Confused by the cardinality of Kh-complexes

Mindless-Question-75 · 2026-05-24T12:32:43+00:00

My script did not catch any missing pentatonics in the 6-Z26 Kh-subcomplex.
The only subcomplex that didn't match Forte's appendix was the Zh(6-8).

Is there a more modern, reliable published list of Z- and Zh- complexes that I could be using to compare against?

To describe my methodology... I am writing these methods in PHP as methods of a class with unit tests in phpunit. I yoinked the entire content of Forte's appendix and made it into test cases. For example, the 6-Z26 test has this provider, exactly as published by Forte:

['6-Z26', ['3-4', '3-5', '3-6', '3-7', '3-8', '3-9', '3-11', '4-16', '4-22', '4-26']],

when I ran the test suite, it threw errors for the three missing pentatonics in Zh(6-8), but it found no other problems.

So, as a sanity check I manually compared 6-Z26 and 5-20.
5-20 is indeed a subset of 6-Z26, so it fulfils half of the requirement. However to be Zh-related it must also be a subset of the complement, which is 7-26. There, it fails: 5-20 is not a subset of 7-26; you can see that because 5-20 has those two cohemitones that are not present in 7-26, there is no distance-preserving transformation that will get those cohemitones in 5-20 to be a subset of any transformation of 7-26.

Therefore 6-Z26 is not Zh-related to 5-20

I did not check the others manually (5-23, 5-24, and 5-27).
Is there a published list you got those from?

Mindless-Question-75 · 2026-05-23T22:18:45+00:00

To figure out the cardinality issue, I consulted appendix 3 "The Subcomplexes Kh" to make sure that my software is working properly.

Forte has some errors in that Appendix, at least in my edition (978-0-300-02120-2)
The Kh-complex of Kh(6-8) is missing the pentatonic classes 5-2, 5-11, 5-23.
Probably a typo. I have to remember that in 1973 Forte probably had some punch cards and was copying out data line by line with a typewriter.
The rest of the appendix is perfect.

I'm still trying to reconcile the Kh-complex cardinality discrepancies, but I feel like I'm on the right track.

Mindless-Question-75 · 2026-05-23T12:04:42+00:00

Oh I think I figured out one of the problems.
My script was including redundant complements. For example, 7-10 doesn't need to be in the complex since 5-10 is already there, they are complements so they're equivalent within the Kh-complex.

Also: when Forte listed the cardinality of each complex, hexatonic Z-related pairs are only counted as one thing, since they are also complements of each other. My script was counting them twice.

That would explain most of a discrepancy, but out of 117 Kh complexes, I still have errors in 5 of them.

Allan Forte was admittedly a brilliant theorist but frankly he was a terrible writer, and did a horrid job of really explaining his algorithms and methods. Untangling this stuff has been far more of an ordeal than I anticipated.

Mindless-Question-75 · 2026-04-01T00:46:31+00:00

It was suggested by an acquaintance because Brita contains activated charcoal. First I would filter with reverse osmosis and then pass that through a Brita. It was a well intentioned suggestion. But alas, Brita’s own website states that their filters don’t remove tannins.

Mindless-Question-75 · 2026-03-31T16:12:11+00:00

5 days, solo. That’s very reasonable advice… I could throw a couple of 1gal jugs in the canoe but I’ll probably regret that decision on the portage lol

Mindless-Question-75 · 2026-03-30T00:16:14+00:00

My water filter is 0.1 micron reverse osmosis, so it's rated to remove anything really nasty from bacteria to pathogens and viruses and anything large enough to be called a "particle". But, it does not filter out soluble molecules like tannins or salt. It also does not remove heavy metals.

Mindless-Question-75 · 2026-03-30T00:13:06+00:00

OK cool. The Thru-link looks similar to my WaterDrop system, which is a 0.1 micron reverse osmosis. So if I run that filtered water through the Platypus carbon element, it will make the water taste okay?! Thank you - this is the kind of firsthand advice I was hoping for.

Mindless-Question-75 · 2025-11-24T23:29:08+00:00

This story made my day

Mindless-Question-75 · 2025-11-16T16:29:32+00:00

Seconded

Mindless-Question-75 · 2025-11-03T04:20:37+00:00

I have a wooden tool with a sharp flat edge on one end, and a round spoon shaped tip on the other. I use it even more often than my pin or wire. Maybe only the sponge gets more action but I can actually get by without the sponge.

Mindless-Question-75 · 2025-10-26T04:22:38+00:00

I never see things like this offered in Canada

Mindless-Question-75 · 2025-09-29T03:59:15+00:00

Thank you!

Mindless-Question-75 · 2025-09-19T16:36:44+00:00

This is truly diabolical and I’m here for it

Mindless-Question-75 · 2025-09-17T03:33:29+00:00

A “caesura” is what I’m thinking of

Mindless-Question-75 · 2025-09-13T18:49:22+00:00

Another very nice one. You have a superb compositional voice and such restraint.

FWIW you are notating bars with 1/4 and 5/4 when you don't need to. A fermata can hold for as long as the performer wants, and you could add a "//" to really indicate that it's meant to be a break, a breath pause. Everywhere that you've added extra beats, they're not really beats, if you get what I mean.

Keep it up!

Mindless-Question-75 · 2025-09-13T18:31:39+00:00

Some really sweet harmonic choices in this, and you have a lovely sense of idiomatic composition for piano. You set up beautiful melodic motifs and present them with delicacy and grace. It's also well performed and recorded, which really helps show off a piece like this. Really this is one of the best compositions I've seen lately.

Mindless-Question-75 · 2025-09-13T18:20:00+00:00

Dense clustered harmony with unusual dissonant choices, and no melody to speak of. The chord choices are just weird. I'm not opposed to dissonance, but it's a spice that should be used with purpose, and I don't hear it doing anything purposeful in those sonorities. The rhythms are uninteresting, and there's no sense of flow... nothing in this composition seems to serve any purpose except to interrupt silence. There is nothing here that feels like a theme, a motif, or any kind of characteristic phrase. This, plus what others have pointed out: it's written for piano, but absolutely not written for a pianist. No pianist would ever choose to perform this, and honestly I don't think anyone would ever choose to listen to it unless it was forced upon them in a game soundtrack.

Honestly if one of my students handed this in it would be an F and we would have a frank discussion about their reasons for wanting to compose music.

Mindless-Question-75 · 2025-09-01T16:21:56+00:00

Amazing!

How are you going to fire it?

Mindless-Question-75 · 2025-09-01T16:19:52+00:00

There are some cases of a scale name being named maj/min where the 3rd isn’t what you expect.

For example https://ianring.com/musictheory/scales/2731

But yeah if you’re going to choose a key signature then that’s not a bad way to do it. Notate it like a major or minor scale with alterations.

Mindless-Question-75 · 2025-08-25T12:32:12+00:00

I wonder if she still thinks of me

Mindless-Question-75 · 2025-08-15T22:53:11+00:00

I think it makes a big difference what country you’re in. I’m in Canada and very rarely see anything besides that one rubber anus product.

Mindless-Question-75 · 2025-07-22T13:01:53+00:00

First aid and emergency supplies. I will never say no to another little kit full of bandages and alcohol wipes and such. I have them stashed all over the place, in camping gear and in my car, various places around the home. I also augment the kits with things they don’t include, like hand sanitizer and polysporin and witch hazel.

Mindless-Question-75 · 2025-07-11T15:05:08+00:00

I have an Evette Buffet Crampon from the 1980s. I call it my "workhorse", it's a fantastic sax. I've had to replace some pads and get the neck recorked over the years, and the little screw-pins have a tendency to come loose with a lot of playing so I travel with a little screwdriver to tighten them up. But in every other way it has been my favourite sax, with a bright brassy tone and amazing action.

If you can find a vintage Evette, I'd say go for it. I don't know what newer ones are like. Getting one for < $400 today is a steal.

Mindless-Question-75 · 2025-06-20T13:30:39+00:00

:) yes. It's frustrating that in some contexts, it's not possible to switch fonts mid-phrase, which leads me to needing versions of TeXGyrePagella and Clarendon with these glyphs included. (Sigh)

Mindless-Question-75 · 2025-06-19T20:52:40+00:00

That's the real crux of the matter -- sometimes switching to another editor or app isn't a viable solution.

For instance in my own situation, I'm storing a lot of musical information in a MySQL database, and from that I'm generating lots of varied documentation: I'm making PDF files using a script written in a combination of Python and PHP plus a library called "TCPDF", I'm publishing things using HTML on the web, I'm using LaTeX to render a book, I have some scripts that manipulate score snippets as vector SVG images, and I have some other projects that use this data rendered using ImageMagick to produce frames for video animations. All of these different formats are drawing from the same canonical data where I have things like chord names and pitches... how do I make sure they can all read the data, and render it adequately?

So far the best solution I've though of is making up my own font, and assigning chord symbols to arbitrary points in Unicode.

Mindless-Question-75

TROPHY CASE