The source of the patterns are cited as best as I am able to figure
out.  The multicolored pattern from Nancy Tinkham has been repeated
since one of them contains corrections which are already put into the
other.
================= cut here ==========================================
The below article was taken from the 12/89 issue of "The Prydonian 
Renegade", the newsletter of the Prydonians of Prynceton.  (A 
correction was printed in the 3/90 issue which has been incorporated 
into the directions below.)
                           TOM BAKER SCARF  
                       by Noel (Mick) Spencer
     This pattern is for one of at least three different 
multi-colored worn by Tom Baker (not including the final "burgundy 
scarf").  It is worn in Tom Baker's sixth through sixteenth stories 
("Terror of the Zygons" through "The Robots of Death").  It is also 
worn in his eighteenth story "Horror of Fang Rock"), his nineteenth 
story ("The Invisible Enemy:), and his twenty first story ("The Sun 
Makers").
     Though the same scarf appears in all these stories, it 
sometimes appears at first glance to be a little different, due to 
lighting, reversing the scarf, wearing a different portion looped 
around the neck, etc.  Also in some stories, it is difficult to 
distinguish some colors due to the lighting, cinematography (and no 
doubt the NTSC transmission system).  In some cases the "medium 
brown" looks like the "olive green", or the "purple" looks like the 
medium brouwn", etc.  After reviewing MANY stories, I think the 
following pattern is accurate.

     PU-PURPLE
     GO-GOLD (dirty yellow)
     RU-RUST (almost brick red)
     BE-BEIGE (creamish, this is the lightest color on the SCARF)
     GR-GREY (medium charcoal)
     OL-OLIVE GREEN (greyish)
     MB-MEDIUM BROWN (sort of olive brown)

START: PU/1"+BE/8"+MB/2"+GO/1.5"+RU/3.5"+PU/1"+OL/3.5"+GO/1.5"+
       BE/6"+RU/3"+OL/1.5"+PU/3"+OL/10"+GO/2"+GR/3.5"+RU/2"+BE/10"+
       PU/1.5"+OL/4"+GR/2.5"+GO/1.5"+RU/4"+PU/1.5"+MB/5"+BE/2"+
       GR/2.5"+RU/8"+GO/3"+OL/4"+PU/1.5"+BE/9.5"+MB/2.5"+GR/4.5"+
       RU/1.5"+PU/2.5"+BE/1.5"+GO/4"+OL/10"+RU/3"+GR/2"+GO/1.5"+
       MB/4"+PU/1.5"+BE/1.5"+GR/6"+RU/1"+GO/1.5" :FINISH

  Needle size 6mm.  American size 9.
  Tassels are made from 1 foot lengths of yarn.
  Seven tassles on each end combining all 7 colors.
  Guage 14 stitches per 4 inches. 20 rows per 4 inches.
  1 oz. balls of double knitting wool.
  3 Purple
  6 Camel
  3 Bronze (dark brown)
  3 Mustard (golden yellow)
  4 Rust
  3 Grey
  4 Olive
  Cast on 40 stitches.  In plain knitting always slip the first stitch!
  Knit as follows:
8 purple                    10 camel
52 camel                    8 grey
16 bronze                   40 rust
10 mustard                  14 mustard
22 rust                     20 olive
8 purple                    8 purple
20 olive                    42 camel
8 mustard                   12 bronze
28 camel                    20 grey
14 rust                     8 rust
8 bronze                    12 purple
10 purple                   6 camel
42 olive                    14 mustard
8 mustard                   54 olive
16 grey                     16 rust
8 rust                      12 grey
54 camel                    8 mustard
10 purple                   20 bronze
12 olive                    10 purple
8 mustard                   12 camel
18 rust                     32 grey
8 purple                    10 rust
38 bronze                   16 mustard
Suggestions:
Weave your ends in while you go. 
Get a good color photo of the scarf to take to the yarn shop to
choose the yarn. 

The source is the BBC.

Pattern for Doctor Who's Multi-Colored Scarf
--------------------------------------------
Requirements:  #9 knitting needle
One ounce balls of yarn as follows:
    3  purple
    6  camel                  The tassels are made from 1 inch [1 foot (c3)]
    3  bronze                 lenghs of yarn.  7 tassels on each end,
    3  mustard                tassels on each end, combining all 7 colors.
    4  rust
    3  grey
    4  greenish brown (referred to as "green")
Cast on 60 stitches (Mine is 40 and is almost a foot wide.  40 should
lengthen the scarf a little).  Always slip the first stitch.
Knit in the following order:
   8  purple rows        10  camel
  52  camel               8  grey
  16  bronze             40  rust
  10  mustard            14  mustard
  22  rust               20  green
   8  purple             88  purple   [8 purple (c1)]
  20  green              42  camel
   8  mustard            12  bronze
  28  camel              20  grey
  14  rust                8  rust
   8  bronze             12  purple
  10  purple              6  camel
  42  green              14  mustard
   8  mustard            54  green
  16  grey               16  rust
   8  rust               12  grey
  54  camel               8  mustard
  10  purple             20  bronze
  12  green              10  purple
   8  mustard            12  camel
  18  rust               32  grey
   8  purple             10  rust
  38  bronze             10  mustard    [16 mustard (c2)]   CAST OFF
Corrections:
     1) The instruction to knit 88 purple rows should instead
        call for 8 purple rows.
     2) The last instruction, 10 mustard, should be 16 mustard.
     3) The tassels are made from 1-foot, not 1-inch, lengths.
[And just to clarify, the #9 (knitting needle) refers to U.S. sizes.]

 Here's the pattern for the Doctor's maroon scarf, as given me
 (on BBC stationery) by The New Fantasy Shop / 5651 W. Belmont Ave /
 Chicago, IL 60634.

Doctor Who's 1980 Season Scarf
------------------------------
Requirements
------------
  Size 7 (U.K.) Knitting Needles
    6 Balls Sirdar Chenille, Terra Cotta, Color No. 523   (rust)
    8 Balls Sirdar Chenille, Claret       Color No. 525   (wine)
    8 Balls Sirdar Chenille, Aubergine    Color No. 526   (plum, dark purple)
    [American Size 6 Needles (4.5mm),  2 oz. Balls
       Possible Colors:
           523 -- Brick Red / Burnt Orange
           525 -- Wine
           526 -- Eggplant / Deep Purple ]
  I don't know the guage, but the scarf is 24' long and of the order of
  1' wide.
  Cast on 42 stitches.
2  inches  Terra Cotta     2  inches  Terra Cotta     2  rows    Terra Cotta
2  rows    Claret          2  inches  Claret          2  rows    Claret
2  rows    Terra Cotta     2  rows    Aubergine       2  rows    Terra Cotta
2  rows    Claret          2  rows    Claret          2  rows    Claret
2  rows    Terra Cotta     2  rows    Aubergine       2  inches  Terra Cotta
4  inches  Claret          2  rows    Claret          2  rows    Aubergine
2  rows    Aubergine       4  inches  Aubergine       2  rows    Terra Cotta
2  rows    Claret          2  rows    Terra Cotta     2  rows    Aubergine
2  rows    Aubergine       2  rows    Aubergine       2  rows    Terra Cotta
2  rows    Claret          2  rows    Terra Cotta     6  inches  Aubergine
2  inches  Aubergine       2  rows    Aubergine       2  rows    Claret
2  rows    Terra Cotta     2  inches  Terra Cotta     2  rows    Aubergine
2  rows    Aubergine       2  rows    Aubergine       2  rows    Claret
2  rows    Terra Cotta     2  rows    Terra Cotta     2  rows    Aubergine
2  rows    Aubergine       2  rows    Aubergine       2  inches  Claret
2  inches  Terra Cotta     2  rows    Terra Cotta     2  rows    Aubergine
2  rows    Aubergine       2  inches  Aubergine       2  rows    Claret
2  rows    Terra Cotta     2  rows    Claret          2  rows    Aubergine
2  rows    Aubergine       2  rows    Aubergine       2  rows    Claret       X
2  rows    Terra Cotta     2  rows    Claret          2  inches  Aubergine
2  inches  Aubergine       2  rows    Aubergine       2  rows    Terra Cotta
2  rows    Claret          7  inches  Claret          2  rows    Aubergine
2  rows    Aubergine       2  rows    Terra Cotta     2  rows    Terra Cotta
2  rows    Claret          2  rows    Claret          2  rows    Aubergine
2  rows    Aubergine       2  rows    Terra Cotta
2  inches  Claret          2  rows    Claret
2  rows    Terra Cotta     2  inches  Terra Cotta
2  rows    Claret          2  rows    Aubergine
2  rows    Terra Cotta     2  rows    Terra Cotta
2  rows    Claret          2  rows    Aubergine
6  inches  Terra Cotta     2  rows    Terra Cotta
2  inches  Claret          2  inches  Aubergine
2  inches  Terra Cotta     4  inches  Alternate rows  all 3 colours (footnote)
2  inches  Claret          2  inches  Claret                     
Repeat from beginning but exchange Aubergine for Claret.
2nd Repeat as originally listed, but stop at X.
(In other words you do all this 3 times.)
footnote: (i.e. Terra Cotta, Claret, Aubergine, ...)

This is the scarf that Tom Baker begins wearing
at the beginning of the Key To Time stories.
Colors:
[       ]
[       ]   = beige:  Woolworth's Wintuk
                      color:  "Fawn"
[+++++++]
[+++++++]   = gold:   WW's Knitting Yarn
                      color 205, "Pineapple"
[^^^^^^^]
[^^^^^^^]   = tan:    WW Wintuk color 35,
                      "Gold"
[:::::::]
[:::::::]   =grey/green :  Wintuk color 99,
                      "Flannel"
(Note:  the last is a compromise.  The actual color
is a hard-to-find shade of soft warm olive called
"archer's green" or "hunter's green".  If you can
find that, use it instead.)
[#######]
[#######]   = warm red: WW Knitting Yarn color
                        249, "Chili"
[///////]
[///////]   = dark brown:  Wintuk color 18,
                           "Mahogany"
This scarf should be from betwen eighteen to twenty
feet long when finished.  Be warned:  it will stretch.
Use #6 needles.
In this diagram,
2 spaces down=1.25"
3 spaces down=2.5"
6 spaces down=5"
9 spaces down=7.5"
4 rows=about one inch with these yarns.  Your
mileage may vary....
1 stitch should = about 5mm (see "Pyramids of Mars")

Fringe:  made of doubled 12" lengths of each
color, gathered together in groups of 6 and knotted.
|||||||||||||||
|||||||||||||||
||||||||||||||| ---------->fringe
   ------------
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
+++++++++++++++
+++++++++++++++
###############
###############
###############
///////////////
///////////////
:::::::::::::::
:::::::::::::::
:::::::::::::::
+++++++++++++++
+++++++++++++++
|             |
|             |
|             |
|             |
|             |
###############
###############
###############
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
///////////////
///////////////
///////////////
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
+++++++++++++++
+++++++++++++++
:::::::::::::::
:::::::::::::::
###############
###############
|             |
|             |
|             |
|             |
|             |
|             |
|             |
|             |
|             |
///////////////
///////////////
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
:::::::::::::::
:::::::::::::::
+++++++++++++++
+++++++++++++++
###############
###############
###############
///////////////
///////////////
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
|             |
|             |
///////////////
//////////////
###############
###############
###############
###############
###############
###############
###############
###############
###############
+++++++++++++++
+++++++++++++++
:::::::::::::::
:::::::::::::::
:::::::::::::::
///////////////
///////////////
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
:::::::::::::::
:::::::::::::::
:::::::::::::::
###############
###############
###############
///////////////
///////////////
///////////////
|             |
|             |
|             |
+++++++++++++++
+++++++++++++++
+++++++++++++++
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
:::::::::::::::
###############
###############
###############
///////////////
///////////////
+++++++++++++++
+++++++++++++++
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^
///////////////
///////////////
|             \
|             |     (that stitch was a mistake...)
:::::::::::::::
:::::::::::::::
:::::::::::::::
+++++++++++++++
+++++++++++++++
###############
###############...then reverse, starting at the
                  yellow stripe above this red one.
That's it!

I got this from an FAQ in FidoNet's WHO echo ...
To those of you who are looking to knit a Doctor Who Scarf in the Tom
Baker tradition, here is a text file that I recieved off a board some time
ago
that goes into detail about the pattern and colours that you need and how to
stitch it.
DOCTOR WHO SCARF INSTRUCTIONS
Here are instructions to knit your very own Doctor Who scarf.  Be the envy of
the other Time Lords with this colorful piece of apparel. Experienced
knitters
will take about eight to ten hours to complete the scarf.  Novices will take
longer, but it's a good beginner's project. (No purling required.)
You can make the scarf in one or two color schemes: brown (from earlier
episodes) or wine (from later episodes).
MATERIALS REQUIRED
(adequate for two 108-inch scarfs)
1 pair knitting needles  (size 11)
4-ply worsted-weight knitting yarn
    one 3 1/2 ounce (100 gram) ball of each of five colors.
Colors:
  For a brown scarf:
   (#1) Dark Brown
   (#2) Medium Brown or Khaki
   (#3) Beige or Life Tan
   (#4) Gold
   (#5) Bright Red
  For a wine scarf:
   (#1) Dark Brown
   (#2) Medium Brown or Khaki
   (#3) Burgundy or Wine
   (#4) Rust
   (#5) Dark Red

GAUGE: 6 1/2 stitches = 2 inches
       5 rows  =  1 inch
Width of finished scarf: 7 1/2 to 8 inches
Suggested length of finished scarf (without fringe):
   Adult size: 120 inches.
   Teen size: 108 inches.
   Children size: 96 inches.

DIRECTIONS (see pattern chart below)
Cast on 25 stitches. Knit all rows. Break off yarn and attach new color as
indicated by pattern chart (below). Repeat the pattern until scarf is desired
length.  (One complete pattern is approximately 52 inches of knitting.) Bind
of
stitches.
   FINISHING: Using crochet hoot of suitable size, weave in all yarn ends.
   TASSELS: Cut 52 strands 12 inches long of yarn color #1 (Dark Brown).
To make a tassel, fold a pair of strands in half.  Using a crochet
hook, pull the looked ends through to the right side, one row in from cast-on
and bind-off edges, then pull the four cut ends of the strands through the
look and tighten. Space 13 tassels evenly across each end of scarf.

PATTERN CHART:
Color #3 - 10 rows
      #4 -  6 rows
      #2 - 10 rows
      #1 - 10 rows
      #5 - 24 rows
      #4 - 30 rows
      #2 -  6 rows
      #3 - 20 rows
      #5 - 10 rows
      #1 - 16 rows
      #4 -  8 rows
#2 - 30 rows
      #5 -  8 rows
      #3 - 24 rows
      #1 -  8 rows
      #5 - 16 rows
      #4 - 10 rows
      #2 - 10 rows
      #1 -  8 rows
Repeat pattern until scarf is desired length.
DO NOT PRESS YOUR SCARF!!
The adaptations and instructions for the scarf were done by Bee Borssuck, a
DOCTOR WHO fan, Central New York designer and author or numerous popular
books
about needlework.  Her latest available work, PICTURE YOUR DOG IN NEEDLEWORK,
will soon be followed by MONOGRAMS UNLIMITED.  She is presently working on a
book about knitting.
Original instruction sheet (c) 1981 WCNY-TV and B. Borssuck


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