An idea from XKCD

[alice]

Get cracking, conlangers!

[bradrn]

Get cracking, conlangers!

Easy. Just vary the third formant!

[WeepingElf]

Of course, the human vowel space does have a third dimension - lip rounding. For a particularly illustrative example, see the famous Turkish vowel cube.

[bradrn]

Of course, the human vowel space does have a third dimension - lip rounding. For a particularly illustrative example, see the famous Turkish vowel cube.

Phonetically at least, I’m inclined to disagree with this view — see https://www.englishspeechservices.com/b ... wel-space/ for some interesting details.

[Travis B.]

Of course, the human vowel space does have a third dimension - lip rounding. For a particularly illustrative example, see the famous Turkish vowel cube.

Phonetically at least, I’m inclined to disagree with this view — see https://www.englishspeechservices.com/b ... wel-space/ for some interesting details.

The problem with this idea is what about central vowels — if rounded front vowels and unrounded back vowels are simply more central than their unrounded front and rounded back counterparts, how do we handle distinctions such as beween [ɨ] and [ʉ]?

[linguistcat]

Also this said extend it along the imaginary axis so we obviously have to multiply by /i/.

[alice]

Also this said extend it along the imaginary axis so we obviously have to multiply by /i/.

Or /j/ if you're an electrical engineer, for example, or a Python programmer.

[Travis B.]

Also this said extend it along the imaginary axis so we obviously have to multiply by /i/.

Or /j/ if you're an electrical engineer, for example, or a Python programmer.

Why Python? Using i as the first loop index variable is traditional across computing. Of course, as for j, that is traditionally used for the second, and in the case of k for the third (generally most people don't have a need for arrays/matrices larger than three dimensions).

Edit: Just checked, and Python does specifically have special syntax for representing complex numbers using j.

[bradrn]

Of course, the human vowel space does have a third dimension - lip rounding. For a particularly illustrative example, see the famous Turkish vowel cube.

Phonetically at least, I’m inclined to disagree with this view — see https://www.englishspeechservices.com/b ... wel-space/ for some interesting details.

The problem with this idea is what about central vowels — if rounded front vowels and unrounded back vowels are simply more central than their unrounded front and rounded back counterparts, how do we handle distinctions such as beween [ɨ] and [ʉ]?

In his view that’s also a centrality distinction — he sees [ɨ] and [ɯ] as the same, and [ʉ] and [ɵ] as the same. Not sure I entirely agree, but either way it’s certainly more complex than ‘lip rounding is an independent variable’.

[Travis B.]

Phonetically at least, I’m inclined to disagree with this view — see https://www.englishspeechservices.com/b ... wel-space/ for some interesting details.

The problem with this idea is what about central vowels — if rounded front vowels and unrounded back vowels are simply more central than their unrounded front and rounded back counterparts, how do we handle distinctions such as beween [ɨ] and [ʉ]?

In his view that’s also a centrality distinction — he sees [ɨ] and [ɯ] as the same, and [ʉ] and [ɵ] as the same. Not sure I entirely agree, but either way it’s certainly more complex than ‘lip rounding is an independent variable’.

From my own personal experience, central vowels definitely have a rounding distinction, in that I can distinguish [ɘ], the usual realization of /ɪ/ not before /r/, and [ɵ], a common realization of /oʊ̯/ adjacent to coronals, despite the fact that they are essentially on top of one another in a 2D vowel space.

[bradrn]

The problem with this idea is what about central vowels — if rounded front vowels and unrounded back vowels are simply more central than their unrounded front and rounded back counterparts, how do we handle distinctions such as beween [ɨ] and [ʉ]?

In his view that’s also a centrality distinction — he sees [ɨ] and [ɯ] as the same, and [ʉ] and [ɵ] as the same. Not sure I entirely agree, but either way it’s certainly more complex than ‘lip rounding is an independent variable’.

From my own personal experience, central vowels definitely have a rounding distinction, in that I can distinguish [ɘ], the usual realization of /ɪ/ not before /r/, and [ɵ], a common realization of /oʊ̯/ adjacent to coronals, despite the fact that they are essentially on top of one another in a 2D vowel space.

But the question is— are they on top of each other, really? The only really sensible way to define a 2D vowel space is via formants (it is well-known that tongue position doesn’t give anything sensible in this respect), and formant-wise those vowels aren’t on top of each other at all.

[Travis B.]

In his view that’s also a centrality distinction — he sees [ɨ] and [ɯ] as the same, and [ʉ] and [ɵ] as the same. Not sure I entirely agree, but either way it’s certainly more complex than ‘lip rounding is an independent variable’.

From my own personal experience, central vowels definitely have a rounding distinction, in that I can distinguish [ɘ], the usual realization of /ɪ/ not before /r/, and [ɵ], a common realization of /oʊ̯/ adjacent to coronals, despite the fact that they are essentially on top of one another in a 2D vowel space.

But the question is— are they on top of each other, really? The only really sensible way to define a 2D vowel space is via formants (it is well-known that tongue position doesn’t give anything sensible in this respect), and formant-wise those vowels aren’t on top of each other at all.

Somehow this feels like the argument that [i] and [j], and [u] and [w], cannot be different because the theory says they cannot be, despite that plenty of people can distinguish [iː] and [ji], and [uː] and [wu]. In this case my [ɘ] and [ɵ] are pronounced essentially identically except that my lips are unrounded for the former and rounded for the latter. Saying that the formants say this cannot be so reflects rather a limitation of relying on two formants to define vowel space. If anything, this points at that a third dimension is needed, i.e. better analysis is needed rather than simply trying to deny reality on the basis of that the theory says that it must be so.

[zompist]

Of course, the human vowel space does have a third dimension - lip rounding. For a particularly illustrative example, see the famous Turkish vowel cube.

Phonetically at least, I’m inclined to disagree with this view — see https://www.englishspeechservices.com/b ... wel-space/ for some interesting details.

I find Lindsey's page very interesting, but also rather eccentric. The focus on acoustic phonetics is great, and I agree that statements about formants are
more easily testable, and lead to more interesting analyses, than talking about tongue positions. But we mostly start with articulatory phonetics for a reason... you can hardly understand phonology at all if you can't say the sounds, and speech is after all composed of both production and interpretation.

But then he wants to reduce roundedness to laxness, and that's just dead wrong. I mean, has he actually heard a rounded front vowel? A [y] is absolutely not just a laxed [i]. Laxness is very important in talking about English phonology-- see Labov-- and it just confuses things to pretend that it's the same as roundedness.

(He's right that in acoustic phonetics the concept can't be "roundedness" but something else, but he sure doesn't make a case that it's laxness.)

What he does with Jones' and Wells' formant diagrams is not even science; to use his own word, it's a fantasy. Again, Labov has actually done this sort of thing scientifically, and it doesn't involve taking just two speakers and their highly idealized perfect vowel; it involves looking at dozens of speakers, and dozens of instances of each vowel. Vowels are regions in the formant chart, not points. And for that matter Lindsey's chart is pure fantasy when it comes to F1: neither of the two sources shows the horizontal relationships he seems to want on his chart.

What's perhaps worth taking away from Lindsey is to discard the notion that cardinal rounded and unrounded vowels will overlap in F1/F2 formant space. I'm not sure anyone actually maintained this, because they were defined in terms of articulation, but it's implied in the standard IPA diagram.

I'm also curious if the laxness thing holds for speakers of languages where roundedness is phonemic. A few minutes Googling produced the following diagram which contrasts American learners with Parisian French (PF); note that [i ] and [y] actually overlap in the dental context. Doing similar searches for German, Turkish, and Mandarin does seem to find [y] significantly backed.

https://www.researchgate.net/figure/Aco ... 2_46146827

[bradrn]

I find Lindsey's page very interesting, but also rather eccentric. The focus on acoustic phonetics is great, and I agree that statements about formants are
more easily testable, and lead to more interesting analyses, than talking about tongue positions. But we mostly start with articulatory phonetics for a reason... you can hardly understand phonology at all if you can't say the sounds, and speech is after all composed of both production and interpretation.

I think this misses the point somewhat. At a high level, Lindsay’s thesis is that the IPA’s articulatory description of the axes of the vowel chart is actively incorrect: if you want an IPA-like vowel chart, or if you want an objective meaning for vowel symbols, you have to make it on the basis of acoustics rather than articulation, with all the logical consequences that follow. This is, as far as I can tell, uncontroversial — I recall seeing more or less the same thing in two of Ladefoged’s books (as well as the third one quoted by Lindsay), amongst other places. I agree there is definitely a place for articulatory descriptions, but no-one seems to have found any which are both successful and correct.

(The Sounds of the World’s Languages actually gives several attempts at creating a vowel chart from articulatory measurements; they look vaguely OK, but there’s many ways to do it, they’re all somewhat arbitrary choices in a way that plotting F1/F2 isn’t, and most choices seem to give fairly odd-looking charts. Oddly enough, the most principled of the articulatory attempts is also the one which makes the least sense linguistically speaking.)

But then he wants to reduce roundedness to laxness, and that's just dead wrong. I mean, has he actually heard a rounded front vowel? A [y] is absolutely not just a laxed [i]. Laxness is very important in talking about English phonology-- see Labov-- and it just confuses things to pretend that it's the same as roundedness.

(He's right that in acoustic phonetics the concept can't be "roundedness" but something else, but he sure doesn't make a case that it's laxness.)

Nowhere does he say ‘he wants to reduce roundedness to laxness’, because that is dead wrong. (He even acknowledges this: ‘F3 mak[es] a particular contribution to the auditory “rounding” of the closer front vowels’.) His point is the same as your parenthetical: if we’re working acoustically, which we have to do for the already-mentioned reasons, then it’s nonsense to talk about a ‘roundedness’ distinction at every single point, because it’s more complicated than that.

What he does with Jones' and Wells' formant diagrams is not even science; to use his own word, it's a fantasy. Again, Labov has actually done this sort of thing scientifically, and it doesn't involve taking just two speakers and their highly idealized perfect vowel; it involves looking at dozens of speakers, and dozens of instances of each vowel. Vowels are regions in the formant chart, not points.

Problem is, this is meant to be highly idealised. I find Lindsay’s reasoning around this very convincing: ‘higher-quality, genuinely natural-sounding syntheses could be produced … providing standardized objective reference vowels … such reference vowels could replace the inevitably variable vowel demonstrations which have been recorded by different phoneticians from Jones onwards’. As useful as it is to figure out how native speakers pronounce vowels naturally, it would also be useful for both teaching and research to create some reference points in the vowel space. For one thing, this would let us actually transcribe speech consistently, which no-one has yet seemed to figure out how to do with regards to vowels. (We can’t even seem to agree on what exactly e.g. [ɯ] is, let alone [ɒ] or [a]…)

And for that matter Lindsey's chart is pure fantasy when it comes to F1: neither of the two sources shows the horizontal relationships he seems to want on his chart.

Admittedly, it gets better when you average them, as he does. I suppose the question now is if this is the right thing to do or not, though given the pursuit of reference points in the vowel space I’d argue it’s no worse than any other approach.

What's perhaps worth taking away from Lindsey is to discard the notion that cardinal rounded and unrounded vowels will overlap in F1/F2 formant space. I'm not sure anyone actually maintained this, because they were defined in terms of articulation, but it's implied in the standard IPA diagram.

Also that the definitions of the two axes of the vowel space given by the IPA are incorrect; that the vowel chart is a triangle rather than a trapezoid, with e.g. [a] neither front nor back; and that the usual vowel samples are too variable to act as objective reference points for defining vowel symbols.

I'm also curious if the laxness thing holds for speakers of languages where roundedness is phonemic. A few minutes Googling produced the following diagram which contrasts American learners with Parisian French (PF); note that [i ] and [y] actually overlap in the dental context. Doing similar searches for German, Turkish, and Mandarin does seem to find [y] significantly backed.

https://www.researchgate.net/figure/Aco ... 2_46146827

This is quite interesting; I wouldn’t be surprised to learn that many languages’ /y/ is actually more like [ʉ]. But that’s more or less irrelevant to defining the meaning of the cardinal vowel ⟨y⟩ in and of itself, which is the sort of thing the post attempts to do.

[bradrn]

From my own personal experience, central vowels definitely have a rounding distinction, in that I can distinguish [ɘ], the usual realization of /ɪ/ not before /r/, and [ɵ], a common realization of /oʊ̯/ adjacent to coronals, despite the fact that they are essentially on top of one another in a 2D vowel space.

But the question is— are they on top of each other, really? The only really sensible way to define a 2D vowel space is via formants (it is well-known that tongue position doesn’t give anything sensible in this respect), and formant-wise those vowels aren’t on top of each other at all.

Somehow this feels like the argument that [i] and [j], and [u] and [w], cannot be different because the theory says they cannot be, despite that plenty of people can distinguish [iː] and [ji], and [uː] and [wu].

This one is a completely different issue, because it’s not related to theory at all. There’s no theory telling us that [ji wu] are undistinguishable from [iː uː]; rather, the equivalence of the two follows directly from how the IPA defines those phonetic symbols, which is that [j w] := [ĭ ŭ].

(Though note that /ji wu/ are entirely different; you can define /j w i u/ however you want, because those ones are arbitrary symbols.)

In this case my [ɘ] and [ɵ] are pronounced essentially identically except that my lips are unrounded for the former and rounded for the latter. Saying that the formants say this cannot be so reflects rather a limitation of relying on two formants to define vowel space. If anything, this points at that a third dimension is needed, i.e. better analysis is needed rather than simply trying to deny reality on the basis of that the theory says that it must be so.

This, on the other hand, is a fair point: the theory that vowels are completely described by F1/F2 is wrong, since a third dimension is needed. Luckily, Lindsay agrees with you: ‘F3 mak[es] a particular contribution to the auditory “rounding” of the closer front vowels’.

(Though I feel the need to point out that your logic here is nonetheless wrong. How do you know that the lip-rounding requires a third dimension to describe? Acoustically, it may well be the case that we can find two dimensions which describe all vowels precisely, including rounding, though in this case that turns out to be wrong.)

[foxcatdog]

Lowered F3 is characteristic of Rhotic vowels (coming from the sounds of the worlds languages via wikipedia). Ever felt unhinged around americans or the chinese? Now you know why they are literally extradimensional beings.

[Travis B.]

Somehow this feels like the argument that [i] and [j], and [u] and [w], cannot be different because the theory says they cannot be, despite that plenty of people can distinguish [iː] and [ji], and [uː] and [wu].

This one is a completely different issue, because it’s not related to theory at all. There’s no theory telling us that [ji wu] are undistinguishable from [iː uː]; rather, the equivalence of the two follows directly from how the IPA defines those phonetic symbols, which is that [j w] := [ĭ ŭ].

(Though note that /ji wu/ are entirely different; you can define /j w i u/ however you want, because those ones are arbitrary symbols.)

The big issue with these is that IPA declares that semivowels are exactly equivalent to high vowels, whereas in reality what we call semivowels are often closer than the highest high vowels, but at the same time are not fricatives either.

In this case my [ɘ] and [ɵ] are pronounced essentially identically except that my lips are unrounded for the former and rounded for the latter. Saying that the formants say this cannot be so reflects rather a limitation of relying on two formants to define vowel space. If anything, this points at that a third dimension is needed, i.e. better analysis is needed rather than simply trying to deny reality on the basis of that the theory says that it must be so.

This, on the other hand, is a fair point: the theory that vowels are completely described by F1/F2 is wrong, since a third dimension is needed. Luckily, Lindsay agrees with you: ‘F3 mak[es] a particular contribution to the auditory “rounding” of the closer front vowels’.

(Though I feel the need to point out that your logic here is nonetheless wrong. How do you know that the lip-rounding requires a third dimension to describe? Acoustically, it may well be the case that we can find two dimensions which describe all vowels precisely, including rounding, though in this case that turns out to be wrong.)

The problem with trying to fit rounding into a 2D scheme is that the vowel spaces defined with and without rounding significantly overlap in reality, so to organize a 2D scheme that would take rounding into account would have to have some sort of nonsensical reorganization of the vowel space to fit both in without overlapping or would have to deny the reality that there are many POA's where both unrounded and rounded counterparts exist. The scheme in the page you linked me seems to do the latter, by insisting effectively that all more centralized front vowels are rounded and all more centralized back vowels are unrounded, something I know to be untrue.

[zompist]

At a high level, Lindsay’s thesis is that the IPA’s articulatory description of the axes of the vowel chart is actively incorrect: if you want an IPA-like vowel chart, or if you want an objective meaning for vowel symbols, you have to make it on the basis of acoustics rather than articulation, with all the logical consequences that follow.

I think F1/F2 formant charts are neat, match linguists' ideas neatly, and are easy to produce. But to say that they are more "objective" is to say that we should, like the drunk man, look for his lost car keys under the streetlight because that's where the light is. We shouldn't ignore articulatory phonetics just because it's harder.

I haven't read Ladefoged but I'll have to!

Nowhere does he say ‘he wants to reduce roundedness to laxness’, because that is dead wrong. (He even acknowledges this: ‘F3 mak[es] a particular contribution to the auditory “rounding” of the closer front vowels’.) His point is the same as your parenthetical: if we’re working acoustically, which we have to do for the already-mentioned reasons, then it’s nonsense to talk about a ‘roundedness’ distinction at every single point, because it’s more complicated than that.

Sure, which means that we shouldn't pretend it's less complicated than that. If F3 is what we need, then we need a way to indicate that third dimension, at least when discussing languages where roundedness is phonemic.

I think you and Lindsey are getting seduced by the (admitted!) neatness of F1/F2 diagrams. If only they'd cover everything! But they don't... except as it happens they work pretty well for English.

such reference vowels could replace the inevitably variable vowel demonstrations which have been recorded by different phoneticians from Jones onwards’.

Who needs reference vowels? Do we still need to define the meter as the distance between two marks on a platinum-iridium bar in Paris?

Reference vowels were needed when acoustic phonetics was not readily available, and honestly the method of "learn the method from Daniel Jones or, now that he's dead half a century, from someone who learned it from someone who learned it from him" was never more than a stopgap. I'm not sure that the notion of a standard [e] is even needed, but if it is, define it as an F1/F2 pair.

Also that the definitions of the two axes of the vowel space given by the IPA are incorrect; that the vowel chart is a triangle rather than a trapezoid

I'll grant you that one, because Labov prefers a triangle... though one with rounded corners, which better emphasizes that phonemes are regions not points. Glancing through his book, I'd also note that an actual speaker's vowel diagrams will not look very ideal at all. And some do look trapezoidal: there is often a distinction between two low vowels.

[bradrn]

At a high level, Lindsay’s thesis is that the IPA’s articulatory description of the axes of the vowel chart is actively incorrect: if you want an IPA-like vowel chart, or if you want an objective meaning for vowel symbols, you have to make it on the basis of acoustics rather than articulation, with all the logical consequences that follow.

I think F1/F2 formant charts are neat, match linguists' ideas neatly, and are easy to produce. But to say that they are more "objective" is to say that we should, like the drunk man, look for his lost car keys under the streetlight because that's where the light is. We shouldn't ignore articulatory phonetics just because it's harder.

Well, what I was calling ‘objective’ was the wanted meaning for vowel symbols, not the vowel chart itself. (And we do surely want vowel symbols to have an objective meaning, right?) But other than that, I can agree with your comments.

I haven't read Ladefoged but I'll have to!

You really should! His books are consistently excellent.

Nowhere does he say ‘he wants to reduce roundedness to laxness’, because that is dead wrong. (He even acknowledges this: ‘F3 mak[es] a particular contribution to the auditory “rounding” of the closer front vowels’.) His point is the same as your parenthetical: if we’re working acoustically, which we have to do for the already-mentioned reasons, then it’s nonsense to talk about a ‘roundedness’ distinction at every single point, because it’s more complicated than that.

Sure, which means that we shouldn't pretend it's less complicated than that. If F3 is what we need, then we need a way to indicate that third dimension, at least when discussing languages where roundedness is phonemic.

I think you and Lindsey are getting seduced by the (admitted!) neatness of F1/F2 diagrams. If only they'd cover everything! But they don't... except as it happens they work pretty well for English.

This is fair too. But I think F1/F2 really is mostly sufficient… actually, it would be interesting to study the correlation of F3 with F1/F2. It might turn up a few surprises.

(As it happens, I didn’t actually know these charts worked well for English. I got the impression they were best with the simpler vowel systems.)

such reference vowels could replace the inevitably variable vowel demonstrations which have been recorded by different phoneticians from Jones onwards’.

Who needs reference vowels? Do we still need to define the meter as the distance between two marks on a platinum-iridium bar in Paris?

Reference vowels were needed when acoustic phonetics was not readily available, and honestly the method of "learn the method from Daniel Jones or, now that he's dead half a century, from someone who learned it from someone who learned it from him" was never more than a stopgap. I'm not sure that the notion of a standard [e] is even needed, but if it is, define it as an F1/F2 pair.

This is just a restatement of the quote! He (and I) were indeed advocating the definition of ‘reference vowels’ by means of F1/F2 pairs — well, F1/F2/F3 triplets, really.

As for whether it’s needed, I’d say it really is. As I said, no-one seems to agree on the exact meaning of any of the symbols, and that’s a real problem in narrow (and even broad) phonetic transcription.

Glancing through his book, I'd also note that an actual speaker's vowel diagrams will not look very ideal at all.

Of course; I never said they would be ideal. The vowel diagrams in Lindsay’s post, as you noted, look very non-ideal indeed!

And some do look trapezoidal: there is often a distinction between two low vowels.

Indeed, though I note these are transcribed as /æ ɑ/ mysteriously often… in fact, those vowel systems often have no /a/ in sight.

[zompist]

(As it happens, I didn’t actually know these charts worked well for English. I got the impression they were best with the simpler vowel systems.)

Well, we don't have roundedness as a parameter.* We make extensive use of laxness and diphthongs (which are really vectors in formant space: onset > offset).

When I refer to Labov here, I'm mostly referring to Principles of Linguistic Change: Internal Factors (1994). It's big and dry, but it's packed with data. He refers to laxness to solve a couple of old puzzles in historical linguistics (for English and some other languages). To over-summarize, tense vowels can be seen as the outer perimeter of the triangle, and lax vowels a track just inside that area, and vowels can move along either track, neatly avoiding each other. (The puzzles came in that earlier studies had vowels in about the same place at the same time, so it was not at all clear how they could re-separate later.)

It wouldn't surprise me at all if the same sort of thing can happen with roundedness, but you'd need a different sort of chart to handle that.

* I've heard rounded vowels in English, but so far as I know they're incidental, not contrastive.

As for whether it’s needed, I’d say it really is. As I said, no-one seems to agree on the exact meaning of any of the symbols, and that’s a real problem in narrow (and even broad) phonetic transcription.

Isn't there general agreement that [i] and [u] are as high and [a] as low as you can manage, while [i] is as front as possible and [u] as back as possible? I realize I'm using articulatory terms, but I do so because that's where the constraints lie. So far as I know a higher-F2 [i] could be generated, just not by a human.

If the IPA wanted to define [e] and [ɛ], I'd say picking an F1/F2 pair would work fine— it would be arbitrary, but so is "whatever Daniel Jones said was a CV".

Still, we should avoid taking the log(F1) dimension too literally. There's a whole domain, psychophysics, which studies the relationships between physical inputs and sensory reports. We could define [e] and [ɛ] at even steps between [i] and [a], but it's an empirical question whether they would sound like they're at even steps. And it's yet another empirical question whether those points correlate well with the median [e/ɛ] heard in languages with four level divisions.