There must be plenty of people who, after learning to read, were left wondering why the English alphabet contains the letter C. Sometimes it functions as a K, sometimes as an S, but what's the point if those two letters also exist? Why have a letter with no independent sound of its own?
The problem lies with the Roman alphabet, of course. They got their alphabet from the Greeks, who got their writing system from the Phoenicians. The Phoenicians in turn got their writing from various predecessors. For the present I'll stick with the Phoenicians as a starting point, on the grounds that the Phoenicians used a writing system with letters that are recognisably similar to the letters that we use today. Thus, the question becomes: where did the Roman C come from?
It turns out that we should blame the Etruscans.
The Phoenician alphabet started with the letters aleph, beth, gimel, daleth, ... . The Hebrew alphabet starts pretty much the same way. In Greek it's alpha, beta, gamma, delta, ...
Notice a pattern? In the predecessors and relatives of the Latin alphabet, the third letter is used for the G sound.
It's not so surprising that two alphabets should disagree with each other. (The Arabic alphabet, for example, arranges the letters in a very different order, although it is also derived from the Phoenician alphabet.) Given any two languages, it's almost certain that there will be sounds in one language that don't occur in the other. That, by itself, ensures that their alphabets disagree. On top of that, there is a certain fuzziness about the order of the letters in the alphabet. Some letters will be missing, and others will be moved about. That's only natural. A disagreement near the beginning of the alphabet is, however, a reason for comment.
The Etruscans were one of a group of people who settled the Italian peninsula. Their language was apparently unrelated to Greek, but their alphabet was a slightly modified form of the Greek alphabet.
At that time, the Greek gamma wasn't necessarily written in the modern Greek way (Γ). It was tilted over, looking more like our modern “less than” symbol (<). It could also be written in a curved form (C). It so happened, however, that the Etruscan language did not include a sound corresponding to the English “G”. Their closest equivalent corresponded to our English sound “K”. So they used the gamma as the written equivalent of their “K” sound. The fact that the Greeks already had a symbol for the “K” sound somehow got lost along the way. To the Etruscans gamma and kappa would have sounded the same (should we call those camma and cappa?), so the kappa could be discarded.
The Romans got their writing system from the Etruscans. The Latin language, did, however, include both a “K” and “G” sound. The K sound could be represented by the < symbol, which the Romans ended up writing in its C shape. That left them with no symbol for their G sound, so a new letter had to be invented. That's why the letter G looks like a C with a bit of ornamentation on it.
The Latin alphabet also retained the Greek K, but it wasn't much used.
Versions of the Latin alphabet spread all over the Roman empire. Old English used it, with the addition of a few letters to represent sounds that weren't needed for Latin. The letter C was heavily used in Old English. The letter K was rarely used, to the point where it's often omitted from the list of letters used in Old English.
Then, many centuries later, English scholars revived the study of Roman and Greek culture. As a side-effect, many words of Latin and Greek origin were imported into English. In the words that came from Latin, the “K” sound was represented by the letter C. In the words that came from Greek, the “K” sound was represented by the letter K.
And so it has remained ever since. We still use C and K to represent the same sound. One day there'll probably be a spelling reform, but that's probably a long way in the future.
I almost forgot to mention the other sound of C. That appears to have come from a sound change in Latin, where the hard “C” sound was replaced by a softer sound when it was followed by an “i” or “e”. This was exported, as a spelling convention, to much of the rest of the Roman empire, although the exact sound of the soft C depended on the language. In English the soft C convention was used for the sound that we now write as “ch”. Since that time, however, English has imported many French words, so our present-day soft C comes from the French soft C.
Remark: the Latin “Caesar” would have been pronounced much the same as the German “Kaiser”. In fact, German borrowed that word from Latin. But that's a bad example, because in that word the “C” is not followed by an “e”. We probably started pronouncing the word with a soft C because of someone's spelling error.
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