An intriguing discovery.
In the Universal Jewish Encyclopedia, page 410 under the heading
Holidays, I quote:
1. Sabbath and New Moon (Rosh Hodesh), both periodically recurring
in the course of the year. The New Moon is still, and the Sabbath
originally was, dependent upon the lunar cycle. Both date back to
the nomadic period of Israel. Originally the New Moon was
celebrated in the same way as the Sabbath; gradually it became less
important, while the Sabbath became more and more a day of religion
and humanity, of religious meditation and instruction, or peace and
delight of the soul, and produced powerful and beneficent effects
outside of Judaism.