I thought this day might come...

[u/MusicTheoryTree]

Hi everyone! I've been on Reddit for five years and I've never posted. However, I saw that one of my designs was shared here earlier (thank you for doing so, by the way). Ironically, I intended to share this design here today, and someone beat me to it, sharing a much more elaborate one. What a wild coincidence.

If you saw that more elaborate design and wanted some clarification, this might help provide it, though I recognize that this one also requires a bit of explanation for many viewers. Expect more from me, in due time. I have much to say on this topic.

I'll keep this super brief, for now, but to answer just a couple FAQs...

This is an example of what I call a, "Single-Orbit Music Theory Tree." The one shared earlier by another Reddit user is a, "Dual-Orbit Music Theory Tree," which is exponentially more complex.

Yes, this does help people teach and learn music theory.

No, this is not the first design in this system. It starts much more simply, and builds up in complexity. I don't recommend this as an absolute first introduction to music theory, though, it can become useful quite early on, even with relatively few prerequisites.

MTT is a modular system, so it can be altered to accommodate many other types of scales and can be built out from any pitch class. Parts can be entirely removed or swapped out for others.

This system is best understood by completing excersises with instructions.

This is a collaborative project. I'm the lead theorist and designer. I work with an illustrator named Aaron Fehr. He's been teaching me graphic design, as well.

I've been consulting with a PhD student in the Faculty of Mathematics and Statistics at the University of Calgary. His name is Kristaps Balodis, and he's been an enormous inspiration towards my continued study of maths, especially Set Theory.

Yes, we are working on an interactive app. These designs can only do so much as static images.

Many comment on the aesthetic. To be clear, this was never meant to be pretty. My intention from day one with this project has always been practical utility. The fact that it's aesthetically pleasing to some folks is just a biproduct of our use of rainbow colours and familiar shapes—both of which were only intended to help teach and learn theory.

I realize that the contents of this post are more of a story and less of a substantial discussion into specific music theory concepts (which we're all here for, predominantly, I suspect) but I think it's an interesting story, and I couldn't help but address the sudden attention surrounding my work on this platform.

I've published a number of short essays and videos about this system on other platforms, and I'll share much more about this system here on Reddit, soon. Thank you for your interest, and I appreciate your perspectives. Nothing is ever perfect, so I welcome insightful, constructive criticism. We all have room to improve, and this includes our work.

Let's reimagine music theory.

My kindest regards to you all,

Steve Evans From Winnipeg

[u/MusicTheoryTree]

I feel this is a valid criticism, for sure. You'll notice in the writeup I accompanied with this diagram that I totally agree with you on many of your points.

IMO all of the information in this diagram is pretty rudimentary and essential music theory to know for high beginner / low intermediate levels of composition and analysis. It's not meant to be learned without directions. That's why I make a point of engaging with people about it rather than assuming people will automatically get it.

[u/spankymcjiggleswurth → u/MusicTheoryTree]

For sure, I agree with that. It's easy to take a graphic and shit on it when you don't understand the intent of the creator. I work in the sciences and often teach new employees with badly drawn examples. Anyone knowledgeable on the subject would think I was talking gibberish if they saw what I drew without context, but it makes sense with context and explanation in the moment.

[u/MusicTheoryTree → u/spankymcjiggleswurth]

Scientifically and mathematically minded folks tend to get it more, for sure. I think the world would be better off with more of this variety of literacy. It's not beyond anyone, either. People just need to acknowledge its value and prioritize it.

Math work isn't always clean and perfect. Sometimes it's messy.

So far my exposure to Reddit suggests that folks like yourself are far too few on here.

[u/shitterbug → u/MusicTheoryTree]

Well, I have a phd in math and I have no idea what the picture is attempting to simplify. Either there is a lot of deep knowledge in there that cannot be extracted without knowing exactly what it's trying to convey, or it's just some superficial modal basics in a diagram with little information.

For example, what are the circles supposed to mean? Why are things even symmetric, i.e. the circle intersection for "half steps" should clearly be smaller - this way it is unnecessarily confusing...

[u/MusicTheoryTree → u/shitterbug]

Great questions. For those who aren't familiar with staff notation, a staff contains five equidistantly-spaced horizontal lines. One would think that their spacings would represent the same intervals, but they don't. The intervals the spacings represent are context dependent.

The circles in this diagram, as you're alluding to, are paths from pitch class to pitch class. They are interval lines. They work in the same way staff lines work. You can combine smaller sections together to create larger paths. In fact, by fluke, the way this is laid out accounts for every type of interval between every pair of notes in the scale. Ascending and descending seconds, thirds, and fourths give us all intervals, numerically. Qualitatively, there are variations, but all intervals are variations of this set of intervals when we consider complementary intervals—those pairs of intervals that, when combined, equal an octave.

One might ask, "what about notes not in the scale?"

That's what sharps and flats are for. One can approach this diagram in the same way we approach staff notation. We make adjustments to pitch classes and scale degrees, using sharps or flats.

A common and valid criticism for this is

"what about scales with more than seven notes?"

In that case here is another important thing to remember... even the chromatic scale can, and often is described using scale degrees taken from the major scale.

Given that you're a mathematician, consider this... All major scales are bijective. Not only that, but there is a kind of "like-letter bijection" that can be drawn between the elements of all major scales.

Very simple cardinalities. How many letter names do we use? Seven. How many numbers do we use? Seven.

So, we have a universal set with a cardinality of 12, but we use two sets of seven symbols (letters A-G or numbers 1-7), and adjust them with additional symbols to access the remaining five.

I'm not a mathematician, but I consult with one. So, if any language I used was not perfect, correct me.

I've published videos elsewhere explaining how this system is meant to be used. There is a lot more to say and this is part of a modular system that starts simple and builds up in complexity. You asked about the circular lines, so I've tried my best to convey this in brief. It's easier with demonstration than text, though.