Erlanger Programm: Titles and Octuple Time

Titles (album, track, whatever) in my work come to me one of two ways. One is the obvious: you do a song or an album, and a title just jumps right at you. This is not what usually happens, and also didn’t happen in case of this project.

The other approach: I keep a list of title ideas (currently about 363 entries and counting) where I write down title ideas when I have them. I put it in the cloud so I can access it practically anywhere. This list can either work as a source for titles, or as a source for inspiration.

In the case of Erlanger Programm, it was such an inspiration when I had the idea for the original project about one year ago: it should work with strange loops, and be very “mathematical”, and then I read the title idea Hilbert redet mit Klein über komische Sachen (Hilbert chats with Klein about odd stuff). Strange loops -> Klein Bottle -> Felix Klein -> Erlanger Programm!

Erlanger Programm – and possible subtitles

When Felix Klein became professor, he published a paper describing the topics he intended to work on – the Erlanger Programm. What Klein was working on was geometry, and so this programme also focused on geometry. Klein is also most famous for his Klein Bottle, which is essentially a Möbius Strip in higher dimensions. It was also at Erlangen where Klein met Hilbert, another hugely innovative mathematician who, among other things, is famous for the concept of Hilberts Hotel.

When I started to sketch out this project, I wasn’t unhappy at all with the concept of track titles being no more than letters – it went well with that math-rock-kind of approach. However, I started to consider the option to have at least subtitles for the main parts, A through D.

Of course, Hotel Hilbert would be a first option.

And let’s not forget that Klein Bottle, albeit slightly rephrased with the Bavarian/Turkish genitive substitution, Am Klein sei Flaschn.

A Klein Bottle, cc-by-nc-nd by Pragmagraphr
A Klein Bottle, cc-by-nc-nd by Pragmagraphr

Now Hilbert did also work a lot with Einstein (in fact, it’s not exactly clear who of them worked out exactly which part of the General Theory of Relativity), so looking at theoretical physics also makes sense. And what better title would there be than Noether-Theorem, referring to Noether’s first theorem, which more or less says that conservation is symmetry and vice versa?

And finally, there’s the beauty of three linked (and unsolved) mathematical problems: the axiom of choice, the well-ordering principle, and Zorn’s Lemma. Bertrand Russell had explained the former quite well by stating that you only need it for (infinitely many) socks, but not shoes…so our fourth title option could be Zorns Lemma, Russells Socken (Socken, or socks, being somewhat more confusing than just shoes).

Emmy Noether of the timeless theorems and lemmata, cc-by-nd MAA
Emmy Noether of the timeless theorems and lemmata, cc-by-nd MAA

With that, we have four title options, albeit none of them, or the use of telling track titles in general, is decided upon. But if I use them, I’d call part A “Hotel Hilbert”, part B “Am Klein sei Flaschn”, part C “Noether-Theorem”, and part D could go by the Zorn/Russell title.

Does “Octuple Time” really exist?

A great many tracks go into double time, espescially reggae tracks. However, with that shared relationship of reggae, calypso, ska, punk, and hardcore, there’s room to go to really fast blast beat-fuelled mayhem. We’re talking about part D here, of course.

The start (and end) of part D is at 70 bpm, which puts it into a contemporary adagio field, the main accents by bass drum and snare drum residing on each quarter note. Going into double time from here would land us in allegro territory, and if we retain the 8-beat, a busy one. Of course, there’s room for more: further doubling that, we’d be in prestissimo, and here we’d typically bring the partition of the cymbals down to the one of the drums – it’s already not exactly slow. Room for more? Of course – multiplying by two again, we’ve reached a prestissimo double time , and the main hits happening on 1/32…go figure.

part D drum groove sketch in piano roll format
part D drum groove sketch in piano roll format

Starting from the beginning, we’ve multipled the tempo by two three times, so we’re at 2*2*2=8, which would be octuple time. And as we started with a rather slow tempo, it’s not that fast…there’s much faster stuff out there in the punk/hardcore domain.

Will I do that? I’m not sure right now. Especially as there are other options, like moving into triple time, and then multiplying that by three again. Or 3, then 5/3, then 7/5…you get the picture. But if I’ll include my buddy Oliver for the drum part (currently busy as a Landvogt), I’ll work it out with him.

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