is the
same note as Ab). So let us look at yet another circle of fifths that
allows each chromatic note a position, but which the different
"spellings" of that note share.
The real reason we need the circle is so we can see the relationships
that go "around the back" of the circle. If you were reading a piece
of music and the key changed from Db (five flats) to F# (six sharps),
you would think that the effect would be jarring. But on the new
improved circle we can see that this is quite consonant because the
positions are adjacent. The only thing that is jarring is the change
in spelling, and if the musician is doing his or her job this is not
audible.
First is how to figure out the tuning on one side of a Stick if you
know one note (this assumes one of the standard fourths on melody and
fifths on bass tunings). Find the note you know on the circle and the
strings will be listed around the circle. For instance if you know
that the lowest melody string on a standard-tuned Stick is a C#, you
can read the tunings of the strings (left-to-right on the Stick) by
reading counter-clockwise on the circle starting at C#.
This technique can also be used to figure out what the result will be
if you move a note or chord over by one string. Moving to the right
corresponds to moving counter-clockwise on the circle. Moving to the
left corresponds to moving clockwise on the circle.
Next moving up by one fret dot on the Stick is moving up a fourth.
This corresponds to shifting one position counter-clockwise on the
circle. For instance, if you are playing a C (note or chord) and you
move it up the neck by one fret dot, the result will be F, one
position counter-clockwise from C on the circle. Similarly moving
down the neck by one fret dot is equivalent to moving one position
clockwise on the circle.
This can also be used to figure out how to transpose a song into a
different key. Let us say that you want to transpose from C to Eb.
Eb is 3 positions counter-clockwise from C on the circle. One
approach which does not involve using the circle is to shift your hand
up 4 frets (the interval between Eb and C). But another approach is
to move to the right by 3 strings. You can substitute moving up the
neck by one fret dot for moving over a string, so you could also move
up one fret dot and over 2 strings.
The circle is a valuable tool that helps you to see the fundamental
relationships that music, and especially the Stick are based upon.
Spending time with it will usually result in a better understanding of
these relationships that can help both your playing and your
composition skills.
Copyleft 1995 Vance Gloster