Lo siento, yo no hablo español.
The name of this organisation is Sociedad Argentina de Autores y Compositores de Música.
So why the acronym SADAIC and not SADAYC?
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Acronyms in Spanish should normally include just the primary words (excluding prepositions like de or en), for which we'd presume the acronym SAACM. Not the most pronunciable thing, the two options would be either spelling out the letters as /esja:θe:me/ which might just be heard read back as SACM, or reading it out which is tough given the -cm.
So by adding the -d- and -y-, you get something a bit more pronounceable, except for the -m: SADAYCM: /sadaik/ + m. Clearly they decided to just drop the M because it's a pain to say, so that gets them SADAYC.
A y is generally not allowed in the interior of a word unless between vowels (exceptions: soy/doy/voy with post-positioned object pronouns as in voyme), so they probably decided that SADAIC made more sense as its abbreviation.
Update: as angus points out, the i stays on its own syllable. Looking around online, it's common for it to be written with only an initial cap, as Sadaíc. Based on that, I'd say the use of the i is simply because up until the most recent orthography of the language, a y couldn't have an accent and obligatorily would form a diphthong with the preceding syllable. Technically, under the new orthography, they could use Sadaýc, but since they're already using it with an i, they're unlikely to change now.