Main thesis
Different homoorganic sounds stand very rarely in one semitic root.
The closer (in organic/positioning sense) two sounds are, the less is the frequency of them appearing together in one semitic root.

Examples and details

(s,ts) pair are typical homoorganics and never stand together in one root. The same is with (z,s)=(heb. zain,samekh) , (ain,khet) , (z,ts)=(zain,tsadi) , (q,k)=(quf,kaf) , (t,z)(tet,zain)

There are a lot of pairs, that occur very rarely: (g,q)(gimel,quf) 1 root (giheq=to burb,to belch) ,
(g,k)(gimel,kaf) 1 root (gikhek=to giggle, to chuckle)
(l,r)(lamed,reish): (rakhel=ewe), (ra`al=poison), (rikel=gossip), (`arel=uncircumcised), (regel=foot)
(b,p)(beit,pei): (bilef=(slang) to lie, to fabricate, to fake, to humbug (coarse slang) to bullshit)
*obviously the previous example comes from english "bluff " so we can actually group this pair to 'neverstandings'

There are a lot of more or less "strong" pairs and their occurrence depends on how close in the mouth the sounds are pronounced.

The analysis of these pairs and their statistics yields a posibility of dividing most of the letters in partially conventional groups. Every two letters from each group never or rarely occur in one root.

Groups:
  1. (beit, pei, mem) labial
    Notes: mem is resonant, thehefore the conflict between mem and beit,pei is not so strong as in the case of beit-pei, that's why there are more "exceptions" with mem

  2. (dalet, tet, tav, tsadi*) dental
    Notes: tsadi in both dental and fricative groups, because of the two sounds [ts]. The sequence of t->s sounds is crucial for statistics in this and the next groups. The roots, where tsadi comes before a dental (specially divided through the middle letter in a 3-letters root), are more frequent, then the roots, where tsadi comes after a dental. And vice versa: the roots, where tsadi comes before a fricative ore sibilant , are more infrequent, than the roots, where tsadi comes after a fricative or sibilant (especially divided through the middle letter in a 3-letter root). This is due to an additional between-sound: in case of dental it is 's', and in case of fricative/sibilant it is 't'
  3. (shin/sin, zain, samekh, tsadi) interdental fricatives and sibilant.
    Notes: a) the tongue position of shin is a little bit different, that's why the pairs with shin occur more often, than other pairs from this group. b) Zain never or rarery appears also with some dentals, which can be genealogicaly explained: zain comes from protosemitic d, which was interdental (see table below).
  4. (lamed, reish) liquids
    Notes: the conflict beetwen lamed and reish is not so strong because the both of them are actually resonants. Nevertheless the quantity of roots with them is very diminutive compared with expected from letter occurrencies in the roots.
  5. (quf, kaf, gimel) velar
    Notes: kaf stands also very rarely with tet and tsadi. This fact supports the hypotese of kaf palatalisation, so, that kaf was pronounced beetwen tet and quf (in tongue position)
  6. (khet,ain) pharingal

There are 5 hebrew letters, that stand out:
(alef,hey,vav,jod,nun) glottal and resonants. We assign them as a "free" group, because they can often stand together with any letter.

  1. (alef,hey,vav,jod,nun) free group.
    Notes: a) jod is close to caf in position and indeed they stand seldom together. You can treat jod as fricative of the same position as caf.
    b) All of these letters are used in inflexies, prepositions, conjunctions, article: alef - future 1st prsn. ; jod - future 3rd prsn ; hey-definite article ; vav = and ; nun - nif'al, noun fem.plur., and so on. The reason of this fact is obvious: infexies shouldn't conflict with root letters.
    Of course there are exceptions: beit, tav, mem and so on.

You can compare this division with the classical table below
(source "Proto-Semitic Language and Culture", John Huehnergard http://www.bartleby.com/61/JPG/proto.jpg)

 

Estimate formula for pair-probability

P(1<->2) = (pos1-pos2)2 * R1*R2

where
P(1<->2) - probability of nearstanding pair (1,2),
pos1,2 - physical position of pronouncing phoneme (1,2)
R1,2 - "extend of resonantness" of each phoneme

This formula shows only tendencies and can't be used for exact value. The simplest cause is, that there are no rational way to estimate exactly the distance beetwen to positions in mouth :) (the same for "extend of resonantness")

 

Why this property is typical for the semitic group?

From Indoeuropian group where analysed the roots and words from the following languages:
Umbrian, Tokharian, Oscan, IndoTyrrhenian, Lydian, Hittite, Macedonian, Lycian, Luwian, Gaulish. In all these languages no statistical correlation was found.

In Latin full-text analysis only weak correlation in main groups and no correlation in repeate-pairs and fore-tonge pairs were found.

The possible explanation of could be the prevailing of internal inflex in semitic language group and as a consequence the possibility of preserving this exclusively consonant phenomenon.

footnotes
  • Homoorganic sounds are sounds, which are produced with the same part of vocal organs.
  • Here we use the hebrew equivalents of protosemitic sounds for convenience and reference with the present database (which is hebrew).
  • As a base for research we take first hebrew roots, but our results were also prooved on protosemitic, akkadian and arabic roots