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The 6691 division divides the octave into 6691 equal parts of 0.17935 cents each. It is a very strong 11-limit division, with a lower 11-limit relative error than any division until 40006. It is also strong in the 7-limit, where only 3125 is both smaller and with a lesser relative error. A basis for the 11-limit commas is {1771561/1771470, 3294225/3294172, 67110351/67108864, 78125000/78121827} and for the 7-limit commas, {78125000/78121827, 281484423828125/281474976710656, 8936733825332544112/8936247052719140625}.