This maamar itself has proposed several:
The seventh as completed descent and the eighth as return.
Moshiach as the eighth dimension of the seven-generation Chabad mission.
Alef plus Zayin as the first generation returning through the seven.
The Alter Rebbe's first note returning as a Messianic octave.
Moshe the seventh singing אז, the word of eight.
The Rebbe's seventh generation likewise singing the Eighth through its Geulah mission.
The Eighth Queen as Malchus revealing her Keter-root without replacing the sevenfold head.
The Messianic world as the moment the recipient becomes articulate.
These are not quotations from classical texts.
They are connections built from them.
Their holiness depends on remaining humble before the sources from which they arise.