odd photoperiod ok for basil?

I am trying to grow basil (multiple varieties) on a south-facing windowsill. I have no outdoor space to do this in, but in this windowsill these plants will see the full sun for about 6 hours a day. I can supplement the sun with some fluorescent lighting (mixed 'cool' and 'warm' bulbs to about a third of the power (per area) of the sun).
I can not put every plant in the windowsill at once, nor can I put every plant under the artificial light at once. Therefore, for optimum light, I must rotate plants. This will result in unnatural periods of light and darkness.
To what extent can basil tolerate unnatural periods of light and dark? (Length of day vs night, variation of the length of one day to the next, so on). Are scientific studies done on such topics? Will it vary based on the particular variety?
Any insight into understanding how basil will respond to this sort of situation would be much appreciated.
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