Albert Barnes Commentary Psalms 81:3

"Blow the trumpet at the new moon, At the full moon, on our feast-day." — Psalms 81:3 (ASV)

Blow up the trumpet – The word translated "blow" means to make a clangor or noise as on a trumpet. The trumpet was, like the timbrel, the harp, and the psaltery, a common instrument of music and was used on all their festive occasions. It was at first made of horn and then was made similar in shape to a horn. (Leviticus 25:9; Job 39:25).

In the new moon – On the festival held at the time of the new moon. There was a high festival on the appearance of the new moon in the month of Tisri, or October, which was the beginning of their civil year, and it is not improbable that the return of each new moon was celebrated with special services. (See the notes at Isaiah 1:13; compare to 2 Kings 4:23; Amos 8:5; 1 Chronicles 23:31; 2 Chronicles 2:4). It is not certain, however, that the word used here means "new moon." Professor Alexander translates it "in the month"; that is, in the month, preeminently, in which the Passover was celebrated.

The word used – חדשׁ (chôdesh) – indeed commonly means the new moon, the day of the new moon, or the first day of the lunar month (Numbers 29:6; 1 Samuel 20:5, 18, 24). However, it also means a month, that is, a lunar month beginning at the new moon (Genesis 8:5; Exodus 13:4; and elsewhere).

The corresponding or parallel word, which is translated in our version as "in the time appointed," means "full moon," as we shall see. The probability is, as Professor Alexander suggests, that the month is mentioned in general at the beginning of the verse, and the particular time of the month – the full moon – in the other part. Thus, the language is applicable to the Passover.

On the other supposition – the supposition that the new moon and the full moon are both mentioned – there would be manifest confusion as to the time.

In the time appointed – The word used here – כסה (keseh) – properly means the full moon, the time of the full moon. In Syriac, the word means either “the first day of the full moon” or “the whole time of the full moon” (Isa Bar Ali, as quoted by Gesenius, Lexicon). Thus, the word means not, as in our translation, "in the time appointed," but "at the full moon," and would refer to the time of the Passover, which was celebrated on the fourteenth day of the lunar month, that is, when the moon was at the full (Exodus 12:6).

On our solemn feast day – In Hebrew, "In the day of our feast." The word "solemn" is not necessarily in the original, though the day was one of great solemnity. The Passover is doubtless referred to.