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You may also find this to be interesting - children from various cultures all around the world tend to sing that syllable in pairs, and always on the same pitches! The basic pitches - nya nya - are put together in a descending minor third. The first pitch is high and the second pitch is always a minor third lower (for example, the pitches "C" and "A"). There can be several syllables strung together - nya nya nya nya - but they are always sung in the same repetitive descending minor third. This interval tends to be the most universal musical interval to children of all cultures around the world, and its easy to sing because it doesn't contain a half step. Musicologists agree that the basis for most music in worldwide culture is that universal descending minor third.
The song "Rain Rain Go Away" contains the same interval, if you need a comparison. Also, the basketball chant "Air-ball! Air-ball!" is always chanted on the same descending minor third interval as "nya nya."
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