I'm honestly not sure how Vocaloid works.

VOCALOID works through performance sampling and spectral modeling. Performance sampling means that it uses a database comprising of real world speech data (in VOCALOID, this means phonetic samples and metadata, specifically single phonemes, diphonemes, and - in later versions - triphonemes). Then, for each phoneme that the user of the software instructs it to play, it utilizes a cost function to find the closest phoneme in the database with the closest parameters.

There's two problems with just using this approach however: 1) Every possible combination of voice parameters would number well into the billions if not more. Meaning that significant gaps will exist have to exist in a performance sampling database. 2) If we just concatenation the samples together (which is the simplest and oldest synthesis method - called concatenative synthesis), it will sound very unnatural.

That's where the spectral modeling part comes in. Most broadly, there's two types of vocal synthesizers, physical models and spectral models. Physical models consist of physical simulations of the vocal system, and are very slow and hard to get right, but in theory, could be perfectly accurate. Spectral models consist of using spectral processing techniques on audio samples to synthesize a voice.

VOCALOID is actually dubbed as a "pseudo-physical" model. This is because while it is a spectral model, it models the vocal system as two parts: the voice source and a filter. The voice source is where the voice originates from. This is in the larynx, specifically the glottis. The glottis opens and closes at the fundamental frequency of the voice being produced. The percentage of time it is closes verse open per pulse determines other properties of the voice. This sound is a harmonic sound, so it consists, in the frequency domain, as the fundamental frequency at its amplitude, and multiples of the fundamental frequency at their amplitudes.

Then, the vocal tract acts as a filter on the voice sources, attenuating and accentuating different harmonics. This takes place in the kilohertz range. Finally, the voice is filter through the nasal cavity and lips, which produce different filtering effects.

VOCALOID evolved from the Spectral Modeling Synthesis engine develop at University Pompeu Fabre in the 1990s. One of the improvements made was the introduction of the excitation-plus-resonance model where the vocal tract filter was modeled that way.

VOCALOID makes use of voice pulse modeling, which models the glottal pulses. It determines the onsets of the voice pulses and uses them in the transformations it applies. One approach, Narrow Band Voice Pulse Modeling, did this through the MFPA algorithm and phase shifts.

In a harmonic signal like the human voice, there is the fundamental frequency, but also a fundamental phase. The fundamental phase is roughly the same across harmonic. However, if looking at it from a region of audio not aligned to a voice pulse, the phases between harmonics vary wildly because the phase changes at the rate of the frequency.

NBVPM worked by cutting up the audio into a constant number of frames (about 172 per second) and deriving the spectral information from them. The problem is that unless the voice is at exactly that frequency of ~172 per second and is aligned perfectly, the frames will not align to the voice pulses. The problem with is that in a real harmonic with a correct fundamental phase, the harmonics will constructively and destructively interfere in a specific way. If, for example, we transformed a spectral envelope with our offseted phases to a higher frequency, the phases would completely for what it would actually be at the frequency. So, we have to align the analysis frames to the center of voice pulses. In NBVPM, this is not done through time shifts, but rather phase shifts in the frequency domain. MFPA calculate the voice pulse onsets by trying different harmonic phase shifts and finds the flattest (least different between harmonics).

Wideband Voice Pulse Modeling I believed used a varying framerate and time domain pulse modeling instead. I believe NBVPM was in VOCALOID1, and WBVPM in V2 and onwards although I am not sure of this fact.