# Derivation of the relationship between clock speed, internal timers and WPM equivalent speed

The following is a table of frequency of occurrence of the alphabet in plain English text taken from a cryptanalysis text, and the length of Morse Code encoding of those characters.

 Letter Frequency (%) Elements Contribution E 0.1300 4 0.520 T 0.0920 6 0.552 N 0.0790 8 0.632 R 0.0760 10 0.760 O 0.0750 14 1.050 A 0.0740 8 0.592 I 0.0740 6 0.444 S 0.0610 8 0.488 D 0.0420 10 0.420 L 0.0360 12 0.432 H 0.0340 10 0.340 C 0.0310 14 0.434 F 0.0280 12 0.336 P 0.0270 14 0.378 U 0.0260 10 0.260 M 0.0250 10 0.250 Y 0.0190 16 0.304 G 0.0160 12 0.192 W 0.0160 12 0.192 V 0.0150 12 0.180 B 0.0100 12 0.120 X 0.0050 14 0.070 Q 0.0030 16 0.048 K 0.0030 12 0.036 J 0.0020 16 0.032 Z 0.0010 14 0.014 Total 1.00000 9.076

Average word duration will be 5 * 9.076 + 7 or 52.38

This represents 60/52.38/10 s (114ms rounded to the ms) per dit interval (Baud) at 10WPM. With that figure, the WPM speed is 2.28 times the dit frequency

The PARIS test has 53 dit elements per word, so dit time of 113ms at 10WPM.

I note that an older ARRL handbook suggests for electronic keyers that the WPM speed is 2.4 times the dit frequency (120ms/dit at 10WPM), but it does not provide the derivation.