In this article I am going to outline how all scales, all 66 of them, are connected to each other, and how to use them in navigating one’s way through the unified field of scales, as explained in my M3 book.
When I say that all scales are connected, they really are. The circle of fifths produces the Major scale, specifically the Lydian mode and the Locrian mode, depending on the direction of travel through the circle.
Clockwise from C = C G D A E B F# = C Lydian = G Major/C
Anticlockwise from C = C F Bb Eb Ab Db Gb = C Locrian = Db Major/C
This, as I explain in my M3 book, is known as the Lydian/Locrian Axis. The remaining notes are alterations of the original 7 notes, C# G# D# A# E# B# , going clockwise, and when they are used in music, relative to the key signature, they alter the scale and move music in different directions.
Now, when alteration occurs in music, say a modulation forward through the circle of fifths from C Major to G Major, the F is sharpened to F# and the modes with it as its root changes from F Lydian to F# Locrian. This is represented by the symbol (+1): F Lydian (+1) = F# Locrian. This is the second time the Lydian/Locrian Axis makes an appearance.
If this same process is applied to every note alteration that can occur in music, all 66 seven note scales are eventually generated. For example, raising the root of the first mode of the C Major scale, we get: C Ionian (+1) = C# Altered (1 b2 b3 b4 b5 b6 b7). This is mode VII of D Melodic. So now we know that by raising the root of the Ionian mode of whatever Major scale we are using, whether we are playing tonal or modal music, the result will be a tendency for the music to be pulled towards the tonal centre of II minor. This can then be resolved or interrupted depending on the musician’s preference.
How about raising the root of D Melodic, which was generated by raising the root of C Ionian, and seeing what occurs. D Melodic = D E F G A B C# and its mode I is the Melodic minor mode so:
D Melodic minor (+1) = D# Alt bb3 (1 b2 bb3 b4 b5 b6 b7) = E Neapolitan Major (mode VII)
If you take a closer look at the diagram, you’ll see the Major scale is the starting point for all of the scales, as it is for all music, shown at the bottom of the drawing. From the Major scale are four possible scales that occur when the roots of its modes are raised, excluding Lydian as the scale generated is another Major scale:
Ionian (+1) = Altered = Melodic
Dorian (+1) = Alt bb37 = Neapolitan minor
Mixolydian (+1) = Alt bb7 = Harmonic minor
Aeolian = Alt bb367 = Locrian natural 7
These now form the first row of scales that have been generated from the Major scale, and now each mode that is able from each scale, undergoes the (+1) operation and generates the scales in the next row. In this way all scales are connected and an overlying structure can now be comprehended.
Take another look at the schematic I have drawn. Complex it may be, but it is merely a representation of how the structure of scales themselves work in a unified manner. It is not supposed to be a reference diagram for musical ideas, although when used in conjunction with the 66 tables of scales in section 2 of the M3 book, it can throw up new ideas and strange relationships between certain scales make themselves known.
Also, once you understand how to recognise the scales in music, you will start to see how frequently lesser known changes or completely unknown ones are actually at work in the music. For example, the Neapolitan Major b5 scale is reached by simply raising the root of the Harmonic minor mode I. It occurs only once in Bach’s Well Tempered Clavier I, specifically in the fugue in B minor, the very last movement number 24. Then, in the WTC II, it occurs in the very first prelude in C, a direct link, and one that shows that this was understood by Bach, or at least that the specific change that he made using the Neapolitan Major b5 scale was reproducible without referring to the actual musical ideas.
Looking at the diagram again, you can trace the Major scale to the Harmonic minor in the first row of four scales, and then from the Harmonic minor scale the Neapolitan Major b5 is reached, shown on the right hand side of the diagram. Also, it is worth noting that the number of alterations it takes to go from the Major scale to the furthest possible scale, the Arcane minor, is the same as the number of notes, namely twelve. I shall be focusing on the relevance of the number 12 in music as well as other areas in posts to come.
When I decided I wanted to be able to represent the unified scale field in a diagram, this was the first of two ways that I thought of accomplishing my goal. The second method I shall present later this week, once I have finished it, and then we can compare and hopefully see the merits of one design over another. Thanks for reading.
Comments