[mutagen]

There are several approaches. I'm not sure what this software uses, machine translation of the site suggests samples.

Pitch shifting samples is one way to do it. A singer is recorded singing a syllable and that is shifted up or down by software. Artifacts creep in relatively quickly, especially with something as nuanced as the human voice. A variety of pitches and syllables can be sampled and the pitch shifting manually tuned to minimize audible artifacts.

Modeling could also be used, from simplistic models not far removed from the ADSR envelopes of basic synthesis to advanced physically based models. Samples and modeling could be combined to expand the palette of syllables.

Our ears and neural processing of speech and singing are finely tuned to process subtle shades of difference so any technique often sounds artificial. Fortunately this can be exploited musically and great music can be made with these 'artifical' sources.

[bdonlan]

UTAU and Vocaloid do indeed use pitch-shifted samples (UTAU even lets you build your own sample libraries). A more recent product, CeVIO, uses modeling IIRC.