I noticed there are a few people with opinions on the subject of Maths in Music which veer into the realms of the philosophical or even metaphysical, which I shall attempt to reverse and to keep in the realm of observable phenomena.
Maths is absolutely fundamental to how music actually works, and I shall take a moment to explain this concept in the area of modulation.
When a key changes up or down via the circle of fifths, the actual process that occurs is an alteration to the root of one of the modes of the key. For example, to modulate from the key of C Major to G Major, the F is raised to become F#, but if the focus is actually on each of the modes of the keys in question, the change that occurs is as follows:
F Lydian - F# Locrian
This raising of the root of F Lydian by a semitone can be shown by the simple mathematical operation of (+1), where (+1) means adding one semitone, and the whole equation is now shown below:
F Lydian (+1) = F# Locrian
Modulations using the Major scale or its relative minor always use this axis of modes when modulating. It is what I term the Lydian-Locrian Axis.
Moving in the other direction C Major to F Major, the note that is altered is B to Bb and the modes are B Locrian to Bb Lydian, respectively. The Locrian mode of C Major has its root lowered by a semitone, represented as (-1), which creates Bb Lydian in F Major. This is the Lydian-Locrian Axis again, moving in the other direction.
B Locrian (-1) = Bb Lydian
So now we have (+1) representing the change forward through the circle of fifths and (-1) representing the change back through the circle of fifths. This is a different way to envisage the change that occurs using the circle of fifths but it goes a long way beyond that application and culminates in a unified scale theory, which I can talk about in the next post, if there is sufficient interest. Thanks for reading.
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