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Background-Explanation: A sound can be described by a list of articulatory features: If the list is sufficient to determine the function of the sound in a particular language, it matches the requirement of phonology, that means not a specific sound has been described, but a class of sounds that fullfill this function, though not identical. For instance, /a/ read by child, male, woman, man with a sorethroat, dwarf, giant etc. is nevertheless recognized as this particular vocal described by a few features (like: openness, nasality vs. orality, position of the root of the tongue etc.)

All features that are of no importance for describing a sounds function in a language are called redundant features. But exactly some of those redundant features are characteristic to describe the persons characteristical voice.

Just imagine, you could by a list of such redundant features capture a voice that could be described as "sounds like Barack Obama", "sounds like Nick Nolte", "sounds like Dave Chapelle", or less specific "sounds like a middle aged, tall white man from the south with a high testosterone level and missing upper front teeth".

Question: What are, or what are possible canditates for these redundant features to describe a sound more characteristically than in phonology?

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To achieve the level of specificity you desire, you'd have to dispense with abstract, high-level features and instead make use of acoustic parameters such as fundamental frequency, formant values, bandwidths, and noise frequency values (if there are consonants involved).

Using your example of just an [a] vowel:

  • The size of the person's throat would affect the relative magnitudes of the formant values, with larger throats (adults as opposed to children, men as opposed to women) corresponding to lower formant values.

  • Older speakers might have more breathiness (more aperiodic noise and less periodic voicing exciting higher formants) and more creakiness (pairs of "double" glottal pulses or less regular cycles of pulses) in their voices.

  • Someone with a more nasal voice quality might have a broader first formant bandwidth.

And so on.

Check out my answer to this related question about voice recognition for more examples.

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In phonology, "feature" is not the same as "property", so no "feature" would be relevant in distinguishing Barack Obama's voice from George W. Bush's. Also, features are not necessarily based on articulation (muscle-movement). Individual voice quality is a consequence of individual differences in physiology (vocal tract length, vocal fold anatomy), individual differences in acoustic goal (i.e. in producing [ɪ], the mental construct that individuals strive for is not the same), and individual differences in articulatory plan (people also walk differently). Constructing a theory of the mechanisms underlying an sound wave is vastly more complex than constructing a theory of the acoustics of a sound wave.

The best way to start would be to focus on one acoustic property and measure that property for a wide range of speakers (preferably constraining dialect, e.g. to "Southern California English"); you could look at age, sex and some measure of speaker size, also social properties like education level, race, gender-identification, income etc. and see if there the data can be sorted according to those factors.

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