I was wondering whether there is any practical way to tell whether differences in formant intensity are due to different harmonics in the source or different formants in the filter. Is there any data out there on what the actual harmonics are? I know that for an ideal string, they are integer multiples of the fundamental frequency, but the vocal cords are not ideal strings. Can anyone point me to any research on what the actual series of harmonics is, and what affects it?
One factor influencing intensity is subglottal pressure, which is immaterial at the segmental level (you can say a word or phrase loudly that way, but you can't limit the increased loudness to a phoneme). The second pertains to the shape of the glottal source wave, and people studying linguistic phonation types focus on that. There are various languages (Hmong-Mien, Western Nilotic, Otomanguean, San) with distinctive breathiness and creakiness associated with vowel. The overall production picture is that with creaky voicing, the vocal folds remain in contact for the longest time and with breathy voice, they are in contact the shortest time. At the breathy end of the phonatory continuum, most of the acoustic energy is in the fundamental, so H0 is high and subsequent harmonics fall off rapidly. At the creaky end of the continuum, energy falls off more gradually. Therefore one classic acoustic diagnosis of phonatory difference is to compare harmonic intensity, for example comparing the first two harmonics. The intensity difference H2-F0 would be in the direction of a large negative number for breathy, and in the direction of a positive number for creaky. One problem that has to be controlled is the interaction between phonation and formants: you need to look at vowels where H2 is further from a formant peak (so, not a high vowel). There is an extensive literature from UCLA looking at how to quantify breathiness: measures have included F0-H2, F0-F1 and H0-F2. The point is that if the upper harmonics are low amplitude compared to the fundamental, this points to the glottal source.
Vocal tract resonances also affect measured amplitude of harmonics. Those resonances (formants) are not precise-frequency "all or nothing" filters, they have a bandwidth where intensity is highest at the resonance frequency, and is a bit lower a bit away from that frequency etc. A narrow bandwidth concentrates most of the energy at that frequency, and a broad bandwidth means the energy is spread out more. Bandwidth is one of the things that you can get in Praat from LPC formant analysis.
The basic idea behind analysis of the glottal source is that the source is "caused" by glottal airflow (which is determined by glottal opening). This page from Praat may help make this clearer.