I'm making a song-synthesizing software, so I built some models about human speech, and I'm testing them. But it turns out there is an obstacle. I seem to have misunderstood how vowels are rounded.

I modeled the mouth to be controlled by two factors: Compression (abbr. COM) and protrusion (abbr. PRO). These play a role when synthesizing rounded vowels, and are represented by a number from 0 to 1. The more COM is, the more the mouth closes vertically. The more PRO is, the more the mouth closes horizontally.

I recorded the "extreme" vowels, a.k.a. [a], [ɶ], [i], [y], [ɑ], [ɒ], [ɯ], and [u]. I've thought three factors, namely height (abbr. C/O; takes a number from -1 to +1), backness (abbr. B/F; takes a number from -1 to +1), and PRO, were sufficient to model them. But it failed, for apparently there were a fourth factor: COM.

So let me summarize how I'm going to refine my model. I set [ə] to be the "neutral" vowel where C/O, B/F, COM, and PRO are all zero. The followings are apparent:

  • For open vowels, the jaw opens (along with the mouth), and C/O becomes negative.

  • For closed vowels, the dorsum lifts, and C/O becomes positive.

  • The jaw-opening and the dorsum-lifting never occur simultaneously. (It's a rather awkward position)

  • For unrounded vowels, both COM and PRO are zero.

For examples:

  • For [a], C/O = -1; B/F = -1; COM = 0; PRO = 0.

  • For [e], C/O = +⅓; B/F = -1; COM = 0; PRO = 0.

  • For [i], C/O = +1; B/F = -1; COM = 0; PRO = 0.

But rounded vowels? This is where I have a confusion. As far as I've observed my own pronunciation:

  • For [u], C/O = +1; B/F = +1; COM = 1; PRO = 1.

  • For [ɶ], C/O = -1; B/F = -1; COM = 0; PRO = 1.

  • For [y], C/O = +1; B/F = -1; COM = 1; PRO = 0...?

Despite Wikipedia states that compression and protrusion are two different types of rounding, I had to model like this, because eventually I would model consonants as well. It seems feasible to model approximants like this:

  • For [β], C/O = 0; B/F = 0; COM = 1; PRO = 0.

  • For [βʷ], C/O = 0; B/F = 0; COM = 1; PRO = 1.

  • For [ʁ], C/O = 0; B/F = +1; COM = 0; PRO = 0.

  • For [ʁ̹], C/O = 0; B/F = +1; COM = 0; PRO = 1.

  • For [β͡ʁ], C/O = 0; B/F = +1; COM = 1; PRO = 0.

  • For [ʁʷ], C/O = 0; B/F = +1; COM = 1; PRO = 1.

So far, is my model, or is the analysis above, consistent with usual phonetics?

  • Not sure if I understand the question. Are you asking if a sound can be both protruded and compressed at the same time?
    – Nardog
    Dec 21, 2021 at 7:10
  • @Nardog Quite yes. Dec 21, 2021 at 7:50

1 Answer 1


Although I think it is correct to distinguish compression and protrusion, both are typically subsumed under one notion of rounding in phonetics. Therefore I would suggest discarding interest in "what most people do" in favor is "what is necessary for the sake of accuracy". It does seem to be a parameter of language variation, and is relevant to the distinction between the in-rounded and out-rounded high front vowels of Norwegian (the in-rounded vowel is also claimed to be more central).

When applied to consonants, the most obvious need for more categories is the labiovelar stop [kp] with compression, which can in fact be distinctively rounded (in Nupe). Also the phonetics of /u, w/ in Japanese is distinctly different from that of either English or French. I would not assume any automatic mapping between IPA letters and your labial constriction values, since data sources usually ignore such fine-grained details as encountered in languages. Your distinctions seem compatible with the phonetic facts, but the real test will be whether the outputs that you create empirically replicate the distinctions made in languages.

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