Everyone knows about the theoretical principles behind the circle of fifths; up a fifth, clockwise, add a sharp, back a fifth, anticlockwise, add a flat. But is there more going one beneath the surface than simply a mechanism used to remember how many accidentals there are in any given key? I think you know the answer to that already.
What exactly happens when the key that music is set in changes, whether forwards or backwards? Let’s take the change from a Major key, say C Major, and move forward into G Major. That gives the change of the note F to an F#. Is there another way to represent this alteration other than saying a move through the circle of fifths? Well, yes there is.
Looking at the mode in C Major that starts on the note of F, we see that it is F Lydian (F G A B C D E). Now, the F is being raised by a semitone, that’s +1 semitone, and can be shown theoretically as F Lydian (+1). This means the root of the mentioned mode has its root raised by one semitone. That now makes (F# G A B C D E) which is the mode of F# Locrian, mode VII of G Major. See below:
(C Major) F Lydian (+1) = F# Locrian (G Major)
What about the movement in the opposite direction? C Major to F Major has the note of B, flattened to become Bb. The mode on B in C Major is B Locrian. So what is happening is the root of the Locrian mode is being flattened by one semitone, or –1 semitone is being removed from the root, and can be represented as B Locrian (-1) = (Bb C D E F G A), mode IV of F Major, Bb Lydian:
(C Major) B Locrian (-1) = Bb Lydian (F Major)
Now you can see that the modulations either way through the circle of fifths involves just two modes, Lydian (+1) = Locrian and Locrian (-1) = Lydian. Always, this is the underlying alteration that occurs and no other notes are involved in the change from a Major key to another either side of it. This I have called the Lydian – Locrian Axis.
Why would anyone want to think of modulations in this way? Well, now we know the actual mechanism for change, how does this apply to all of the other possible modulations in music. Let’s start with the relative minor, C Major to A minor. To change between these two keys, often a dominant chord on degree V of the minor key is played, in this case E7, which contains a G#, and creates a perfect cadence when followed by an A minor chord. Let’s zoom in again and see what is actually occurring.
C Major = C D E F G A B and then rearranging its notes with the focus on A we get A B C D E F G. The E7 chord changes the G to G#, and the mode in C Major on G is G Mixolydian. Raising the root of Mixolydian by a semitone, G Mixolydian (+1) = G# A B C D E F which is mode VII of A Harmonic minor, G# Alt bb7. So now we can see that the mode involved in the change from a Major key to its relative minor is the Mixolydian mode, always. The reverse is also true, to move from a minor key to its relative Major involves the flattening of the root of the mode on degree VII of the Harmonic minor scale, G# Altbb7 (-1) = G Mixolydian.
What about the change to the parallel minor, I hear you ask. C Major to C minor. The easiest way to perform this change is simply to lower the third in the C Major scale to Eb and the result is C Melodic. The mode on the note of E in C Major is E Phrygian, and lowering its root, or –1 semitone, makes Eb F G A B C D which is Eb Lydian +, mode III of C Melodic. Shown below:
(C Major) E Phrygian (-1) = Eb Lydian + (C Melodic)
The music can now resolve to the parallel minor and the chosen scale can be used, whether natural minor (Aeolian mode) or Harmonic minor etc.
So you can now understand, that by reframing the concept of circle of fifths modulations into the mathematical operations of (+1) or (-1) actually means that all changes in music can be shown in this way, therefore all changes can be represented as simple equations that can be easily recalled from memory at will, as shown below:
Major key forwards: Lydian (+1) = Locrian
Major key backwards: Locrian (-1) = Lydian
Relative minor: Mixolydian (+1) = Alt bb7
Parallel minor: Phrygian (-1) = Lydian +
These are just a selection of the possible changes, and when you consider the full range of 66 scales and all of the modulations that are possible involving their modes, which I have outlined in my M3 book, a whole new musical landscape is possible and attainable to anyone who has grasped this simple, rudimentary observation. Thanks for reading. For those that have their interest piqued, here is the link to the M3 book. https://www.bedwellmusic.co.uk/general-7
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