h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Long ago I came up with an idea for explaining musical chords to aspiring guitarists. It was a wheel with 12 spokes, and I wrote the names of the notes around the outside, the order C, G, D, A, E etc, that is going up in fifths. Inside this, I wrote the relative minors: Am, Em, Bm etc, so that Am was inside of C, Em was inside of G etc.

I showed this to someone and they said "Oh that's just the Circle of Fifths". So someone had thought of it before.

It always irked me that when you get as far as C# and notes like that, you don't know whether to call them C sharp or D flat. Guitarists don't care which name you use, but other musicians can get very narky - "A D flat isn't the same as a C sharp!". I'm sure there are solid theoretical reasons for this, and I even now know some of them, but when you're a guitarist banging out chords you don't care.

Then over the weekend an idea occurred to me. Why not make a spiral and divide it into 12 using 12 spokes? The notes spiral around in fifths and by the time you get to C#, it is on the same spoke as Db. I've dubbed this new creation the "Ammonite of Fifths" because that's what it looks like.

Sounds like you just need a bit of Fibonacci in there to make it trendy.

Gilding the cephalopod.

Fibonacci was also known as Leonardo of Pisa.

Did you know that Galileo dropped an ammonite off the top of the Leaning Tower of Pisa to see which way it would bounce?

Do ammonites (snails/winkles etc) in the Southern Hemisphere coil in the opposite direction?

Visiting Pisa in the 17th Century sounds like a Health and Safety nightmare.

Ammonites and Nautiluses are a 'flat spiral', so you can get them to coil in the opposite direction just by looking at them from the other side.

But snails which go to one side as they twist ... that's an interesting question. I don't know whether snails always go in the same direction or not.

I remember visiting a Roman villa in central England (Chegsworth or something like that) and there was a spring at one point, flowing into a little stream. My daughter El, who is fascinated by animals, found some rather odd-looking snails beside the spring. They were like garden snails but slightly bigger and had light brown shells. She started poking at them gently.

Then she saw a sign saying "Don't poke the snails - these are Roman snails, brought to England by the Romans for food". Their descendants have been living by the spring for about 1,700 years.

'Don't Poke The Snails' must be one of the more unusual signs.

There were little signs put around Versailles in the 18th century saying things like 'Keep off the grass' apparently. They were called...

Etiquettes.

Every student should make their own circle of fifths diagram. Trouble with diagrams is, unless you have the scientific mind that prompts you to explore them, they just contain more information than a student is going to assimilate, so they just go 'Whatever' and are not much the wiser. Starting with a blank sheet and adding things as the student thinks of them is the way to go.

I know my fretboard well enough, but looking at fretboard diagrams...

Books on music theory are great. Everyone who wants to know something about music theory should write one

"Don't poke the snails"...

Always good advice.


As to the chirality (direction of the spiral) of snail shells, they can be either right or left handed but individual populations or species of snail tend to share the same chirality as sex between opposites is prohibitive.
Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182695/


Ducks have a similar chirality.
If you decide that a better metaphor would be a helix, then I might suggest the "Duck's Penis of Fifths".

I may have paraphrased the wording of the sign slightly.

I remember in a town called Amélie-les-Bains in the French Pyrenées, there was a little fountain with a sign beside it. In front of the sign was a large, friendly cat. I thought that the sign might tell me something about the fountain, so I went over to read it. It said:

"Please do not feed this cat"

Did you know that chirality anticommutes with parity?

As anticommuters go, this one's on a par with Southern Trains.

I didn't know that, Icy. Nor do I know what it means. It sounds interesting. Can you explain?

I attempted to look it up and came across the Schwinger-Dyson equation, which sounds like someone getting the short straw at a wife-swapping party.

It's just the mapping thingie associated with the reflective property.

The term 'chiral' was coined by Lord Kelvin in 1894 from the Greek word for 'hand'.

I know what chirality means. I don't know what you mean by "anticommutes with parity", though.

This is the cat who wasn't to be fed, although I haven't a picture of the sign.

https://www.flickr.com/gp/eoinmcauley/sJ1Kh

http://www.flickr.com/gp/eoinmcauley/sJ1Kdd

Gnomon, in regard to your OP: that's very clever. I love it when anybody (including, rarely, me) 'reinvents the wheel' like that. In your case, a literal wheel. It shows how things work.

Now I hope Icy's going to explain that anticommute business, because I probably only *think* I've understood it.

I think it is something to do with quaternions.

i² = j² = k² = i.j.k = -1

i.j = k
j.k = i
k.i = j

but multiplication of quaternions isn't commutative:

j.i = -k
k.j = -i
i.k = -j