Vowels - Morphemes

Vowels can be interpreted as d-degree steps or intervals, with consonants as the fixed borders, according to one of the views on these. Or vowels as a secondary field level (4'), consonants as the quantifying, "substantiating" force from lower d-degrees.
Cf. that vowels in writing of some languages as Hebrew, were marked as dots or dashes under / over the line of consonants, when they didn't belong to the pronunciation of the consonant.)
Dimension steps implies also angular steps type "180°—> 90°—> 45° ..." according to hypotheses in our model, and differentiation of vowels may be seen from this aspect:

Coordinate axes:

x-axis: windpipe — lips: tongue back-/inwards, lips forward as in the o-sound, <——>

y-axis: bottom — ceiling of oral cavity: tongue downwards the bottom, jaws-lips vertically opened as in the long a-sound 2.

z-axis: tongue in middle position, widened, jaws-lips widened, as in the e-sound.

Phoneticians' classification of vowels, tongue positions most critical:
   Back — Front*, here the x-axis, concerns tongue position horizontally.
   Low — High, here the y-axis, concerns tongue position in height
(= in "open" - "closed" vowels).
   Rounded — not rounded, (~ along the z-axis), concerns form of lip opening
   Long — Short, time for the pronunciation, a differentiation within the other characterizations above.

* Back vowels implies raise of tongue towards soft palate, front vowels raise of tongue towards hard palate. Cf. the file about consonants, tongue contracted to a mass, ~ 3-dimensional, and more flattened to a surface, ~ d-degree 2.

Number of vowel heights (hence vertically) in a language can be up to 4, so it is said, but are often reduced in numbers as 4 —> 3 —> 2.

Dimensional aspects when it concerns the speech organs, a first sketch:

4: Direction outwards / inwards (posterior - anterior): x-axis, opposition "180°". d-degree 4, <====> .

3: Radial/ circular, tongue - palate, height positions: y-axis, polarity "90°".
d-degree 3, __|__.

2: In the differentiation through shapes of lip-opening, circular to elliptical, the z-axis is involved (see "Annotations" below.)
(Mouth opening max about "45° ".) Note also that a convex/concave form of the tongue - as poles of d-degree 2 in our model - separates vowels e - i.

1: Long / short vowels: a polarization in mouth opening and in the dimension of Time, corresponding to intermediate stages in the 4 - 3 - 2-steps.

The vowels as step displacements, describing 90° arcs in 3 planes:
(Sw.) for Swedish vowels.

Back, "rounded" vowels: long o, long å (Sw), short å (or o), "often" long a:
D-degree step 4 —> 3:
Long vowels o —> å —> a describes a an arc from the inner part of x-axis to the y-axis, in xy-plane, equivalent with a polarization of the x-axis 180° to 90°.
- Lips opening stepwise towards the y-axis.
- Tongue position stepwise lower.

Front, "not rounded" vowels: short a, short ä (Sw.), long ä, e:
D-degree step 3 —> 2:
short a —> ä —> e (—> i) describes the arc from the y-axis to the z-axis, in yz-plane.
- Lips opening stepwise towards the z-axis. (About the i-vowel, see below.
- Tongue position stepwise higher.

Front, "rounded" vowels: y - u - ö (Sw.) - , open ö / u, about the sound in English "early".
D-degree step 2 —> 1:
y —> u —> ö —> : Lip movements from z-axis back to x-axis, in zx-plane, in one step, a return.
- Lip-opening stepwise then along the y-axis (a secondary kind for y and ö: only lip- opening, not the entire lower jaw).
- Tongue position from high in y lower and lower in following vowels.

Annotations:

1) According to phoneticians (BM), following pairs of vowels have the same tongue position in height:
The difference is only "rounding" of the lips in the y - ö - sounds.

y- and ö-sounds as a polarization up / down in tongue position in relation to the xz-plane:

The small lips opening in y and long ö-sound, without opening of jaws, could illustrate the assumed narrower angles towards lower d-degrees in a dimension chain.

2) Along the x-axis ("D4") there is a double-direction tongue-lips in the o-sound, becoming a unidirection in the u-sound, to compare with increasing one way direction towards lower d-degree in the dimension model.

The Swedish u-sound has developed from an inner elevated position (as the o-sound also is described) through a process in which the tongue has been pushed forwards. Hence, the long u above may perhaps be regarded as having the same tongue position as the o-sound.
All three steps according to the figures above taken together can be regarded as a "pole exchange" from d-degree 4 and inner pole 0 via steps → 3 → 2 → 1 to 00 as outer pole, and "the other way around" to the x-axis again.

3) The i-sound is defined as the highest vowel and the vowel articulated most in the front. It is assigned to the group front, not rounded vowels: short a - ä - e - i (from below upwards in tongue height position), step 3 - 2, y —> z-plane in our figures above.

In the series short a - ä - e however, steps in height position of the tongue is combined with the form of jaws and lips - stepwise closing to something of a "streak" in the e-sound. The i-sound then hardly implies any change in the jaws lips shape, only requires raising of the inner organ, the tongue.
In this respect, the i-sound appear as an expression for a branch from step 2-1 inwards step 3 - 2: 3 —> 1 <—2.
Formants of the i-sound are the most polarized in the frequency spectrum. (Most polarized - as in last step of a dimension chain, moreover designed as a simple line with a dot over it as an illustration of this last step!) The tongue raise from z-axis of e-sound, depicted with dashed lines in figure y-z-plane above could perhaps represent the formants?

(The reason why o- and i-sounds are described as with the same high tongue position by phoneticians, depends perhaps upon the palate being narrower inwards - a relative determination of the height?)

4) The "development" from back towards front vowels as in a step 4 →3 to 3 → 2 to 2 → 1 coincides with the interpretation of consonant developments 3-2 —> 2-1: plosives → fricatives in the transformation (in Swedish) of back plosives to fricatives when preceding front vowels: ke, kä, ki.. They transform to fricative sounds, here typed "tje". and the plosive g becomes a j-sound. This transformation however, doesn't occur before the u-sound, developed out of a back vowel a more direct way.
Note the term "soft vowels" for the front ones, which with the dimension model could refer to less structure, more motional moments) in lower d-degrees.

5) 3 series of vowels, if all with 4 vocal heights: 4 + 4 + 4:

(Special signs are those of phoneticians, but Swedish o, u, å-letters used.)

Circular arches of "90° " between the coordinate axes, according to the principle schedule above, will be divided by number of vowel heights in each series. It gives an "angle" of about "30° " on average. 4 vowel heights and 3 steps:

(Sin "30°" = 1/2, sin "60°" = √ 3/4; tan "30°" = √ 1/3, tan 60° = √ 3.
Vowel heights as sin-cos-tan functions and roots out of d-degrees and quotients between d-degrees!)

6) The terms "rounded - not rounded" vowels can be discussed. It could be argued, as in the figures above, that it is the direction of lips outwards along the x-axis that characterizes the o-sound, and the motions of lips and jaws in vertical direction, along the y-axis, that characterizes the transition to a long a-sound.
   The rounding of lips opening could be perceived as merely an indirect consequence of these straight directions, when the mouth opening and lips happen to have a horizontal position!
   The front vowels, short a - ä - e - i, which are called not rounded, are actually a gradual transition from round to elliptical to more elongated elliptical to "streak"-formed mouth opening.
   Ellipses: the form of a circle when its centre gets split to 2 focal points. Such forms as well as "back rounded" vowels, may be regarded as secondary results of the transition from y- to x-axis.
   Compare Lissajou's figures for geometries, created by particle rotations in 2 planes simultaneously: the changes circular - radial - streak forms.)

7) With phoneticians' description all back vowels are rounded, the front vowels e - ä - short a not rounded But in the last series y - u - ö the rounding reappears - as a kind of "feedback", also corresponding to the connection between steps in the loop version of the dimension model:

"Rounding", if one accepts phoneticians' definitions, becomes associated with x-y-axis, here representing "step 4 - 3" with reference to analysis of the organs. Compare circular structure as geometry for the 3a-pole of d-degree 3 according the dimensional model.

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Some readers may ask how it's possible to find 4 and up to 5 dimensions among phonemes when there is - "obviously" ? - only 3 dimensions or coordinate axes in the speech organs.

Physicians' answer would surely be: in the processes, representing motions, thus Time. In our model: d-degree 0/00 of motions.

Other kinds of answers here:

Among consonants:
h-sound: - A deep sigh from step 5-4. The body as the 5-dimensional whole, the underlying level.

Among vowels:
A groan - with tongue totally passive, irrelevant, not needed,
or - with closed lips - a kind of m-sound: A moan...

Vibration of vocal cords as the motional expression for d-degree 5 when transformed to d-degree 4.

Click-sounds, not treated here: implosion versus explosion in stops. Expressions for he dual directions of d-degree 4.

Morphemes

Some words about
syllables, morphemes, word stems

Number of phonemes in a syllable appears to be of the order of 1-5 , usually 2-3; when more, they are probably often contractions of original two or more syllables. Maximum number perhaps given by an underlying 5-step structure?

About syllable boundaries, the learned are said to disagree. The linguist Saussure wrote about the transition from direction towards a consonant as "recharging" against a barrier, to following explosive in direction outwards towards the vowel "up>|<per": turn from directions (Vconv - Vdiv) in terms of the dimension model - and a correspondence to plosives on the level of phonemes.

The syllable boundary could represent the concept "discontinuity", illustrated here in a little different way than the very simple illustration of it in Physics I, a transition from boundary to the interval:

Vowels along the "0-line", direction from 0 outwards. Consonants as the quantifying 00-pole, meeting from outside in different steps:

In some languages, two consonants cannot occur next to each other, it is said.

Morphemes has been defined as the smallest group of sounds carrying sense, connected or derived from the semantic level.

Number of syllables in a morpheme seems mostly to be 1-2. This could be compared with our proposed positioning of morphemes as in step 2 - 1 in the big chain for levels in languages: the development from the meaning or sense to a linear sentence.

If morphemes should be interpreted as syntheses of phonemes, or the phonemes as decomposed from morphemes, can be discussed. If two words or morphemes is crossed at right angles as in crosswords, the "letter", the phoneme, gets precipitated.
As examples show in section above: With a dimensional interpretation of phonemes, as well as of human situations and the environment, the individual sounds cannot be denied connections with semantic sense either.
Compare Robert Beard (RB) about earlier word stems with mostly geometrical sense that have been reduced to a "parasitic existence".

As written in another file (?), it's said that Semitic morphemes, the "smallest sense-carrying units", consisted of 3 consonants, originally 2 defining the main sense, developed with a 3rd that differentiated the sense (LB).

Example: p-a-l-a-g = divide, p-a-l-a-h, ~ split up

Thus the basic form for a morpheme (and syllable) becomes CVC, extended with VC, 5 phonemes. C = consonants, V = vowels.

An Indo-European consonant radical, type *brg (aspirated b and g) gave words as berg, borg (Swedish words meaning hill/mountain and castle/stronghold (SEO).

Fiji language has had morphemes of the type CVC, a closed type that now have become open and got the form CV. Thus, 3 —> 2 phonemes (BR).

Hence, we have 2 - 3 consonants or phonemes for one sense - as there are 3 - 2 bases (nucleic acids) in the codons for the identification of each amino acid in the genetic code - often described as a language. However, in numbers it's the number of phonemes that are of the same order as coded amino acids, and there don't seem to be any simple parallel to the only four bases. (Yet, it wouldn't be astonishing if there existed some deep correspondence.)

The CV-type can be regarded as representing a first polarization c - ac, 0 —> 00, outward direction from a barrier centre. The second consonant in a CVC-morpheme provides a secondary barrier, as the circumference of a circle relative the radius. CV to CVC should, looked upon this way, imply an angle step towards a lower d-degree, as a step 4 —> 3.

The relation vowel - consonant may be compared with verbs as open, nouns as closed.

(CVC-morphemes with examples from Swedish: s-a-k, (= thing).
VCC-morpheme a-s-k (= box), a noun, a closed morpheme.
CCV: s-k-a, (= shall), a verb, an open morpheme.)

A development CVC to CV morphemes could perhaps be interpreted as analogous to ionization of atom groups, vowels as "free valences" for the capture of substitutions = other consonants, e.g. H2O —> OH- —> O-H-Cl.

Morphemes could appear out of small mini-groups or "bubbles" of phonemes as a "molecular soup" (or similar to first cells in an embryo?), out of a multidimensional system and its plane and space quadrants, through partial couplings between different coordinate axes and angle steps - with phonemes decoded dimensionally. (Cf. what physicists assume to be carriers of the strong force, the "gluons".)

Different neurones could potentially be activated by different geometrical properties of the steps in a dimension chain (cf. how the eye analyzes visual stimuli: e.g. distance to a centre (amplitude), vectors (direction), angles, ascending / descending lines, curves, etc.) They could in various combinations correspond to phonemes or groups of phonemes, and the network of connections between them evolve from the hearing of language. A counterpart on the levels of phonemes and morphemes to how the grammatical structure also could be analyzed and stored?

"Word stem" or a "word bush"?