Very few people in the Western hemisphere pronounce Russian correctly, nor is it expected (or even appropriate) that radio announcers should do so. The intricacies of correct Russian pronunciation are often obscured in the transliteration from Cyrillic to Latin letters, nevertheless there is an accepted standard of "Americanized" Russian that is not at all difficult to grasp.
Russian is the only language frequently encountered in radio that is written originally in a different alphabet: Cyrillic. Always remember that when you read a Russian name on a CD or LP cover (unless it's the Melodiya label and you know how to read the original Cyrillic), you're reading a transliteration: the Latin letters are put together artificially to reproduce the sounds of the name. Unfortunately, different record labels sometimes follow different conventions for transliterating Russian. These conventions differ particularly according to the nationality of the people who are intended to read them.
When speakers of English transliterate Russian names into Latin letters, they usually try to produce the most logical spelling that will tell speakers of their own language how to pronounce the names correctly (or at least, passably). In these cases you need only apply the normal rules of English pronunciation, bearing a few specific rules in mind (see below), and you'll be okay. The problem is that speakers of German, French, Polish, Czech and Dutch do the same thing, for speakers of their own languages. Thus you may sometimes have to apply the rules for these languages instead. That is why you'll sometimes come across alternate spellings of any well-known Russian name. For example:
Usually you'll see the English spelling, though German spellings are also not uncommon, so don't be confused by them (i.e. DON'T EVER SAY chi-kow-skee, THAT'S NOT HIS NAME!). Other spellings are less common, but one comes across them occasionally on foreign record labels.
The following letter-sound correspondences are primarily for reading English/American transliterations of Russian. For German and other transliterations, follow the normal pronunciation rules for the appropriate language, and the hints on stress given below.
The biggest thing to watch out for is that e may be pronounced either eh or yeh depending on circumstances. This is a distinction that exists in Cyrillic spelling but is often (though not always) lost in transliteration. One must learn to recognize certain names in which e means yeh, for instance, Evgeny = yehv-gehn-ee (it's usually yeh at the beginning of a word, and also often if the e is in a stressed syllable). More examples can be found in the list of names.
There's also the distinction between e and ë: these are actually two distinct Cyrillic letters with different sounds (written the same way in both alphabets), but just to make life interesting for us the Russians often omit the umlaut, thus causing it to be omitted in the transliteration as well. This is why familiar names like Gorbachev and Khrushchev sound like they have different vowels in their last syllables than they appear to: in fact they should be spelled Gorbachëv and Khrushchëv.
|e||eh, e.g. Arensky = ah-rehn-skee; or yeh, e.g. Evgeny Onegin = yev-geh-nee oh-nyeh-gin ; or even aw, equivalent to ë, e.g. Gorbachev = Gorbachëv = gor-bah-choff|
|ë||aw or yaw, e.g. Khrushchëv = khrush-choff (the umlaut is often ommited so that ë is written e; see above)|
|i||ee or ih|
|o||oh, when stressed, otherwise aw or uh|
|u||oo, as in "root"|
|y||ee or ih|
When e follows another vowel it usually means yeh, so the combination is actually two separate vowels, not a diphthong. All other combinations are fairly self-explanatory.
|ae||ah-yeh, or iy-yeh, e.g. Nikolaev = nee-kuh-liy-yev|
|ai, ay||iy, like the word "eye"|
|ee||ay-yeh, e.g. Sergeev = sehr-gay-yev|
|ia, ie, io, iu||yah, yeh, yoh, yoo|
|oe||oy-yeh, e.g. Dostoevsky = dost-oy-yev-skee|
|ou||oo, as in "root" (occurs mainly in French spellings, e.g. Moussorgsky)|
As in German, Russian voiced stops lose their voicing at ends of syllables, which means primarily that -ov becomes -off (or -ev becomes -eff). Some transliterations reflect this and some don't: that's why Rachmaninov is sometimes spelled Rachmaninoff. Otherwise consonants are fairly straightforward.
|ch||ch, as in "church", or less frequently, kh, a light gutteral sound, only at ends of syllables, e.g. Rachmaninov = rahkh-mah-nee-noff (this is most likely a German spelling), or even less frequently, sh, in French spellings, e.g. Chaliapin = shah-lyah-pin|
|kh||kh, light gutteral sound, usually approximated as k, but technically closer to h; e.g. Irina Arkhipova = ee-ree-nah ar-khee-po-vah|
|r||r, trilled as in Italian|
|shch||sh-ch, in a single sweep; may also be described as "sh with bite!", e.g. Rodion Shchedrin = ruh-dyohn sheh-dreen|
|w||v (Russian has no w sound, w only appears as a German spelling of v)|
|zh||zh, like the s in "measure"; e.g. Gennady Rozhdestvensky = geh-nah-dee rozh-dyest-ven-skee|
Russian stress is largely unpredictable, and most famous Russian names are conventionally pronounced with the wrong stress by English speakers. Thus it's not the end of the world if you get it wrong, though some errors are less acceptable than others. If you have no idea how to accent a certain name, first try looking it up in the list of names. Otherwise, keep the following hints in mind.
You may have noticed from some of the phonetic spellings employed here that many vowels tend to become neutral uh sounds when not stressed. In general, Russian stress is very strong, to the extent that stressed syllables are pronounced very clearly in comparison with unstressed syllables, whose vowels are often glossed over and practically ignored in ordinary speech. This is not worth worrying about too much on the radio: attempts at hypercorrection can always backfire.