The Rizhiner was once sitting at a Rosh Chodesh feast with the Apter Rav. It was Rosh Chodesh Tammuz.
They discussed how much Mashkeh [bottles of spirits/whiskey] to serve [literally: place on the table]. The Rizhiner had the custom of serving Mashkeh based on a numerical pattern of 72, 36, etc.
The Rizhiner said that he would put down 6 or 7 bottles of spirits. The Apter asked him why this specific number.
He answered that Tammuz [in Hebrew] – means Tam 6 or 7 (תם ו’ או ז’), i.e. the number 6 or 7 was completed.
[The explanation of this idea] is that Moshe did not ascend from the mountain [i.e. from Mount Sinai right away, as it is written] “When the people saw that Moses was so long in coming down from the mountain,” Rashi writes that it depends whether Moshe ascended [the mountain] on the 6th or 7th day of Sivan.
Since he descended from the mountain on the 16th of Tammuz, it was then determined whether he ascended on the 6th or 7th day of Sivan.
Therefore, Rosh Chodesh is the rectification of 6 or 7 [i.e. the 6th or 7th day of Sivan).
I.F.