From Hreinn Benediktsson´s edition and commentary on the First Gram-
matical Treatise:

5.2.2. The Nasality and Quantity Distinctions
5.2.2.1. The Evidence of the FGT

In the second and third sections of the chapter on vowels the FG
then establishes the two correlations into which the nine qualitat-
ively distinct vowel phonemes entered, viz., the correlations of
nasality and quantity, repectively.
In the second section (85:18-28) the author shows that to each of
the nine units previously established there corresponds one unit
that differs from it by being 'pronounced through the nose'. In
compliance with his basic principles (cht.3.4.2.4 and 5.2.1.1) he
produces a list of nine pairs, followed by illustrative sentences,
distinguishing each nasal vowel, by means of a superscript dot, from
the corresponding oral vowel:

(Notes: As my keyboard will not make a 'superscript dot', I will use
paratheses to show the nasals instead; '(hooked)' = tail below)

har 'hair' : (har) 'shark'
ro (hooked) 'yard' : (ro) (hooked) 'corner'
þel 'woollen nap' : (þel) 'file'
fer (hooked)'sheep' : (fer) '(it) conceives'
isa 'ice-flows' acc.pl. : (i sa) '(one could) look through'
orar 'madness' : (orar) 'our' fem.pl.
öra (=lined o)'to vex' : (öra) (=lined o) 'younger' neut.
þu at 'you (were)present : (þuat) 'pressed down' past part.
syna 'laps' gen.pl. : (syna) 'to show'

It should be noted that although most of these forms certainly had
long vowels (for further details, see chp.5.2.2.2c and k), they are
here left without the superscript accent mark, since at this point
the distinction of vowel length has not yet been introduced by the
author (see note to 85:21-22 and cht.5.2.1.1 above).' (end quote)

This should be enough for now. In order to make it clear WHY some of
these words are nasals ans others not, I will post their etymologies
shortly. Old Norse can be very deceptive. Without etymological help,
it would be hard to see the difference between forns like 'syna' and
'syna' (= 'sýna' and 'sýna'). Not only do they look identical, but
in 'y' in each case stands before a 'n' - this means that both are
nasals, right? No, not according to the First Grammarian. What is
the reason? The reason lies in etymology: 'sýna' (laps) is merely a
gen. pl. (oblique case) of a noun in which 'ý' does not otherwise
stand before 'n', whereas 'n' in 'sýna' (to show) is a fixture.

The title of this post is 'The Nasality and Quantity Distinctions'.
Techically, the 'quantity distinctions' will come in the next post,
where I will quote the examples provided of this. After having done
this, I will post the etymologies of these word. Perhaps this will
lead to some interesting discussion of nasalization in Norse.

Regards,
Konrad.