Matrix Teeth Pattern

[Dave Hughes]

Received by email from Michel Gallot in Belgium:

I would like to find the relationship between the No. of a channel and the teeth's combinaition for a Intertype C4.

For example:
If we note from up to down 1 for a tooth (a triangle) and 0 for a vertical line:


lettre--- n° channel-- pi matrix
e                  1           110 0000
t                   2           101 1000
a                  3           101 0000
z                 26          001 1100

and so on. Is there a logical relation? (I am thinking of the ASCII code)

[Dave Hughes]

I found the following on the excellent http://www.linotype.org

Linotype matrix distribution is, in many ways, the most ingenious part of the whole machine. It has been achieved through the use of matrix tooth combinations, each character running in the magazine having its own particular combination. The term "tooth combination" refers to the teeth Line drawing of an annotated matrix or projections on the inside of the "v" notch of the matrix. There are seven of these teeth on each side as illustrated. The various combinations of matrix and distributor bar make it possible for the matrices to find their proper magazine channels properly and automatically. In this way the matrices are used over and over. Properly cared for, they will wear indefinitely. Carelessly used, without attention being given to machine adjustments, matrices suffer unnecessarily.

Although it does not go into the amout of detail required to answer Michel's question, it gives an overview, and the illustration is quite useful.

[CAYLUS]

Here are the results of my observations:



 

 
 

 
 
 


 
 
 

 
 
 

 
 
 



 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

letter	e	t	a	o	i	n	s	h	r	d	l	u	c	m	f
channel (decimal)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
pi mat (hexadecimal)	60	58	50	30	70	08	48	24	68	28	10	38	78	04	44
letter	w	y	p	v	b	g	k	q	j	x	z	F.I.	fl	ff	F.F.	F.L.
channel (decimal)	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
pi mat (hexadecimal)	6E	64	14	54	34	74	0C	4C	2C	6C	1C	??	??	??	??	??
letter	...	,	.	:	;	?	En	(	|	"	!	-	TS	)	En	'	*
channel (decimal)	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48
pi mat (hexadecimal)	43	62	12	32	52	72	??	4A	??	??	1A	1D	??	7A	??	??	??
letter	1	2	3	4	5	6	7	8	9	0	$	UP
channel (decimal)	49	50	51	52	53	54	55	56	57	58	59	60
pi mat (hexadecimal)	66	16	56	36	76	4E	2E	6E	1E	5E	??	??
letter	E	T	A	O	I	N	S	H	R	D	L	U	C	M	F
channel (decimal)	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75
pi mat (hexadecimal)	7E	49	41	09	61	11	51	39	71	31	01	??	69	19	59
letter	W	Y	P	V	B	G	K	Q	J	X	Z	@	&	£	Em-Dash
channel (decimal)	76	77	78	79	80	81	82	83	84	85	86	87	88	89	90
pi mat (hexadecimal)	7C	79	05	45	25	65	3C	55	35	75	5C	??	??	??	??
letter	û	â	ô	-OE-	+	é	-	ê	è	à	<<	>>	ù	î	ç
channel (decimal)	??	??	??	??	??	??	??	??	??	??	??	??	??	??	??
pi mat (hexadecimal)	15	0D	4D	2D	22	18	5A	6A	2A	06	26	0E	3E	21	02

[SwissTypesetter]

I couldn't take a look myself today, but shouldn't, logically, the tooth combination be strictly binary?

[CAYLUS]

Every number in hexadecimal has a number in binary representation.

Example:
le letter "e", in hexadecimal is 60H.
6 is translate to 110B (1*4+1*2+0*1=6).
0 is translate to 0000B
Thus 60H=110 0000B.
Let's take "z" which in pi matrix in binary is 001 1100B= 1CH (1100B is 1*8+1*4=12=CH)

[Dan Williams]

Fascinating and no doubt reasonable depiction of binary and hexidecimal relationships.
However, I believe the original question dealt with the relationship between channel and matrix combination. The relationship between tooth pattern and channel being a different topic than the relationship between channel assignment and hexidecimal identification. I do not discourage either discussion. In fact, curious study suggests that the hexidecimal topic may be relevant for digital actuation of keybars, for whatever purpose that carries.
Incidently, does anyone remember the cartoon series REBOOT and the anthromorphic HEXADECIMAL. 

[CAYLUS]

First, sorry for the mistakes for the letters "t,h,d,l,w,6,7,T,O,H,L,W,K" : hexa code was false.
After further observations, the solution was the RAIL.


As showed, it seems that the constructors minimized the alternance of tooth and vertical line.

On the Rail, we find a code whose complement to one ( changing all 1 to 0 and all 0 to 1) give the pi matrix.
Here is a short BASIC programm ( in QB) that does the conversion.

DIM n AS INTEGER, i AS INTEGER, k AS INTEGER
DIM code AS STRING, c AS STRING, bit AS INTEGER
n = 1
CLS
WHILE n > 0

INPUT "Nø du canal;0 pour terminer "; n
IF n > 0 THEN
  k = n + 2
  code = ""
  c = ""
  FOR i = 1 TO 7 ' nø OF bit
   bit = k AND 1
   k = INT(k / 2)
   c = c + STR$(bit)
   code = code + STR$((bit + 1) AND 1)
  NEXT i
  CLS
  PRINT "canal="; n, "Matrix="; c, "Rail="; code
END IF
WEND
END

Before putting this on the web, I would like a confirmation of my observations.

[Dan Williams]

Egad. Reminder of a long-past FORTRAN class. Still have the cards to prove it.

To seriously consider your proposal, I suggest studying the basics.

From my Useful Matrix Information booklet the following combinations (rail teeth cut - matrix teeth remain) are:

e1   2
e     1,2
t      3
a     1,3
o     2,3
i     1,2,3
n      4

My estimated binary assignments for these few lower case letters are:


              matrix            rail
e1      0100000       1011111
e        1100000       0011111
t         0010000       1101111
a        1010000        0101111
o        0110000        1001111
i          1110000        0001111
n         0001000       1110111

As reflected here, the negative binary of the matrix combination is the rail combination. Not PI.

PI combinations

0000000             1111111

If a mat has no teeth, it falls out with the spacebands. It is PI. If it has no cut teeth, it ends up in the PI tray. It is still PI.

Tomorrow, lets study hexadecimal

Dan

[CAYLUS]

I thanks you for beeing so patient (sorry for my poor english).
Thus there are only 2 PI combinations 000 0000 (no teeth) and 111 1111(special characters).
What is  "e1" (010 0000)?
What 's meant PI?

[Dan Williams]

The definition of PI is discussed on another forum page. I think that PI collectively refers to loose sorts, special characters and symbols that are not in a magazine or case. PIED refers to hand type that has been spilled. Lets defer to the forum board for other opinions.
On a linotype and intertype, e1 designates the channel for extra lower case "e" matrices. Extra mats were necessary for high speed typesetting in small fonts at long measure. Especially with 36 and later 42 pica machines.
Discussion about hexidecimal.
Hexadecimal and the term binary are simply ways of describing the numeric base of a numbering system. Normal people think in terms of base 10 figures. Such are the decimal figures we use in everyday life.
For those of us who have been spent too many years in school, there are other base or radix numbering systems. We think of base 2, 4, 8, 10 and 16. Binary numbers represent the base 2 numbering system. Hexadecimal numbers represent the base 16 numbering system. Bases 2, 8 and 16 are commonly used in computers.
These different numbering systems can all represent the same value, however the number represented is different both symbolically and (apparently) numerically, depending on the base or radix of the system.
A change of base is possible using arcane and esoteric procedures.
From my CRC Standard Mathematic Tables to convert a base 10 number into another base:
(These steps pertain to the numbers to the left of the decimal point)
1 Divide the number by the new base, getting an integer quotient and a remainder
2 Write down the remainder as the last digit of the number in the new base
3 Using the quotient from the last division in place of the original number, repeat the above two steps until the quotient becomes zero
(The following steps pertain to fractional number to the right of the decimal point of the original number)
1 Multiply this number by the new base
2 Write down the integer part of the product as the first digit of the fractional part in the new base
3 Using the fractional part of the last product, repeat the above two steps as many times as desireable
Lets see if it works
Convert 232.5 base 10 to base 2
231/2=115r1
115/2=57r1
57/2=28r1
28/2=14r0
14/2=7r1
7/2=3r1
3/2=1r1
1/2=0r1
For the left side of the base 10 digit, the binary representation now is 11110111
For the 0.5 base 10 conversion,
0.5x2=1r0
I think then that the full binary representation of the base 10 figure 232.5 is then
11110111.1
Based on the fact that base 16 requires alphabetic characters for the conversion, and the difficulties in going from base 2 to base 10 and then to base 16, I will forgo that complicated summary in this post.The CRC has got some tables to simplify the hexadecimal conversion, and I might try to use those and simply post the result and let you check it.

[CAYLUS]

Thank's for the lesson in hexa.
In fact, I am a teacher of mathematics and a assembly s' programmer (masm).
I have only put the hexadecimal code of mat in order to reduce the mail ( binary code is more longer)

The last resume should be

16\u	0	1	2	3	4	5	6	7	8	9	A	B	C	D		F
0	--	--	--	--	--
1	--	--	--	54	--
2	--	--	--	--	--
3
0
4
5
6
7
8
9
A
B
C
D
E
F

54H mat's cod  for the channel 13H :letter  "v"

channel 13H=0001 0011B=16+3=19 thus for the "v" letter.

Remark: i have written 16 in order to say "seizaine in french" maybe "sixteenth ?(10H)

[Dan Williams]

I am glad you are a math teacher, thus explaining your nearly losing me with the hexadecimal discussion. I was almost, but not all the way lost with it. Integral calculus would have left me wheezing some time ago.
My explanations are my way of grasping the topic, and hopefully by posting the material I can share with others the underlying thought process that you have worked through.

Getting back to channel codings on linecasters. This is what my CRC handbook tells me (for CHANNEL & ESCAPEMENT positions only NOT matrix teeth combinations):

letter   Base 10 value             base 16 value                      base 2 value
e               0                                       000                                    0
e                1                                      001                                    1
t                2                                       002                                  10
a               3                                       003                                  11
o               4                                       004                                  100
i                5                                        005                                 101
n               6                                        006                                 110
s               7                                        007                                  111
h               8                                       008                                1000
r                9                                       009                                1001
d             10                                       00A                                1010
l               11                                       00B                                1011
u              12                                       00C                             10100
c              13                                       00D                             10101
m             14                                       00E                             10110
f               15                                      00F                              10111
w             16                                       010                             10000
y             17                                        011                             10001
p             18                                        012                             10010
v             19                                        013                             10011 
b             20                                        014                             10100
g             21                                        015                             10101
k             22                                        016                             10110
q             23                                        017                             10111       
j              24                                        018                           101000
x             25                                        019                           101001
z             26                                        01A                           101010

As this goes pretty far beyond the original scope, so I'll let this topic sit.
The only other thing of vague academic interest is depicting a full binary or hexa for the teeth combinations.
Not anytime soon, here.
As a footnote, let me mention that there are better explanations of hexadecimal and binary configuration on the 'net, especially as they are formatted for digital programming. An example is http://myweb.tiscali.co.uk/whitefiles/b1_s/1_free_guides/fg2cd/pgs/c01.htm
Dan

[CAYLUS]

Je dois d'abord m'excuser d'avoir coupé court la discussion sur le code hexadécimal.
Je pensais vous ennuyer avec mes questions infantiles et poluer le forum de discussion.
Mais, il semble (après une traduction automatique des mails) que cela ne soit pas la cas.
Mon travail de recherche portait sur le codage de la denture des matrices d'une intertype C4 et de comprendre le pourquoi de cette codification.
Je ne possède pas de machine à composer et le travail que je fais, est pour un musée en Belgique: le musée de l'imrpimerie et des lettres de Thuin.
J'ai donc observé de haut vers le bas un jeu de matrices dont certaines dents étaient usées ( explications des erreurs de code!).
Ainsi, la denture de la lettre "e" de haut vers le bas apparaissait comme "//|||||"
En utilisant des "1" pour les "/" (une dent) et des "0" pour "|" pas de dent,
on pouvait voir l'image "1100000". Le premier "1" était situé en haut.
J'ai voulu garder cette image mentale des dents (donc me pas retourner la notation), et voir
le code 0110 0000.
1: codé en 8 chiffres binaires (le zéro du devant)
2: séparation en groupe de 4 chiffres binaire (quartet en français et nibble en anglais)
Ce nombre binaire valait donc 0*2^7+1*2^6+1*2^5+0*2^4  +0*2^3+0*2^2+0*2^1+0*2^0=0+64+32+0+0+0+0=96
Décimal: 96
Binaire:
quotient|reste (divisions successives par 2)
96 |0
48 |0
24 |0
12 |0
6 |0
3 |1
1 |1
0             lecture de bas vers le haut: 110000B
Hexadécimal:
quotient|reste (divisions successives par 16)
96|0
6|6
0             lecture de bas vers le haut: 60H


Conversion rapide du binaire en hexadécimal:
0110000B=(0110 0000B)=6 0H
car 0110B=0*2^3+1*2^2+1*2^1+0*2^0=4+2=6

Ceci ne me permettait pas de comprendre la logique de la codification.
La solution se trouvait sur le rail portant les matrices que je m'avais pas lors de mon premier mail.
Pour qu'une seule matrice X se détache à un certain endroit du rail, il faut que à toute dent de la matrice X qu'il n'y ait pas de dent sur le rail
et que à toute abscence de dent de la matrice X corresponde une dent sur le rail.
Le code du rail etait donc la négation (complément à 1 ) du code de la matrice.
Le code du rail de la lettre "e" est donc C(110 0000B)=001 1111B
Ceci est illustré par le dessin de « Reply #6 on: September 28, 2006, 05:55:53 PM ».
Ce dessin montre que les constructeurs ont minimisé le nombre de changement de dent et de non dent sur le rail.
J'ai pu ainsi partant du code sur le rail, en prenant son complément à 1, trouver le code de la matrice.
Le programme écrit en QB montre ce calcul.

J'ai ecrit ce texte en français pour la précision de ses mots.
J'espère avoir été clair.

[Dave Hughes]

This is going well over my head now, first complicated maths, now a foreign language!

[Dan Williams]

Michel:
Votre travail de musée est important et avec optimisme mes postes n'ont pas fait une digression.
Je suggère vraiment votre considération d'autres facteurs d'augmenter votre analyse mathematic. La réduction de vêtements et d'aisance de fabrication est des facteurs non-mathematic possibles dans la configuration de la combinaison de rail. Une recherche de journal de premières archives (Mergenthaler, John Thompson et d'autres) semble nécessaire de régner - de ces autres possibilités.
Merci pour vos commentaires et analyse.
Dan

AOL Translator
Your job of museum is important and with optimism my post offices <1> did not make a digression. I really suggest your consideration of other mailmen <2> to augment your mathematic analysis. The reduction of clothes and wealth of manufacture<3> is factors not - mathematic possibles in the shape of the combination of rail. <4> A research of newspaper of first archives (Mergenthaler, John Thompson and others) seems necessary to <5> reign - of these other possibilities. Thank you for your comments and analysis.



<1> hopefully my POSTS not post offices..did not cause digression
<2> other possible explanations ....NOT other mailmen
<3> reducing wear and facillitating manufacture .....NOT reducing clothes or wealth of manufacture
<4> A journal search of....NOT research of newspapers
<5> rule-out...NOT reign

hahahaha
sigh