The circle of fifths has many applications. First off, I have my students write it out: 1. draw a circle of a piece of paper 2. beginning at 12 o'clock, write C, then progressing clockwise, you count up a 5th from 1 o'clock through 6 o'clock: C – G – D – A – E – B – F#. The right hemisphere of the circle deals in sharps and the left in flats.
To complete the left hemisphere, begin at 12 o' clock ( C ) and now proceed counter-clockwise in 4ths ( 4ths and 5ths are reciprocally inverse ) this produces: F – Bflat – Eflat – Aflat – Eflat – Dflat – Gflat.
I suggest students write this out everyday for a week or two by then you'll have a good handle on it.
A rudimentary use for the circle of fifths is to identify the accidentals in keys, here's how: G is at 1 o'clock and has one sharp, D is at 2 o'clock and has two sharps and so on ( A = 3 sharps, E = 4 sharps, B =5 sharps, F# = 6 sharps ) In other words, the numbers of sharps on the right hemisphere of the circle corresponds to the position on the numbers on the clock that are replaced by letters.
The left hemisphere deals in flats, to find them, proceed counter-clockwise from C ( 12 o'clock ) progressively adding one flat with each successive step on the clock. Ex. 11 o'clock = one flat, 10 o'clock = 2 flats, 9 o'clock = 3 flats and so on.
The exciting moment you've all been waiting for - yes, the 2nd part of Thinking Tonally...! (Start here if you missed part 1)
Now, let's get right to the exercises: Play your low E string and let it ring, then play an E major scale starting on the D string. What this exercise is doing is it's beginning to train your ear to become familiar with the essence of the major tonality. Then do the same with the other three tonalities. (E minor, major blues and minor blues)
The next exercise is very similar but instead of the open E note as the comparison to the scales you will play chords to compare to the scales: An E major chord against the E major scale, E minor chord against the E minor scale, E7 chord against the E major blues and the E minor blues. This will train your ear to hear the reflections of the scales in the chords and vice versa.
In the last exercise, we'll use the high E and B strings to create double stops ( two notes at once ) that define the four tonalities. We're going to harmonize the four scales in 3rds, that means you'll play the root and 3rd (or flat 3rd for a minor chord ) together. Begin with the E on the B string, fret 5 and the G# on the E string, fret 4. ( E to G# is a 3rd ) Then you simply ascend within the E major scale one step at a time on both strings simultaneously, then repeat the same process with the other three scales.
Once you do this exercise you'll have a much better understanding of the defining characteristics of the tonalities.
This is a very useful concept I teach to all my students, it really helps to define and classify the fundamental tonalities I teach intermediate beginners, which are: major, minor, major blues and minor blues.
“Tonalites” have characteristic sounds which are created by specific intervals. As a musician, you need to develop the capacity to identify these four tonalities. (and later, others)
We'll begin by basing each tonality on a corresponding scale, which respectively are: major, minor, major blues and minor blues scales.
Major scales are the only scales with no intervallic alterations, it's formula is simply: 1 – 2 – 3 – 4 – 5 – 6 – 7. C major scale = C – D – E – F – G – A – B.
The minor scale formula is: 1 – 2 – flat3 – 4 – 5 – flat6 – flat7. C minor scale = C – D – Eflat – F – G – Aflat – Bflat.
The major blues scale formula is: 1 – 2 - flat3 – 3 – 5 – 6. C major blues scale = C – D – Eflat – E – G – A.
And the minor blues scale formula is: 1 – flat3 – 4 – flat5 – 5 – flat7. C minor blues scale = C – Eflat – F – Gflat – G – Bflat.
What I'm about to say is quite abstract but as you practice and study it will slowly begin to make more and more sense: when you play the major scale and chord progressions beginning on the I chord in the same key, each is tonally reflected in the other. Ex) A C major scale evokes the overall tonality of playing a I – IV – V progression in the key of C and the same is true of the relationship between the other three scales and the progressions you'll play them over.
In the next blog I'll give very concrete exercises to play that will help clarify these concepts...