N.B. The email exchange below may have been edited, e.g. to remove content not essential to the main point(s) or to standardize English spelling/grammar.
...How was the cuneiform script deciphered?
Dear Mr. B. P.,
It was very good to hear from you, and to learn that you are finding the website of value.
I'll try to summarize the way in which the cuneiform script was deciphered. In a sense, it was done through guess work; by a somewhat more favorable description it was done by methods comparable to those in archeology.
You know that copies of the inscriptions were being brought to Europe at the end of the 18th century, more in the 19th, and that various scholars tried to read them. It was clear that Persepolis inscriptions were written in three types of cuneiform. The simplest type was found to have 42 signs. So specialists like Grotefend set out to try to read it.
From patterning of the signs they decided that, at the beginning of the inscriptions, there were repeated combinations of symbols that were partially the same. On the basis of knowledge of forms of reference to rulers in the Middle East, they decided that these combinations meant 'king of kings'.
They also knew the names of the great Persian rulers, Hystaspes, Darius, Xerxes. They then assumed that the inscriptions would begin with a sequence like "Darius, king of kings...son of Hystaspes...," "Xerxes..."
As you have noted, they first assumed that the cuneiform signs coresponded to letters. In time, comparing the Sanskrit syllabary, they found that correspondence to syllables would be more accurate. So they proposed these for the inscriptions that had only 42 signs, and then moved from the signs in the sequences like that cited above to determine the value of the other signs, and thus identified that inscription as Old Persian. They enlarged the number of identified signs in the two other inscriptions as at Behistun, and in this way identified the other two languages, finding that the inscription with the largest number of different signs was Babylonian. Gradually identifying all the signs in it provided access to all the cuneiform tablets and inscriptions, and full knowledge of the cuneiform system of writing was obtained.
With best wishes, W. P. L.