Psalm 81:3-6 (NIV)
3 Sound the ram’s horn at the New Moon, and when the moon is full, on the day of our festival; 4 this is a decree for Israel, an ordinance of the God of Jacob. 5 When God went out against Egypt, he established it as a statute for Joseph... I am the Lord your God, who brought you up out of Egypt. Open wide your mouth and I will fill it.
Assuming that the NIV is right in rendering the word בכסה as when the moon is full, the Psalmist here refers to a month in which the horn is blown in the beginning of it (new moon) and then again on the full moon in honor of the festival. The Psalmist however does not specifically name this month, leaving it up to us to speculate. It can either be referring to the first month Nissan or the seventh month Tishrei since in only these two months will there be a festival on the 15th day of the month (which almost always coincides with full moon).
The tradition mentioned by the Psalmist seems to agrees well with a similar tradition found in the book of Numbers 10:10,
Also at your times of rejoicing-your appointed festivals and New Moon feasts-you are to sound the trumpets over your burnt offerings and fellowship offerings, and they will be a memorial for you before your God. I am the LORD your God.
Here too we find a tradition to blow the horn on the beginning of every month, and on the festivals as well; it is most likely this tradition that the psalmist here is referring to (although here it is a silver horn and in Psalms it is most likely a ram's horn as the NIV has it).
My question is, what significance does the psalmist attach to this tradition and how does it relate to the Exodus? Does the psalmist merely wish to relate that this tradition is so old that it dates back to the days the Israelites sojourned in the land of Egypt, or is there any deeper connection between the two?
In regards to the question, which month the Psalmist is referring to, i’m in agreement with K&D that it is about the month of Nissan, since in verse 5 and again in verse 10 images of the Exodus are evoked. If it is about the month of Tishrei it would be hard to understand why the Psalmist would allude to the Exodus in this Psalm. Furthermore, in verse 5 this festival is intimately connected with the Exodus. It is more likely that this psalm is about the month of Nissan in which the Israelites would signal the coming of Passover, which is celebrated on full moon, in the beginning of the month Nissan by blowing the horn. This is possible answer to my question, but i'm not completely satisfied with it, and I would like to hear other opinions on the matter.