Main Index Pablo Honey The Bends OK Computer Kid A Amnesiac Hail to the Thief In Rainbows The King of Limbs A Moon Shaped Pool Thom Yorke Jonny Greenwood Ed O'Brien Colin Greenwood Philip Selway
A few related lines appeared in the 'scrapbook' section of radiohead.com:

scrapbook
scrapbook
scrapbook
scrapbook
In 2004 or 2005, a line which may be related to the song's lyrics appeared on the start page of radiohead.com:

start page
In 2005 and 2006 (possibly already in 2004), the lyrics to the song scrolled across the bottom of radiohead.com on some browsers:

scrolling bar
On March 27th 2005, 'Arpeggi' was premiered at the Ether Festival. 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 that appeared on the blackboard the band used during two weeks of rehearsals from september 19th to 30th 2005. At the end of that session, Colin posted a picture of this board on Dead Air Space on september 30th, unfortunately (and probably intentionally) in rather low resolution, so that some of it can't be deciphered:
The following pictures show the band recording 'Arpeggi' during the sessions with Mark "Spike" Stent. On January 10th 2006, the first of those pictures was posted on Dead Air Space under the title 'winter studio', the other two were posted on February 22nd 2006 (click images to enlarge):

dJG jonnyarpeggi3
thomarpeggi12
On March 8th 2006, shortly after sessions with Mark Stent had come to an unfruitful end, another photo of a blackboard (and a perhaps slightly worried Ed) was posted on Dead Air Space. A tour had been scheduled for may and june to escape the frustration of the recent sessions and to breathe new life into the project. Rehearsals for the upcoming dates had begun recently, and this board shows which new songs were at this point considered for inclusion in the setlists. 'Arpeggi' was one of these, and would indeed be played (click image for full size):
On May 1st 2006, Thom and Jonny performed 'Arpeggi' acoustically for the first time at a Friends Of The Earth benefit gig at the Koko in London:
In December 2006, this photo was taken at Nigel's studio at The Hospital in London. It was posted on Dead Air Space on February 6th 2007 and was titled "Ed and Thom in Arpeggi":


Ed and Thom in Arpeggi (Winter 07)
On March 27th 2007, a similar one was posted:


ed and thom arpeggi 1
On April 9th 2007, yet another photo was posted in the Hodiau Direkton section of radiohead.com:


Thom on da mike
On March 29th 2007, a short videoclip appeared in the Hodiau Direkton section. The clip featured Thom singing a line from the end of the song:
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.
On November 9th 2007, an electronic piece that uses the backing vocals from 'Weird Fishes/Arpeggi' was heard in the Thumbs_down webcast:
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:
On July 19th 2009, Thom premiered a solo arrangement of the song at the Latitude Festival.

On February 25th 2010, he played that same solo arrangement at a gig in Cambridge:

Live performances #94 to #96 during the making of The King of Limbs:
94. january 24th 2010 The Music Box Theatre at The Fonda Los Angeles, CA USA Link
95. february 25th 2010 Corn Exchange Cambridge UK Link
96. june 25th 2010 Glastonbury Festival Pilton UK Link
Live performances #97 to #120 during the touring for The King of Limbs:
97. june 28th 2011 Glastonbury Festival Pilton UK Link
  The King of Limbs tour (1st half) 09/'11 02/'12 march 2012 april 2012 05/'12 june 2012
15 Step [23] 28 29 03 05 09 11 15 09 11 12 14 17 18 21 29 31 01 03 05 06 08 10 13
Weird Fishes/Arpeggi [23] 28 29 27 29 01 03 05 06 07 09 11 13 15 09 12 14 18 21 29 31 06 08 10
All I Need [6] 28 29 29 03 11 15
Videotape [1] 09
Live performances #121 to #140 during the touring for The King of Limbs:
  The King of Limbs tour (2nd half) july 2012 september 2012 october 2012 november 2012
15 Step [21] 10 11 13 15 25 27 29 20 22 23 25 30 08 14 15 16 18 09 12 13 16
Weird Fishes/Arpeggi [20] 10 15 27 29 20 22 23 26 29 06 08 09 12 15 16 18 06 12 13 17
Videotape [7] 10 29 09 12 16 12 16
  2016 A Moon Shaped Pool tour may 2016 06/2016 july 2016 august 2016 sept./oct. 2016
15 Step [1] 26
Weird Fishes/Arpeggi [17] 20 23 27 01 03 17 02 27 29 31 04 06 20 11 30 03 07
All I Need [4] 21 03 04 07
Videotape [1] 20
  2017 A Moon Shaped Pool tour march/april 2017 june 2017 july 2017
15 Step [23] 05 08 09 11 14 17 18 21 06 07 09 11 14 16 18 20 23 28 30 02 04 07 19
Weird Fishes/Arpeggi [17] 30 05 09 14 18 06 09 11 14 16 23 28 30 02 04 07 19
All I Need [19] 30 01 05 09 11 17 21 06 07 11 16 18 20 28 30 02 04 07 19
Videotape [5] 30 03 18 07 02