Which is correct: synced or synched? Is one of these American and the other British spelling or are they interchangeable?
I have only ever seen sync used in the computing industry.
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The Corpus of Contemporary American English has 30 incidences of synced and 14 of synched. Over half of the incidences of synced are from the magazine PC World, though. Synced does appear to be most commonly used in computing contexts.
Synched is more popular than synced for both American and British English, but the gap is closer in British English.
I've seen both used in the computer industry. The common and my preferred way of abbreviating synchronous is sync, rather than synch, partly because it makes more sense to pronounce it as sink than sinch and the shorter abbreviation is simpler and clearer. Also to avoid any confusion with the slang word cinch (pronounced sinch).
For similar reasons and consistency, I'd recommend synced over synched and async over asynch.
You'll also save ink and disk space.
Merriam-Webster on 'sync' versus 'synch'
In the United States, many publications (including PC World, which nohat specifically mentions in his answer) use Merriam-Webster's Collegiate Dictionary as their default guide to spelling words, and the historical preference of Merriam-Webster for sync over synch goes back very far—certainly to an era before personal computers.
The first time sync/synch shows up in the Collegiate Dictionary series in in the Sixth Edition (1949). Here is the relevant entry:
sync, n. & v. Also synch. Motion Pictures & Television. Short for SYNCHRONIZATION, SYNCHRONIZE.
This brief entry tells us that from 1949, when sync/synch first became common enough to merit (in the eyes of Merriam-Webster's lexicographers) an entry in the Collegiate Dictionary series, the publisher viewed sync as the more common spelling of the word. The entry also tells us that the original preference for sync probably arose in the film and television industry, a field where the fact that the ch in synchronize can be traced to the chi (χ) in chronos (χρονος) was probably not of widespread interest or concern.
The Seventh Collegiate (1963) dispenses with the -ch spelling altogether:
1sync n : SYNCHRONIZATION, SYNCHRONISM —sync adj
2sync vb synced syncing : SYNCHRONIZE
The spelling synch makes a comeback in the Eighth Collegiate (1973):
1sync also synch n : SYNCHRONIZATION, SYNCHRONISM —sync adj
2sync also synch vt synced also synched syncing also synching : SYNCHRONIZE
The Ninth (1983), Tenth (1993), and Eleventh (2003) Collegiates have retained the skeleton of the entries from the Eighth Collegiate, but they have added a couple of examples of sync as a noun, and they report that sync as a noun dates to 1929 and sync as a verb to 1945.
As this chronology demonstrates, for the past 57 years, Merriam-Webster's Collegiate Dictionary has always expressed a preference for sync over synch as the primary spelling of this truncated word—and for the period 1963–1972, it didn't include synch as even a variant spelling.
Ngram charts of 'sync' versus 'synch' and 'synced' versus 'synched'
In his answer, Hugo provides Ngram charts of relative frequency of use of synced and synched in American English and in British English for the period 1960–2000. These are interesting charts, but they don't reflect a rather significant difference in frequency of use between sync and synch. Here is the chart I got for sync (blue line) versus synch (red line) for the period 1900–2008, with no year-to-year smoothing and no distinction between British English and U.S. English sources:
And here is the corresponding Ngram chart for synced (blue line) versus synched for the same period with the same conditions:
The rather startling thing here is the difference between the results for sync/synch (where sync has a huge advantage in frequency of usage over synch) and synced/synched (where between 1989 and 2005 synched was the more common form).
On this record it appears that people are far more likely to choose sync over synch than to choose synced over synched. Nevertheless, in the most recent years for which Ngram offers graph data (2006–2008), synced appears to have moved ahead of synched in overall frequency, too.
Returning briefly to nohat's remarks about PC World magazine, I observe that PC World began publication in 1983, well into the era of Merriam-Webster's express preference for sync (and synced) over synch (and synched). When I started working at PC World in 1995, I tried to use the spelling synch—because of the ancient Greek single letter (χ) for ch, obviously—and I was told that house style was sync, synced, syncing because Merriam-Webster recommended it. Case closed. Under the circumstances, it's surprising that synched has done as well as it has against synced, especially when you consider how thoroughly sync has dominated synch during the same period.
I have several computer-savvy friends, and they use the word a lot. I have only ever seen synced.
Looking at the Ngram of "synced" vs. "synched", I see that since the widespread use of computers, "synched" is becoming more popular. However, the spellchecker on this site does not recognize "synched", and Dictionary.com does not help with the past tense form of "sync". So make of that what you will.
I'm a longtime American IT executive, not a linguist, but I see both variations in IT:
In the Roman Alphabet, the voiceless velar fricative is represented by the ch digraph. However, most words containing a voiceless velar fricative in borrowee language have the voiceless velar fricative coverted into a voiceless velar plosive, due to English-speakers' traditional inability to voice the appropriate pronunciation.
Thus, in the english language,because the H in Synchronise no longer serves a purpose at all (the ch digraph being converted into a sound that can be represented solely by C), Sync would be more correct that Synch would if you're following the rules established in the English language.
The grammar rule which has applied to words ending with the letter C states the addition of the K, as in picnicked, shellacked, tarmacked, mimicked, zincked, etc. While we're talking about the abbreviations of synchronize which allow sync or synch, the version we choose determines what is proper. Ultimately, this is a decision between synched (which I would discourage, but that's just my opinion) or syncked, never synced.