6691edo: Difference between revisions

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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 [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[40006edo|40006]].

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 [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[40006edo|40006]]. It is also strong in the [[7-limit]], where only [[3125edo|3125]] is both smaller and with a lesser relative error.

~~It is also strong in the 7-limit, where only [[3125edo|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}.

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}.

[[Category:Equal divisions of the octave|####]]

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 {{Infobox ET}}
-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 [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[40006edo|40006]].
+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 [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[40006edo|40006]]. It is also strong in the [[7-limit]], where only [[3125edo|3125]] is both smaller and with a lesser relative error.
-It is also strong in the 7-limit, where only [[3125edo|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}.
+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}.
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 [[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->