Shiras Ha'azenu Vs. Shiras Hayam

The Rambam at the end of Ch. 8 of the Laws of Sefer torah goes through all the parshiot that are פתוח וסתום.  He says that Shiras Ha'azenu in written צורת שירת האזינו כל שיטה ושיטה יש באמצע ריוח אחד כצורת הפרשה הסתומה ונמצא כל שיטה חלוקה לשתים וכותבין אותה בשבעים שיטות ואלו הן התיבות שבראש כל שיטה ושיטה.  On the other hand, Shiras Hayam is written שירת הים כותבין אותה בשלשים שיטות שיטה ראשונה כדרכה ושאר השיטות אחת מניחין באמצעה ריוח אחד ואחת מניחין הריוח בשני מקומות באמצעה עד שתמצא השיטה חלוקה לשלש ונמצא ריוח כנגד הכתב וכתב כנגד הריוח.  Why is there this difference between the two songs?  The difference in writing represents the different natures of the two shirot.  What is their nature, and how is it reflected by its construction?

The number three represents that which is the head, that which is greater as in the three faculties of the brain.  However, even more than that, a person's head isn't covered, it is left open.  That is because the head is the higher aspect of mankind, that which didn't becomes contaminated by the sin of the atz haddas.  That is shiras hayam.  It is a time of a great revelation of Hashem, it is a great, revealed light.  That is the reason why the words are on top of the breaks between the words as well, for even that which is covered over is touched by that which is revealed.

The number seven represents that which is covered over by nature. טבע comes from the word טבע בים, the light of Hashem is hidden over. That is why the creation of the world goes through the seven lower sefirot to cover over the light of Hashem.  That is the shira of Ha'azenu. Besides the very words being enigmatic, the message contains times of darkness and doom.  That is why there is a column of empty space in the middle, for the revealed words are engulfed by that which is hidden.

However, ultimately it is Ha'azenu that is a greater shira than that of Beshalach.  אז ישיר משה is a hint to techias hamasim but the full message of geulah is contained in Ha'azenu. That is the the paradox; the greater darkness turns into the greatest light (based upon Mishkan Blvavi Evne.)