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'Reckoner' was written in late 2006 or early 2007, and is not to be confused with another song that used to have the same title for several years and was finally released in 2009 under its initial title: 'Feeling Pulled Apart by Horses'.

However, both songs are strongly connected. 'Feeling Pulled Apart by Horses' (under the title "Reckoner") was part of the 2005/2006 sessions for what would become In Rainbows and was even considered for the 2006 tour, though it remained unplayed. After that tour had ended, the band began sessions with Nigel Godrich, and during this period an attempt was made to write a new section for the song. This new section then took on a life of its own and became a separate song, which was released on In Rainbows as 'Reckoner'.
In the autumn of 2006, the band continued working on the "old version" of 'Reckoner' with Nigel Godrich, and soon the idea came up to write another part for the song. This new part then took on a life of its own and turned into this song, and the band gave up trying to record the old song for this album. In late november the phrase "In Rainbows" appeared on the start page of radiohead.com, and in december the band worked on this new song at Nigel's London studio at The Hospital in Covent Garden.
The album title phrase "in rainbows" can be clearly heard in this stereo extraction from the released version of 'Reckoner':
On july 11th 2008, Thom posted a piece related to 'Reckoner' on his page at w.a.s.t.e. central. It was titled "robot reckoner celeste", and the info embedded in the mp3 suggests it is a sketch, probably something he or Jonny did on a laptop. In a post at his page from the same day he briefly mentions finding it:


Reckoner
This piece can also be put onto the middle of 'Reckoner', as it fits harmonically and has the same length as the break of the song. It is possible that this piece was a sketch of an idea for the middle of the song, which ultimately wasn't used:
A more cut up version had appeared more than a year before already, though it wasn't known that it had anything to do with 'Reckoner' at that time. On april 4th 2007 the following clip appeared in the Hodiau Direkton section of radiohead.com, titled 'Quiet Day at the Office'. It shows distorted footage taken at Tottenham House in october 2006 and features the piece as the soundtrack. It dates the sketch to early 2007 at the latest:
This recording again fits perfectly into the middle of 'Reckoner', and musically it even sounds better than when the original sketch is overdubbed. It is possible that the sketch was messed up a bit to make it sound better before the idea was entirely abandoned. This is a reconstruction of what the section might have sounded like:
On november 9th 2007, the song was played live to an audience for the first time during the Thumbs_down webcast:
On april 2nd 2008, the band did an excellent version of 'Reckoner' for Nigel Godrich's From The Basement. The program was aired on May 3rd 2008 on VH-1, and later uploaded by the band to YouTube:
Live performances #69 to #72 during the making of The King of Limbs:
69. september 21st 2009 Age of Stupid premiere Los Angeles, CA USA Link
70. january 24th 2010 The Music Box Theatre at The Fonda Los Angeles, CA USA Link
71. february 25th 2010 Corn Exchange Cambridge UK Link
72. august 6th 2010 Big Chill Festival Ledbury UK Link
Live performances #73 to #105 during the touring for The King of Limbs:
73. june 28th 2011 Glastonbury Festival Pilton UK Link
74. september 17th 2011 European Fish Fry Crackington Haven UK Link
  The King of Limbs tour (1st half) 09/'11 02/'12 march 2012 april 2012 05/'12 june 2012
Bodysnatchers [20] 28 29 27 29 01 05 07 13 15 14 21 29 31 01 03 05 08 10 11 13
Nude [21] 28 29 27 29 01 03 07 11 13 09 12 17 18 21 31 03 05 08 11 13 15
Reckoner [31] 28 29 27 29 01 03 05 06 07 09 11 13 15 09 11 12 14 17 18 21 29 31 01 03 05 06 08 10 11 13 15
House of Cards [5] 18 21 06 08 13
Live performances #106 to #134 during the touring for The King of Limbs:
  The King of Limbs tour (2nd half) july 2012 september 2012 october 2012 november 2012
Bodysnatchers [20] 11 13 15 29 23 29 30 09 11 12 14 15 16 18 06 09 12 13 16 17
Nude [28] 10 11 13 15 25 27 29 20 22 23 26 29 30 06 08 09 11 12 14 15 16 18 06 09 12 13 16 17
Reckoner [29] 10 11 13 15 25 27 29 20 22 23 25 26 29 30 06 08 09 11 12 14 15 16 18 06 09 12 13 16 17
House of Cards [5] 11 25 22 25 16
  2016 A Moon Shaped Pool tour may 2016 06/2016 july 2016 august 2016 sept./oct. 2016
Bodysnatchers [23] 20 21 23 24 27 28 01 03 17 02 08 26 29 31 06 08 20 21 11 30 03 04 07
Nude [19] 21 24 26 28 03 17 02 08 26 29 31 04 06 21 11 30 03 04 07
Reckoner [14] 20 24 26 17 08 27 31 08 20 21 11 30 03 07
  2017 A Moon Shaped Pool tour march/april 2017 june 2017 july 2017
Bodysnatchers [22] 30 01 03 08 11 14 17 21 06 09 11 14 16 18 20 23 28 30 02 04 07 19
Nude [17] 30 03 05 09 11 14 18 06 16 18 23 28 30 02 04 07 19
Reckoner [14] 30 05 08 09 17 21 06 16 18 28 30 02 07 19
House of Cards [2] 01 18
Thom played 'Reckoner' a few times during his 2018 Tomorrow's Modern Boxes tour, with Thom on guitar and Nigel on bass playing with the original studio drum track. This is a video from the performance on December 4th 2018: