Return to Santa Fe Amateur Radio Club website
Chapter
27 Contents
Chapter 29
The letter
frequency counts (left-most column) are taken from one of the common books
on cryptanalysis, based on number of
occurrences
per thousand of normal English text material. Each character is analyzed
("structure") into units, 1 for minimum
signal duration
(one dit), 111 (three units duration) for a dah, and each equal unit of
silence denoted by 0 (zero). The required three units of silence
separating each character is added (000) to each one below.
Freq. Letter
Structure Units
Total
130
E
1000 4
520
92
T
111000 6
552
79
N
11101000 8
632
76
R 1011101000
10
760
75
O 11101110111000
14 1050
74
A
10111000 8
592
74
I
101000 6
444
61
S
10101000 8
488
42
D 1110101000
10
420
36
L 101110101000
12
432
34
H 1010101000
10
340
31
C 11101011101000
14
434
28
F 101011101000
12
336
27
P 10111011101000
14
378
26
U 1010111000
10
260
25
M 1110111000
10
250
19
Y 1110101110111000
16
304
16
G 111011101000
12
192
16
W 101110111000
12
192
15
V 101010111000
12
180
10
B 111010101000
12
120
5
X 11101010111000
14
70
3
Q 1110111010111000
16
48
3
K 111010111000
12
36
2
J 1011101110111000
16
32
1
Z 11101110101000
14
14
1000 Ave. Structure length 11.23 Ave. 9.07 9076
From the above,
if we take five times the above average letter length and add the space
required for word spacing (seven total
or 0000000)
we arrive at the normal English word length as 5 x 9.076 + 4 = 49.38.
This is just a bit less than 1% shorter than
50 units per
standard word. (By contrast, a random five-letter group averages
60.15 units. This is 20.3% longer than normal
English word
length.)
A similar analysis of numbers will show that the average length of a number is 17 units (minimum 12, maximum 22) or a group of five numbers takes about 1.78 times as long to transmit as a five letter word.
Comparing these calculations will show some of the reasons why receiving speeds vary with the kind of material being sent.
As a matter
of interest, we list here the letters from the shortest to the longest
by the number of units (less letter space) -- notice that all lengths are
odd numbers: 1 - E; 3 - I, T; 5 - A, N, S;
7 - D, H, M, R, U; 9 - B, F, G, K, L, V, W; 11 - C, O,
P, X, Z; 13 - J, Q, Y.
FOREIGN
ADAPTATIONS OF THE INTERNATIONAL MORSE CODE:
If the same
kind of calculations are carried out for several foreign languages, the
following results are obtained for the average character length:
(Frequency data from Secret and Urgent, Fletcher Pratt l942 Tables II to
IV, p. 253 ff.)
German
8.640, French 8.694, Spanish 8.286 . These range on the average
from 5 - 9% shorter per character than in English.
There seem
little doubt that if the code were somewhat redesigned and adjusted to
optimize it for English a reduction of about 5% could be made.
For the Original
American Morse code:-
Mr. Ivan Coggeshall
made an analysis of American Morse comparatively, using the same normal
dah lengths and word spacings one unit shorter, and arrived at an average
letter (frequency) length of 7.978 (as compared with 9.076) and average
number length of l4. As noted in Chapter 16,
American Morse timing is open to considerable variation.
Top Chapter 27 Contents Chapter 29
Return to Santa Fe Amateur Radio Club website