What rules govern the romanisation of Greek υ

Question

English is troubled by what appears to be an unsystematic plethora of spelling rules, not to mention the rules for pronunciation. In general, there seems to be a consensus on how Greek and Latin is romanised in English, but now and then something pops up to remind us that it is not so simple. Greek κ, for instance, is often romanised as c, apparently being based on the Latin spellings. The letter υ, however, is more problematic: Mostly it is (problematically) romanised as u,¹ but in some combinations, the y is preferred, e.g.:

• words with the prefix syn-, such as syncopate
• words with μυ-, ψυ-, φυ-, such as myth (but music), psyche, physics
• words with initial hard breath followed by upsilon, such as ὑποθήκη → hypothek

But there are so many situations in which the expected romanisation of Greek → English υ → y is instead turned to υ → u, such as in αὐ to au, ευ/εῦ to eu, not to mention the standard romanisation of Greek words where English u is (to the best of my knowledge) always used, such as:

hypothec […] Origin Early 16th century from French hypothèque, via late Latin from Greek hupothēkē ‘deposit’ (from hupo ‘under’ + tithenai ‘to place’).

― Oxford Dictionary: ‘hypothec’

Thus my question: When should Greek υ be romanised as English u and y? I suspect the rule is that words that have been taken into the English language prefers y for monophthongs and u for diphthongs, whilst any romanisation of unassumed Greek words prefers u, but I am not sure this observation is correct, based on words such as music. My working hypothesis is that the following applies:

1. If a monophthong and borrowed either directly from Greek or via French, the preferred spelling during the great spelling reform was y.
2. If a diphthong, the preferred spelling was u.
3. If borrowed directly from Latin, the word having been naturalised in Latin, the preferred spelling was u.

Notes

¹ By this, I also refer to the transliteration rules that usually are followed, as per the quote, in which υ → u is the standard method.

Answer 1

English has two sets of (conflicting) rules to translitterate Greek into Latin letters:

1. The traditional way, which is that of classical Latin; it is mostly based on how the pronunciation of Greek was best rendered in Latin letters and how those were pronounced in Latin.
2. A modern, less common way, in which whatever Latin letter is chosen that developed out of the Greek letter in question (and which resembles it in minuscle (lower-case) shape).

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Greek ypsilon (capital Y, minuscle υ) was pronounced like French u in classical Greek (/y/ in the International Phonetic Alphabet). Latin did not have this vowel (neither does English, incidentally); it therefore used the Greek letter Y for that sound (Latin and Greek normally only had capitals). Our lower-case y is an adaptation of this capital letter.

• Examples: hybrid, psychology, ypsilon, cycle.

However, Latin did have vowels that strongly resembled Greek diphthongs αυ and ευ, to wit, au and eu. And so Greek AY and EY were rendered as AV and EV (Latin used V for both v and u).

(A diphthong is a vowel written in two letters, even through it is really one (complex) sound. It does not sound the way the two letters would sound separately in succession; and so, while Latin A sounded like Greek A, and Latinised Y sounded like Greek Y, the Latin sequence AY would not automatically sound like the Greek diphthong AY, whereas Latin AV would.)

• Examples: automaton, pause, eulogy, heuristic, therapeutic.

The Greek diphthong ου was apparently perceived to sound like Latin u (which sounds like German u, International Phonetic Alphabet /u/), and so OY was rendered as V.

• Examples: Thucydides, utopia.

Note that you will probably find some exceptions in classical Latin; nobody is ever consistent 100 % of the time.

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In the modern way, any Greek letter is just translitterated into whatever Latin letter developed out of it, or into that which sounds most like it in the target language. (The Latin alphabet is an adaptation of the Greek alphabet to Etruscan and other languages of Italy.) In classical Latin, c was the normal letter to render the k sound, so it was used to translitterate Greek kappa; Latin k did exist, but it was very rare. In the modern way, Latin k is used to render Greek kappa, because Latin k was originally an adaptation of Greek kappa when the Latin alphabet was developed, and because c does not always sound like k in various modern languages. The shapes of kappa and k are also almost identical. The same applies more or less to Greek υ and Latin u (although the shapes of the Greek capital Y and the modern Latin capital U are somewhat different). So any υ is rendered as u in that system.

For whatever reason this system was first used (just to easily render Greek in Latin script in case the audience couldn't read Greek, or by some authenticist movement?), it was not originally intended for creating actual words in modern languages, but only ad hoc, when indicating vaguely what an actual Greek word in Greek signified or sounded like. Nevertheless, sometimes people do create and use words so transcribed, in English and other European languages, e.g. French and Dutch. The result is the 'mess' you have observed... I believe style books always recommend the traditional system of translitteration, mainly for consistency.