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I understan that with modal phonation the glottal wave has a triangular shape, whereas with breathy voice, the source wave is closer to a sine wave. This means that the higher harmonics are more prominent.

Are there any other crucial differences between these glottal airflow functions?

Forgive me my elementary understanding of articulatory phonetics!

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Besides the difference in the overall amplitude profiles of the harmonics, breathiness can be correlated with cycle to cycle irregularity in period and amplitude. I find it easiest to conceptualize this with constructed waves. In the first case, modal voice would be a more-triangular wave where each cycle has the same duration, and breathy voice would be a more-sinusoidal wave where the duration of cycles varied randomly. (Though not too great a variation, otherwise you add the building blocks of creakiness). This variation is referred to as jitter. The second is turbulent noise (added amplitude at random frequencies), hypothesized to come from greater airflow though the glottis -- also known as shimmer. One other measurable difference is RMS amplitude, where breathy voicing is associated with lower amplitude. However, I think that is a consequence of the basic sine / triangle glottal wave distinction, and not an independent fact.

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