[Svartalfiar]

The first six tones appear with their respective syllables initiating the first six phrases.

The 7th tone does not appear as a phrase-initiating syllable. Sancte Ioannes does not even touch tone 7.

Right. The SI was added later because the system uses 7 notes but the hymn the sounds were taken from only had 6 of the lines. So in order to finish the system, they had to add a note-word to complete the set and get to 7.

[map]

Yes. The mediaeval system did use the 7th tone but named it in a round about way.

Note seven of the ut/do (C) hexachord was arrived at in two ways:

1) 4th tone of the fa (F) hexachord (B flat)
2) 3rd tone of the sol (G) hexachord (B natural).

The tone existed, but was named as 4 of 4 (B flat of F) or 3 of 5 (B natural of G).

If I remember correctly, this is from where the flat, natural and sharp signs derive. They are all based on the letter b.