A few related lines appeared in the 'scrapbook' section of radiohead.com:

A line that may be related to the creation of the lyrics appeared on the start page of radiohead.com in 2004 or 2005:

On some browsers the lyrics to the song scrolled across the bottom of radiohead.com in 2005 and 2006, possibly already in 2004:

'Arpeggi' was premiered at the Ether Festival on march 27th 2005. Thom sang while Jonny played Ondes Martenot. They performed the song with the London Sinfonietta (including six Ondes Martenots played by Valerie Hartmann-Claverie, Bruno Perrault, Nathalie Forget, Fabienne Martin-Besnard, Nadia Ratsimandresy and Pascale Rousse-Lacordaire) conducted by Martyn Brabbins with the Arab Orchestra of Nazareth.
This video, edited from two sources for this website, uses the audio recording that was aired by the BBC:

in the deepest ocean
the bottom of the sea
your eyes
they turn me

why should i stay here
why should i stay

i'd be crazy not to follow
follow where you lead
your eyes
they turn me

sunk without a trace
the bottom of the deep
your eyes, they turn me

turn me into phantoms
i follow to the edge of the earth
and fall off

everybody leaves
if they get the chance
and this is my chance

i get eaten by the worms
and weird fishees
picked over by the worms
and weird fishees

hit the bottom to escape

'Arpeggi' was one of the titles seen on the first of two blackboards, a picture of which was posted on september 30th 2005 on Dead Air Space. The photo shows a list of songs Radiohead had been working on during the two weeks of rehearsals from september 19th to 30th:
Transcript

The following pictures show the band recording 'Arpeggi' during the sessions with Mark "Spike" Stent. The first was posted on Dead Air Space on june 10th 2006 under the title 'winter studio', the other two were posted on february 22nd 2006 (click images to enlarge):

'Arpeggi' was one of the songs on the Tour blackboard, an image of which was posted on Dead Air Space on march 8th 2006, shortly after the rehearsals for the tour had begun (click image for full size):

Thom and Jonny performed 'Arpeggi' acoustically for the first time on may 1st 2006 at a Friends Of The Earth benefit gig at the Koko in London:

This photo, that was taken at Nigel's studio at The Hospital in London in december 2006, was posted on Dead Air Space on february 6th 2007 and was titled "Ed and Thom in Arpeggi":

A similar one was posted on march 27th 2007:

Yet another photo was posted on april 9th 2007 in the Hodiau Direkton section of radiohead.com:

On march 29th 2006 a short videoclip appeared in the Hodiau Direkton section, which featured Thom singing a line from the end of the song:

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On june 15th 2007 Nigel posted a video on Dead Air Space, that showed the playback of a reel of assembled tape snippets, which were cut out during the editing process.
The reel contains 2 fragments from the finished recording of 'Weird Fishes/Arpeggi', which actually flow seemlessly into each other and can be combined if one switches the order around:



Click here for a more detailed description of this reel, including all 20 snippets in isolation.

An electronic piece that uses the backing vocals from 'Weird Fishes/Arpeggi' was heard in the webcast from november 9th 2007:

Arpeggiremix by CitizenInsane;

An excerpt from a remix of 'Weird Fishes/Arpeggi' was used at the end of Scotch_mist, which was produced in mid december 2007. The full version was posted in early may 2008 on Thom's page at w.a.s.t.e. central. The file name suggests it was created by Jonny:

ArpeggiRMXjonny by CitizenInsane;

Thom premiered a solo arrangement of the song at the Latitude Festival on july 19th 2009. This performance, however, is from the gig in Cambridge on february 25th 2010: