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PostPosted: Mon Oct 26, 2015 6:34 am 
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No, I'm not attempting to overturn decades' worth of study by people vastly more qualified than myself. I'm just wondering how much merit there is in an idea I had after reading Lass's [i]Phonology[/i] and some other material on dependency phonology.

Ignoring rounded vowels for now, since I'm not sure how rounding fits into this, we start with three non-negative integral values, one for each of:

- i-quality, or high-frontness
- a-quality, or openness
- u-quality, or high-backness

implicitly treating vowel space as triangular rather than rectangular, which we justify on the grounds that triangular vowel systems are much more common.

We restrict these values such that at least one must be zero, and the sum cannot exceed 4.

So, as fundamentals, we have [i] = 400, [a] = 040, and [u] = 004; this can be extended to [e] = 310, [ɛ] = 220, [æ] = 130, [ɔ] = 022, and [o] = 013. 202 will then represent [ɨ]. Note that these all sum to 4, and are the most distinctive vowel phones. If we characterise [ə] as 000, we then have [ɪ] = 200, [ɐ] = 020, [ʊ] = 002; and [ɜ] = 110, [ɘ] probably = 210.

OK, so this is only a beginning, and it needs some tweaking to allow for rounding; but there might be something in it, assuming it hasn't been done before. It might be relevant to synaesthesia in some way, too. Any thoughts?

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Last edited by alice on Tue Oct 27, 2015 6:24 am, edited 1 time in total.

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PostPosted: Mon Oct 26, 2015 8:00 am 
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How to distinguish [a], [ʌ] and [ɑ]?


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PostPosted: Mon Oct 26, 2015 8:04 pm 
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What does this have to do with phonology? It seems to be a cipher, or a game of some kind. Real phonology is about understanding languages, and your gematria can't help with that - for instance, a phonologist cannot simply "treat vowel space as triangular rather than rectangular", because vowel space is not in fact triangular.

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PostPosted: Tue Oct 27, 2015 12:47 am 
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Salmoneus wrote:
What does this have to do with phonology? It seems to be a cipher, or a game of some kind. Real phonology is about understanding languages, and your gematria can't help with that - for instance, a phonologist cannot simply "treat vowel space as triangular rather than rectangular", because vowel space is not in fact triangular.


This response seems excessively scornful to me. "Vowel space" is not a rectangle either, but we can model it as one. Triangular models of vowel space have been used before; see this post: http://englishspeechservices.com/blog/the-vowel-space/


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PostPosted: Tue Oct 27, 2015 3:23 am 
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PostPosted: Tue Oct 27, 2015 6:23 am 
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Sumelic wrote:
Salmoneus wrote:
something I won't stoop to quote here


This response seems excessively scornful to me.


Oh look, Salmoneus doesn't suffer fools gladly. But perhaps "Phonology" was too broad a word; note the change of thread title.

Sumelic wrote:
"Vowel space" is not a rectangle either, but we can model it as one. Triangular models of vowel space have been used before; see this post: http://englishspeechservices.com/blog/the-vowel-space/


Which is my point: what I was wondering is if this is a useful way to represent a triangular model of vowel space, or if it's extensible to consonants.

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PostPosted: Tue Oct 27, 2015 10:23 am 
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alice wrote:
So, as fundamentals, we have [i] = 400, [a] = 040, and [u] = 004; this can be extended to [e] = 310, [ɛ] = 220, [æ] = 130, [ɔ] = 022, and [o] = 013. 202 will then represent [ɨ]. Note that these all sum to 4, and are the most distinctive vowel phones. If we characterise [ə] as 000, we then have [ɪ] = 200, [ɐ] = 020, [ʊ] = 002; and [ɜ] = 110, [ɘ] probably = 210.

Shouldn't [ɘ] be 101, as it occupies the space between 000 and 202?

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PostPosted: Tue Oct 27, 2015 3:09 pm 
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Pole, the wrote:
alice wrote:
So, as fundamentals, we have [i] = 400, [a] = 040, and [u] = 004; this can be extended to [e] = 310, [ɛ] = 220, [æ] = 130, [ɔ] = 022, and [o] = 013. 202 will then represent [ɨ]. Note that these all sum to 4, and are the most distinctive vowel phones. If we characterise [ə] as 000, we then have [ɪ] = 200, [ɐ] = 020, [ʊ] = 002; and [ɜ] = 110, [ɘ] probably = 210.

Shouldn't [ɘ] be 101, as it occupies the space between 000 and 202?


I'm glad somebody's paying attention :-) Congratulations, you have found the hidden typo.

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PostPosted: Tue Oct 27, 2015 5:29 pm 
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This all reminds me of that xkcd comic about string theory, which I shall paraphrase:

"Suppose the vowel space were modeled in a triangle instead of a rectangle."
"Okay. What would that imply?"
"I dunno."

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PostPosted: Wed Oct 28, 2015 5:20 am 
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I thought some more about the geometry of this. It seems like what this gets you is a tetrahedral model. You can form it by slicing off the corner of a cube; the vowels can go on three faces composed of half-square triangles. The weird thing about this to me is that compared to a 2D model, the center will be more dense (I think -- correct me if I've made a mistake here).

Theories of vowels can be phonetically motivated (formant frequencies) or articulatory motivated (ATR, tongue "height" and "frontness," etc.) But I don't really see how your system is motivated. Wikipedia talks about a theory that sees vowel articulation as characterized by three main movements of the tongue, but it's a bit different from yours: the categories are "front," "raised," and "retracted"; the main difference from the usual descriptions being that back vowels are eliminated as a category. This theory seems to be more about articulation than about phonology, though.

The system is completely trilaterally symmetrical. One problem I see with this is that in many phonological systems, /i/ and /u/ seem to form a natural class that excludes /a/. The concept of "vowel height" isn't perfect for this either, since /ɨ/ seems to often pattern slightly differently from the other two. But I don't know that much about /ɨ/, and there are languages like Turkish where the four vowels /i u y ɨ/ all are part of the same group.

Analyzing vowel height as just being the opposite of "a-quality" doesn't quite work because the schwa (0,0,0) has no more a-quality than /u/ or /i/.


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PostPosted: Wed Oct 28, 2015 3:56 pm 
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Sumelic wrote:
Analyzing vowel height as just being the opposite of "a-quality" doesn't quite work because the schwa (0,0,0) has no more a-quality than /u/ or /i/.

It does seem quite neat that schwa should be (0,0,0).

A dual view is interesting. You have a high region (bounded by [i, ə, u] - a coefficient is zero), a front region (bounded by [i, ə, ä] - u-coefficient is zero) and a back reɡion (bounded by [u, ə, ä] - i-coefficient is zero). Whether that yields any insights is another matter.


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PostPosted: Thu Oct 29, 2015 7:16 am 
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Xephyr wrote:
This all reminds me of that xkcd comic about string theory, which I shall paraphrase:

"Suppose the vowel space were modeled in a triangle instead of a rectangle."
"Okay. What would that imply?"
"I dunno."


I think you've nailed it. I should have remembered that "there is no one structure which is universally appropriate".

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PostPosted: Thu Oct 29, 2015 4:11 pm 
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Regardless of the discussion about whether or not this view meaningfully contributes to the understanding of vowel systems--

--Shouldn't [ə] be 222?

000 Isn't possible, as it would simultaneously be a high/front vowel (that is, 0 openness and 0 high/backness), an open vowel (that is, 0 high/frontness and 0 high/backness), and a high/back vowel (that is, 0 high/frontness and 0 openness).

Clearly, schwa cannot have a value of 0 for each of the three variables, because they 0 on one scale corresponds to 4 on one of the others.

- -

As for its usefulness: It divides the vowel space in pretty much the same way as we already do (in terms of open/close vs front/back), but adds a layer of complexity by encoding each value for no apparent reason. At the same time, it removes flexibility and it becomes less representative of the actual 'vowel space' in our mouths, as that space is continuous along both of the axes, rather than having 4 discrete points along 3 axes. Additionally, two of the axes (high/front and high/back) are essentially the same and should therefore be merged.

But it was still a fun mental exercise. There's nothing wrong with challenging a common view every now and then, even if it didn't lead us anywhere this time :)

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PostPosted: Sat Nov 14, 2015 1:44 pm 
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A serious theory I've seen along these lines (though I do not have a reference offhand, sorry) similarly accepts only three main components of vowel timbre: I, A and U. However, instead of assigning values for each separately, it ends up positing that a vowel can have one or more secondary timbre in addition to its primary timbre. Thus for example while /i/ /a/ /u/ would be simply (I, -), (A, -) and (U, -), some of their combinations would be as follows:
/e/: (I, A)
/ɛ/: (A, I)
/y/: (U, I)
/o/: (U, A)
/ɔ/: (A, U)
Also possible are trinary combinations:
/ø/: (U, IA)
/œ/: (A, IU)
The source I saw was working mainly on the phonology of Finnish though, and ended up positing that U cannot be dominated by I, hence (I, U) and (I, AU) are not possible vowels. I have no idea if this could be made work for other languages by positing e.g. (I, U) as /ɨ/ and (I, AU) as /ɘ/ or /ɤ/.

Distinctions like English /i ɪ/ or /e ɛ æ/ would also seem to require adding a further variable such as tenseness.

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PostPosted: Sat Nov 14, 2015 2:23 pm 
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Tropylium wrote:
I have no idea if this could be made work for other languages by positing e.g. (I, U) as /ɨ/ and (I, AU) as /ɘ/ or /ɤ/.

Distinctions like English /i ɪ/ or /e ɛ æ/ would also seem to require adding a further variable such as tenseness.

The scheme won't handle a 4-way contrast /i/ ~ /y/ ~ /ɯ/ ~ /u/. The use of tenseness is, of course, a red flag warning of hocus pocus. Complex tones and complex vowel systems require impressionistic quantisation rather than bundles of features. Like pitch levels, the precision required varies from level to level, and Alice's scheme could be improved by having non-negative values summing to no more than 1·0. Tenseness makes sense if it refers to multiple characteristics, but if it only affects vowel height it's bogus, like the use of /ʌ/ rather than /ɐ/ for many Enɡlish accents. (Some may prefer to write 'bogus' as 'traditional'.)


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PostPosted: Sat Nov 14, 2015 2:34 pm 
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Richard W wrote:
Tenseness makes sense if it refers to multiple characteristics, but if it only affects vowel height it's bogus, like the use of /ʌ/ rather than /ɐ/ for many Enɡlish accents. (Some may prefer to write 'bogus' as 'traditional'.)

Are there any commonly seen analyses where tense/lax distinctions are in fact supposed to only surface as vowel height (as opposed to, at minimum, also backness)?

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PostPosted: Mon Dec 28, 2015 12:14 pm 
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Tropylium wrote:
A serious theory I've seen along these lines (though I do not have a reference offhand, sorry) similarly accepts only three main components of vowel timbre: I, A and U. However, instead of assigning values for each separately, it ends up positing that a vowel can have one or more secondary timbre in addition to its primary timbre. Thus for example while /i/ /a/ /u/ would be simply (I, -), (A, -) and (U, -), some of their combinations would be as follows:
/e/: (I, A)
/ɛ/: (A, I)
/y/: (U, I)
/o/: (U, A)
/ɔ/: (A, U)
Also possible are trinary combinations:
/ø/: (U, IA)
/œ/: (A, IU)
The source I saw was working mainly on the phonology of Finnish though, and ended up positing that U cannot be dominated by I, hence (I, U) and (I, AU) are not possible vowels. I have no idea if this could be made work for other languages by positing e.g. (I, U) as /ɨ/ and (I, AU) as /ɘ/ or /ɤ/.

Distinctions like English /i ɪ/ or /e ɛ æ/ would also seem to require adding a further variable such as tenseness.

I once read a paper that analyzed Icelandic's vowel system according to this criteria. I'll see if I can find it.

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PostPosted: Tue Dec 29, 2015 10:46 am 
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vec wrote:
Tropylium wrote:
A serious theory I've seen along these lines (though I do not have a reference offhand, sorry) similarly accepts only three main components of vowel timbre: I, A and U. However, instead of assigning values for each separately, it ends up positing that a vowel can have one or more secondary timbre in addition to its primary timbre. Thus for example while /i/ /a/ /u/ would be simply (I, -), (A, -) and (U, -), some of their combinations would be as follows:
/e/: (I, A)
/ɛ/: (A, I)
/y/: (U, I)
/o/: (U, A)
/ɔ/: (A, U)
Also possible are trinary combinations:
/ø/: (U, IA)
/œ/: (A, IU)
The source I saw was working mainly on the phonology of Finnish though, and ended up positing that U cannot be dominated by I, hence (I, U) and (I, AU) are not possible vowels. I have no idea if this could be made work for other languages by positing e.g. (I, U) as /ɨ/ and (I, AU) as /ɘ/ or /ɤ/.

Distinctions like English /i ɪ/ or /e ɛ æ/ would also seem to require adding a further variable such as tenseness.

I once read a paper that analyzed Icelandic's vowel system according to this criteria. I'll see if I can find it.
This works pretty well for describing Old Norse short vowels, which historically developed from a four vowel-system (where *i and *e were only marginally contrastive) that were affected by three major types of umlaut (secondary timbre). Note that the Younger Fuþąrk essentially only distinguished three vowel qualities (not counting the Óss-rune), as did the unstressed vowel system of Old Norse.

<e> from a-umlaut of *i (I, A)
<ę> from i-umlaut of *a (A, I)
<y> from i-umlaut of *u or rarely u-umlaut of *i (U, I; I, U)
<o> from a-umlaut of *u (U, A)
<ǫ> from u-umlaut of *a (A, U)

And the trinary combinations:
<ø₁> from combined i- and a-umlaut of *u or rarely from the combined a- and u-umlaut of *i (U, IA; I, UA)
<ø₂> from the combined i- and u-umlaut of *a (A, IU)

You could perhaps add the breaking of *e:
<ja> from a-breaking of *e (I, AA ?)
<jǫ> from u-breaking of *e (I, UA ?)

This isn't quite historically acurate, though:
  • <e> is mostly inherited directly from PG, only rarely from actual a-umlaut of *i.
  • <ø₁> is not historically from a combined a- and i- or u-umlaut. The i-umlaut occured mostly on *o that had to be analogically introduced from other forms with a-umlaut or form other sources such as *we (where *we > *o is an irregular change). The u-umlaut would have affected inheritited *e, but this is an extremely rare change, breaking is the typical outcome here. Short <ø₁> is not really the regular outcome of any PG source and is quite rare in ON.
  • The status of <ø₂> as a phoneme distinct from <ø₁> and <ę> as distinct from <e> is controversial (especially the former).

Elmer Antonsen proposed a (not widely accepted) twelve-vowel system for late Proto-Norse, which is essentially the system above with two added unrounded back vowels that represent u-umlaut of *i and *e, distinct from i-umlaut of *u and *o. Antonsen considered the effect of u-umlaut to be backing but not rounding, it seems:
http://www.jstor.org/stable/40916464?se ... b_contents


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PostPosted: Wed Dec 30, 2015 2:00 pm 
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Thanks! The book turns out to be in Iceland so I can't get to it now.

Was it Proto-Norse or Old Icelandic that went through a phase of no /o/?

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PostPosted: Wed Dec 30, 2015 6:03 pm 
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vec wrote:
Was it Proto-Norse or Old Icelandic that went through a phase of no /o/?
Proto-Germanic lacked short *o, since earlier *o and *a merged as PG *a. But Proto-Norse (and Northwest Germanic in general) developed a new *o from a-umlaut of *u. There is a lot of variation, though. Generally, West Norse has more examples of u > o than East Norse. And Old Gutnish seems to be the exception within Northwest Germanic, in that it lacks the effect of a-umlaut completely. It does have a shift u > o before rC, though (although it's not completely regular, apparently). So there is a marginal /o/ in Old Gutnish, but it generally has /u/ where other Norse dialects have /o/. Old Gutnish is similar to Gothic in this respect.
https://www.academia.edu/1670089/Old_Gu ... se_Context

I'm not too familiar with the shifts from Old Icelandic to Modern Icelandic, but I don't think there would have been a phase where there was no [o~ɔ]-like vowel.


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