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]]. It is also strong in the [[7-limit]], where only [[3125edo|3125]] is both smaller and with a lesser relative error.

6691edo is a very strong [[11-limit]] system, with a lower 11-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any smaller 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.

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}.

=== Prime harmonics ===

~~{{stub}}~~

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

=== Subsets and supersets ===

6691edo is the 863rd [[prime edo]].

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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]]. It is also strong in the [[7-limit]], where only [[3125edo|3125]] is both smaller and with a lesser relative error.
+{{EDO intro}}
+edo is a very strong [[11-limit]] system, with a lower 11-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any smaller 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.
 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}.
+=== Prime harmonics ===
 {{Harmonics in equal|6691}}
-{{stub}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== Subsets and supersets ===
+edo is the 863rd [[prime edo]].
+{{Stub}}