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Group by day of the week (using arithmetic).
We can use modular arithmetic to calculate the day of the week.
We happen to know that 20 May 1962 was a Sunday. We calculate the number of days from that day and take mod 7 value. This tells us the day of the week: 0 is Sunday, 1 is Monday...
SELECT MOD(wk - TO_DATE('1962-05-20','YYYY-MM-DD'),7), COUNT(song) FROM gisq.totp GROUP BY MOD(wk - TO_DATE('1962-05-20','YYYY-MM-DD'),7)
Dates may be subtracted. The answer is in units of days.