Formant frequencies of consonants

Question

In the old days, phones were defined by the requisite articulation, both consonants and vowels. As time wore on and science and technology advanced, vowels became better defined by their acoustic properties, specifically the relationship between the 1st and 2nd formants, which now defines the ubiquitous vowel trapezoid, and that the 3rd, 4th and 5th formants contribute somewhat inelegantly to things like rounding, rhoticity and nasalization.

However, I haven't heard much of anything of the sort for consonants. I know that fricatives are defined by turbulent airflow, and thus have a "noisy" timbre, and there is a somewhat controversial claim that "rhotics have a lowered 3rd formant" (although that might only apply to vowels), but that's about it.

Do consonants have an acoustic definition analogous to vowels? And if so, what is it?

Answer 1

Unfortunately, the answer is no.

The space of vowels is continuous: given any two vowels, you can find a midpoint between them, and that's also a perfectly valid vowel that people can pronounce.

But for consonants, that doesn't work. What would be the average of a bilabial plosive and a labiodental nasal, for example? There's no real point of articulation you can use in between bilabial and labiodental, and it's not clear what a "half-nasal stop" would sound like.

There are acoustic definitions for certain types of consonants:

• Plosives, for example, are defined by a period of complete silence, and by how they "bend" the vowels around them. Labials "bend" vowel formants sharply downward, while uvulars "bend" them sharply upwards, and everything else is in between. (I'm sure there's a better word for this but I don't know it.)
  • Since the space of plosives between alveolar and velar is somewhat continuous, you can define these ones acoustically! But bilabials are still defined as "using both lips" because it's a discrete value: you can't be "a little bit in front of" or "a little bit behind" it.
• Voicing can be represented by "voice onset time", the time between when the airflow starts and when the voicing starts. This is negative for voiced plosives, near-zero for voiceless, and positive for aspirated.
• Voiceless fricatives don't really have formants per se, since they're made of noise instead of a periodic signal, but they do show spectral "bands" that can be measured. "Sibilant" fricatives are the ones with a bunch of extra noise in the upper frequencies.
• Nasals and approximants do, technically, have formants. But they're complicated and you have to look for "anti-formants" too. In practice, I don't think there's any reliable way to use these yet.

However, these don't really generalize. In other words, we can define coronal plosives by their acoustic properties, or plosive voicing, but there's no Grand Unified Theory of Consonants yet. (Or even a Grand Unified Theory of Plosives, for that matter.)

Answer 2

All segments were given an acoustic definition in the feature theories of Jakobson, Fant & Halle (1951) and Jakobson & Halle (1956). Many of the features were passed down to Chomsky & Halle (1968) where the definitions were supplemented with an articulatory definition. This table compares the articulatory and acoustic definitions of the J&H features, for example "consonantal" being "Low total energy" vs "Obstruction in vocal tract". The surmountable difficulty is figuring out what "compact" refers to. JFH say

Compact phonemes are characterized by the relative predominance of one centrally located formant region (or formant). They are opposed to diffuse phonemes in which one or more non-central formants or formant regions predominate...

In the case of the vowels this feature manifests itself primarily by the position of the first formant (11): when the latter is higher (i.e. closer to the third and higher formants), the phoneme is more compact. The closer the first formant is to the upper formants, the higher will be the intensity level of the region above the first formant, especially the level between peaks.

In the consonants, compactness is displayed by a predominant formant region, centrally located, as opposed to phonemes in which a non-central region predominates; (cf. Fant's analysis of Swedish stops (3)). The compact nasals have a dominant formant region between the characteristic nasal formants (200 cps and 2500 cps), Delattre's observations on the positions of the first formant in stops and nasal consonants (12) corroborate the parallelism between the compactness feature in vowels and consonants.

Formants are the filtering properties of a sound, defined by where the constrictions are. Both consonants and vowels have constrictions, so they have formants (well, h and ʔ don't have constrictions). However, figuring out where the formants are for a vowel is simple, not so much so for a consonant.

The distinction acute / grave applies to front / back vowels and labial/dental/velar consonants:

Acoustically this feature means the predominance of one side of the significant part of the spectrum over the other. When the lower side of the spectrum predominates, the phoneme is labeled grave; when the upper side predominates, we term the phoneme acute.

Front vowels are acute, coronal consonants are acute: this matches the more recent equation of coronal qua V-place feature with "-back".

Answer 3

Provided you understand that consonants are identified in large part by the vowel transitions before and after the articulation of the consonant itself, the very same theory of vowel quality based on cavity resonances in the mouth works also for consonants. This is called "locus theory" and has been current since forever (well, since I took my first course in acoustic phonetics back in 1966 from Ilse Lehiste).