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In many chumashim a masoretic note appears at the end of Parshat Yitro which states that there are 72 verses in the sidrah. (See e.g. here)

How is this number arrived at?

By my count, if one uses ta'am tachton for the Ten Commandments there are 75 verses in the sidrah. (27 verses in Chapter 18, 25 in Chapter 19 and 23 in Chapter 20.)

If one uses ta'am elyon there seems to be only 71, as the printed ta'am elyon I found reduces the number of verses in the 10 Commandments from 13 (20:2 - 20-14) to nine.

Is it possible that there is another version of ta'am elyon that is being used to get to 72?

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This is indeed another version of the Ta'am Elyon. A nice overview is given in the Likutei He'aros Mesorah, who assumes that this happened by accident:

In Exodus, Chapter 20 contains 20 verses according to the Eastern tradition, but 22 verses according to the Western tradition . The Eastern tradition counts 10 verses in the Ten Decrees, counting one verse for each Decree, while the Western tradition counts 12 verses. Thus, according to the Eastern tradition, Exodus contains 1207 verses, and Parashath Yitrô contains 72; while according to the Western Masoretic tradition, the book contains 1209 verses and the parasha contains 74. If we consider all the different traditional verse divisions (counting a verse for every occurrence of sillûq, in both upper and lower accentuation), there are 26 verses. Many modern printed editions have 23 verses in Chapter 20, following the Western tradition except for separating the first two Decrees, which are combined in the Western tradition. The printed editions that show the upper accentuation in Yithro often count 19 verses. They mistakenly combine the first two Decrees as the Western tradition does, thus counting 9 verses in the 10 Decrees. In doing so, however, they mix the upper and lower accentuations.

Minchas Shai here quotes Chizkuni, who lists the te'amim as many chumashim have them, in an arrangement which would leave 9 pesukim in the ta'am ha'elyon according to his view. He gives the reason that it is because the first two dibros were said together, but it's possible that he is making the same mistake as the others mentioned above, and that this was simply a mix up:

גם בדברות אנכי ולא יהיה לך יש נגינה גדולה לעשותן שתיהן פסוק אחד לזכרון שבדבור אחד נאמרו, כיצד בתיבת אנכי פשטא ובתיבת אלהיך זקף קטן ובתיבת הוצאתיך תלישא ובתיבת מארץ מצרים קדמא ואזלא ובתיבת עבדים רביעי.

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There are indeed 72 verses using the Ta'am Elyon split up. I counted on Mechon Mamre.

That's 62 for the rest of the Parsha and 10 for the Ten Commandments.

(It seems you stumbled upon a mistaken rendition of the Ta'am Elyon. Until quite recently, the two sets were always written overlaid. When various people started printing them separately, they unfortunately confused which notes went where and invented a half dozen different mistaken variations. Your question is but one proof of many.)

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