The Exciting Universe Of Music Theory

May 2024 progress update

Hello!
Lots of progress lately. I've spent lots of time fixing the calculation engine, getting the tooling moved to a new Linux server where I'll be running everything remotely; no more crunching data here on my macbook, it's all happening in the cloud baby! This was long overdue.

Among other things I added some simple methods to get "Pressing Scales", and those are being added to the book in a chapter that lists a few various "scale candidacy" schemes. Ie systems that should tell...

Intense amounts of work

With the acquisition of some new names, I had to acknowledge that my database was a mess. Most of the names I've collected over the past decade(s) are unattributed, unresearched, unverified, and have no validating citations.

So I'm remedying that.
Over the past week I've acquired original source material for many of the scale namers (like Messiaen, Cochrane, Tcherepnin, Schenker, Bedwell, Zeitler, Pecot etc); and I've created a system that parses the names directly from the source...

tons of new scale names

I recently acquired a copy of a new theory book: "The Modal Method of Music" by Robert Bedwell. In it, Robert describes an interesting way to organize heptatonic scales in families governed by semitone alterations, and he provides a good practice regime for an instrumentalist wanting to get those scales into muscle memory.

Robert also gave thoughtful names to a whole lot of obscure heptatonic scales, and catalogued tons of exotic modes with sharp and flat accidental alterations.
2024-03-21 02:57:34 +0000 UTC View Post

Stymied by tools, again

Was working on the book this morning, and found that my SFTP plugin for Sublime Text no longer works, since upgrading my Mac to Sonoma.

This is a wet blanket on my productivity, since I use it nonstop, any time I make an adjustment to the LaTeX or the figure SVGs, I use that tool to upload to the rendering server. And it's a plugin I paid for! A bug report has already been filed... and I see on the forums that it's affected EVERYONE who uses the plugin on Sonoma.

This isn't a cr...

Cardinality = Variety

I've pretty much finished the section describing CV. Though just before posting this I noticed that spelling error "degeneerate".

Does this make sense? When I was learning this stuff it was so badly explained it was utterly mystifying. Now that I get it, I hope that I'm able to explain it better...

~ i 

3 gap theorem

Today I drew these diagrams to illustrate the "3 gap theorem", which applies to the intervals we find in generated scales -- When a scale has a generator, why there can only be 3 interval sizes. This applies banally to 12-TET tones, but it's far more interesting when applied to microtonal generators. That's what Erv Wilson's "moments of symmetry" are all about... that's a deep rabbit hole...

anaphoria.com...

So productive!

Hey everyone,
The solstice holiday was a very productive one for me, for the theory textbook. I did a fair bit of writing and editing, but the most ambitious thing was re-exporting all the illustrations and figures and diagrams, and swapping them into the LaTeX file as vector PDF instead of raster PNG. It lowered the file size of the finished document DRAMATICALLY. Now instead of being a whopping 800MB+ file, it's a lean 53.7MB.

It was nice having two weeks of break where I could ...

Visualizations, reimagined

So... I started generating all those images, and then I did some napkin math

The file storage it would take to have them all pre-rendered at full size is more than my server can handle. Like, a LOT more. Terabytes more.

I'm thinking of putting them in the cloud, perhaps in an S3 bucket. But that has an extra cost, not just for the persistence of storage, but also in the time it takes for a script (like the one I use to generate videos, PDFs, web assets) to fetch the image from t...

Fixing up all the assets

I noticed that once in a while, I get a 404 error in the server logs, for images in the general music theory assets. That shouldn't be happening! Perturbed, I looked in some folders and saw that there are random files missing. Maybe they were victims of a bad transfer, or perhaps they've always been gone and I never noticed.

Most of the scale visualizations you see on my website are SVG, which is great because the download is tiny and fast, and they render perfectly at any magnificati...

Hierarchy of Truncations (new!)

This is a better version of a diagram I made back in 2016 or so. These are the truncations of modes of limited transposition, described by Messiaen. A truncation is when you remove tones from a scale to produce a subset with preserved rotational symmetry. Solid arrow indicates removal of 2 tones (preserving symmetry of 6 semitones), a dashed arrow indicates removal of 3 tones (preserving symmetry of 4).

It's fun to note scale 1365 can be arrived at from 1 path through 1911, or via two ...

common triad species in a tonnetz

September update

Firstly, thank you to the new patrons who have signed on recently! When a new patron joins, Patreon sends me a notification to my phone and I get a little "ding!" and it always makes my day.

August wasn't very prolific on the music theory front, but as usual your support has covered all the costs of hosting the website, and for that I am very _grateful_. Alas, very little work was done on the book.

It's been hard to get quality time for the Exciting Universe when the kids are g...

New scale metrics: Center of Gravity

I had a brief conversation with user u/howaboot on reddit. They had calculated all the centroids for heptatonic scales, and shared the results with me; and I noticed it is a generalization of what I had previously written about "balanced" scales. A balanced scale is one where the "centrifuge problem" was solved, meaning center of gravity is in the exact center of the unit circle. But what about scales whose center of gravity is *near* the center, but not quite exactly? What does it matter if ...

Revamped scale summaries

Book 2, "the scales" is supposed to have one page for each scale... I shuffled some things around and this is the way they look now. I like that everything fits on the page, but the asymmetry turns me off. It might not stay this way.

Interval Matrices

It took a long time to get around to this. I was preparing some of these diagrams for the book and realized that I never put them on the website.

So, several hours later I have 2048 of these tables, rendered with a handsome clarendon font... and on the website they are annotated with circles and lines showing contradictions and ambiguities.

A contradiction is when a small generic interval has a larger specific size than a larger generic. A nice example of a contradiction is fou...

Update on things

Hello patrons!

Last time I wrote, I was going to upgrade my web server... and I did it. Mostly pain-free. There are some broken links and notation images, still. I will fix those, when I generate sufficient time and motivation. My plan is to replace some of the notation figures so they use Lilypond instead of Vexflow. I was having some really rotten performance from a mariadb database, so rather than spend more on a server with more RAM, I just cached all the things that could be cach...

Presenting: hierarchizability

This new scene is going to appear in the next generation of scale data videos. Version 4 is slowly evolving, I can't promise when it'll be launched but it will probably be some time later this year. I'm making a whole fancy publishing bot that will let me more easily re-render and upload new videos when I want to make corrections.

Hierarchizability is a scale candidacy algorithm by Niels Verosky. I collaborated directly with Neils to reproduce his algorithm, and then I designed a visua...

a geeky shift of focus, temporarily

Busy times as ever, here... but I am still diligent about always spending at least a few hours per week on music theory things.

The past couple of weeks, I have not been working on the book; instead I've been doing the mundane chore of software maintenance. A lot of the scripts used on the website and in my analysis tools are kind of old, and adhere to the syntax of PHP7. That's been fine because the version on the webserver is also PHP7, I had PHP7 running on my local machine, and th...

So much progress

The past couple of months have afforded me some free time, which I spent making great strides on writing the book.

A lot of time is spent doing calculations to make sure that every fact in the book is 100% absolutely correct -- this is not a trivial task! All the tables, lists, and even some of the diagrams are generated by the same scripts that do real-time scalar calculations for the website. The book is being constructed with LaTeX, which means it has a build process to output a PD...

Subscription Billing

Patreon rolled out a new thing, it's called "subscription billing". With it, patrons are charged on the day they sign up and then monthly thereafter, on that same day of each month. That way, there are no situations where someone gets charged twice in a month.

This seems like a good idea, it's fair, it's what people would probably expect anyways. So I switched my patron account over to use that.

Thought you would all want to know.
Cheers ~ ian

Hi Patrons! An update.

It seems like a long time since I posted anything here. Much has been happening. As always, the website with all the scale data is up and running, and for that I thank my patrons because your contributions cover the whole cost of the hosting! Thank you - because of your help that's one less bill that I need to worry about covering.

The latest thing going on is that I've been working directly with the brilliant scholar Neils Verosky to introduce "hierarchizability" data to the website ...

Good news, and progress

In the past month, things generally have aligned better with working on the book. I have been working on it at least once a week anyways, but in the past while I've had the motivation to spend a little time on it almost daily. I finished a decent first draft of the chapter on coherence, and I worked on the introduction and did some polishing of everything in the introductory chapter.

No significant changes to the web materials. As always, I thank my patrons for contributing enough to ...

Progress Update

Hi Patrons,
After some time shuffling priorities and sorting out some personal shit, recently I've been occasionally spending some time working on the Music Theory book. Yesterday I spent some time getting the rough outline done for the chapter about modes. The book in its entirety has grown to about 100 pages, and I feel like it's only half way done. So maybe the finished thing will be 200 pages? That's just a wild guess at this point. Maybe it will be longer. I want the thing to be quite...

Good morning, Patrons!

It is with gratitude and humility that I checked my Patreon account today to send this update. The update is, frankly, that I'm not doing much these days... since life has thrown some curve-balls my way, and the time I used to spend on The Exciting Universe (making videos, working on the book, tinkering with the website) has dried up - for the time being.

This isn't to imply that the book project - which I'd estimate is about 2/3 complete - is "shelved" forever, nor that I'm abandonin...

Tons of video corrections!

Over the past two weeks, I've made dozens of corrections to the video scripts, and I added two whole new scenes.  Among the improvements: long scale names won't overlap in the layout; animation sync with sound will be better; lots of errata in the scale names are corrected, some minor typos are corrected, and some of the phrase pronunciations by my robot narrator "Daniel" are improved. I'm rendering a few videos now to do some QA tomorrow. If they're all OK then I'll start queueing up th...

Upgrades! And Progress!

Hi, patrons! For the past few weeks I've been getting intermittent crashes on the web server, and the database that holds all the scale names and other stuff. It didn't always cause a 500 error, sometimes it merely manifested as a PHP error on the scale detail pages.  It was time for an upgrade to increase the CPU and RAM ... which I did tonight. Thanks to all my patrons for making it possible! Your donations are sufficient to cover the increased server costs (which frankly isn't a LOT) ...

A mind-map of topics

Hi patrons!  

Sorry it's been a while since I posted an update here. There isn't a lot to report, because I'm not really planning to make any new videos and I don't have any new material to post on the website. Really my focus (in the spare time that I'm able to devote to it) is on writing the book.   

Before an update, first let me take a moment of gratitude to all my patrons who are contributing month after month. Your patronage is allowing me to cover server ho...

Oh hey guess what. Video updates.

In the next few days/weeks I'm rendering a big batch of videos to replace ones that have incorrect scale names in them. The new ones will have the Patreon credits at the end with the names of everyone who is a Patron right *now*, at this moment (I exported the list to use it in the videos).

Cheers
Ian

More work, and some errata

Well it seems the days are long, but the weeks are short. Since my last update I have done some more work on the book; particularly on a chapter sub-section about "Cohn Sets". These are scales that can form optimally smooth "Cohn cycles" made by a "Cohn flip" where a pcs is flipped to its inverse by moving a tone by just one semitone. These were named after the eminent theorist Richard Cohn.

The kicker is, this is a concept that I explored many years ago thinking it was a novel and un...

Good morning patrons

An update for mid-October: I spent a bit of time on writing the book last week, adding some better explanations on a section about Interval Vectors. Other than that, my energy has mostly been focused on preparing an EP for release (it'll be out Oct 31), along with domestic stuff and day-job antics. I'm grateful that the support on patreon is enough to cover my server costs (more or less) to keep those music theory pages alive on ianring.com. Thank you!

My latest reading has been "Compo...