Advanced Scale Math & Fun Scale Trivia for Theory Nerds

Advanced Scale Math for Theory Nerds

I’ve been working super hard in the past 8 months on a scale book.
This book had been a couple of years in the making, but I kept getting pulled in different directions with so much teaching going on, music projects, and life in general.
This year, however: one of my big goals is to finally get this book published.

This is going to be THE best scale study book for guitarists ever written. There is nothing like this out there yet.
This book will list EVERY scale that exists in music, covering ALL music of the entire planet, with guitar necks, modes, scale theory, everything.

I want to show you some really cool, fascinating scale stuff today, that I discovered while writing the book.

In order for this to really make sense, you need to have a good grasp of the material covered in the following 2 blogs first.

Key Signatures of Modes.
How To Figure Out and Practice Keysignatures of Modes.

To give a quick recap of the gist of these blogs:
When you organize the 7 modes of the major scale by key signature, you get:

Lydian –> C Lydian = 1#
Ionian –> C Ionian/major scale = 0#
Mixolydian –> C Mixolydian = 1b
Dorian –> C Dorian = 2b
Aeolian –> C Aolian = 3b
Phrygian –> C Phrygian = 4b
Locrian. –> C Locrian = 5b

Notice the progression, going from Lydian where a note goes up from the major scale to Ionian, which IS THE major scale, to Mixo where a note goes down from the major scale, Dorian 2 notes go down, Aeolian 3 notes go down, etc.

It’s interesting to note that our binary concept of major and minor, happy and sad scales, really only started somewhere in the 14-1500’s Renaissance. Before that, Greek, Medieval and Gregorian chant times, they had more mood gradations than just these 2.

The above 7 modes are organized down the list from happiest, brightest sounding mode (Lydian), to darkest (Locrian).
Dorian is considered the most “emotionally” balanced sounding scale between happy and sad, being centered right in the middle of the list.
Interesting that that scale perfectly in the center, Dorian, is also a palindromic scale. It consists of the same intervals ascending and descending.

You can learn more about that here Modal and Tonal Music.

This same concept of modes as mood creators is heavily used in Indian music. That is what Indian ragas are. There is more of an emphasis on using scales as a means to evoke a larger array of different colors and moods, rather than operating within a limited major-minor happy or sad storytelling.

Modes = Inversions

Another really cool insight I gained from writing the scales book, is that the words inversions and modes are one and the same thing.
Chord and interval inversions are actually modes and modes are inversions.
Funny that despite the many years of top-level music education I enjoyed during my music student years, this had never been made clear or pointed out.

As an example: you know how we learn in music theory that a major 7th interval is the inversion of a minor 2nd?
Think of what you do when you invert an interval: an inversion is what you get when you start an interval from the next note in that interval.
For example:
C to E major 3rd… when instead of C, I start on E… to C = minor 6th.
Conclusion: a minor 6th is an inversion of a major 3rd.

Same for chord inversions: the notes in a C chord are C E G.
When I start from the next note I get E G C, then G C E, which we call chord inversions.

Interestingly enough: that is exactly also what modes are.
A Dorian scale is what you get when you start a major scale from the next note. When you start from the next note after that, you get a Phrygian scale.
So Dorian is really “an inversion” of Ionian.

As a result: you could say that the minor 6th is a mode of a major 3rd.

As you can see, modes and inversions are different names meaning the same thing.
I’m not sure where the concept came from that when it comes to chords, we call it inversions, but when it comes to scales we call it modes.

Tying into all this: while there are 2048 possible note combinations in music, there are actually only 351 unique fingerings.
That is because all modes have the same fingering. The guitar neck that shows all the notes of a D Dorian scale, looks EXACTLY the same as a guitar neck that shows all the notes of the E Phrygian scale, and EXACTLY the same as the guitar neck showing all notes for the C major scale, and so on.

So good news: only learning 351 guitar necks/fingerings, you’d master EVERY music scale (including mode, arpeggio, and chord inversion) that exists on the planet.
The book explains all this really well.


Hit me up anytime at if you have any questions, or if you would like to book a lesson.

These free lessons are cool, but you will never experience the progress, joy, and results that my students experience in lessons when you’re learning by yourself from blogs and videos.

That is why people take lessons: way better results and progress, much more complete information, exposed to way more creative ideas than you can get from a blog or YouTube video.
There is only so much that self-study can accomplish.

If you want to see amazing results and progress in your guitar playing, buy your first lesson here and get started ASAP.

  • 1 Lesson = 75

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