The most prominent acoustic features in speech are intensity modulations, represented by the amplitude envelope of speech. Synchronization of neural activity with these modulations supports speech comprehension. As the acoustic modulation of speech is related to the production of syllables, investigations of neural speech tracking commonly do not distinguish between lower-level acoustic (envelope modulation) and higher-level linguistic (syllable rate) information. Here we manipulated speech intelligibility using noise-vocoded speech and investigated the spectral dynamics of neural speech processing, across two studies at cortical and subcortical levels of the auditory hierarchy, using magnetoencephalography. Overall, cortical regions mostly track the syllable rate, whereas subcortical regions track the acoustic envelope. Furthermore, with less intelligible speech, tracking of the modulation rate becomes more dominant. Our study highlights the importance of distinguishing between envelope modulation and syllable rate and provides novel possibilities to better understand differences between auditory processing and speech/language processing disorders.