1848edo: Difference between revisions

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~~The~~ 1848 equal division divides the octave into 1848 equal parts of 0.64935 cents each. It is a super strong 11-limit division, having the lowest 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[6079edo|6079]]. It tempers out the 11-limit commas 9801/9800, 151263/151250, 1771561/1771470 and 3294225/3294172. It also tempers out the 7-limit landscape comma, 250047/250000. It is distinctly consistent through the 15-limit, and tempers out the 13-limit commas 4225/4224 and 6656/6655. In the 5-limit it is an atomic system, tempering out the atom, |161 -84 -12>; and also the minortone comma, |-16 35 -17>.

~~1848~~ is ~~highly composite~~, ~~factoring~~ as 2^3 * 3 * 7 * 11. ~~Among its~~ divisors are ~~[[12edo|~~12]], ~~[[14edo|~~14]], ~~[[22edo|~~22]], ~~[[24edo|~~24]], ~~[[28edo|~~28]], ~~[[56edo|~~56]], ~~[[77edo|~~77]], ~~[[84edo|~~84]], ~~[[88edo|~~88]], ~~[[154edo|~~154]], ~~and [[231edo|~~231]].

== Theory ==

It is a super strong 11-limit division, having the lowest 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[6079edo|6079]]. It tempers out the 11-limit commas 9801/9800, 151263/151250, 1771561/1771470 and 3294225/3294172. It also tempers out the 7-limit landscape comma, 250047/250000. It is distinctly consistent through the 15-limit, and tempers out the 13-limit commas 4225/4224 and 6656/6655. In the 5-limit it is an atomic system, tempering out the atom, |161 -84 -12>; and also the minortone comma, |-16 35 -17>.

1848 factors as 2^3 * 3 * 7 * 11. It is a superabundant number in the no-fives subgroup, that is if only numbers not divisible by 5 are counted. Its divisors are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 231, 264, 308, 462, 616, 924.

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-The 1848 equal division divides the octave into 1848 equal parts of 0.64935 cents each. It is a super strong 11-limit division, having the lowest 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[6079edo|6079]]. It tempers out the 11-limit commas 9801/9800, 151263/151250, 1771561/1771470 and 3294225/3294172. It also tempers out the 7-limit landscape comma, 250047/250000. It is distinctly consistent through the 15-limit, and tempers out the 13-limit commas 4225/4224 and 6656/6655. In the 5-limit it is an atomic system, tempering out the atom, |161 -84 -12&gt;; and also the minortone comma, |-16 35 -17&gt;.
+{{EDO intro|1848}}
-is highly composite, factoring as 2^3 * 3 * 7 * 11. Among its divisors are [[12edo|12]], [[14edo|14]], [[22edo|22]], [[24edo|24]], [[28edo|28]], [[56edo|56]], [[77edo|77]], [[84edo|84]], [[88edo|88]], [[154edo|154]], and [[231edo|231]].
+== Theory ==
+It is a super strong 11-limit division, having the lowest 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[6079edo|6079]]. It tempers out the 11-limit commas 9801/9800, 151263/151250, 1771561/1771470 and 3294225/3294172. It also tempers out the 7-limit landscape comma, 250047/250000. It is distinctly consistent through the 15-limit, and tempers out the 13-limit commas 4225/4224 and 6656/6655. In the 5-limit it is an atomic system, tempering out the atom, |161 -84 -12&gt;; and also the minortone comma, |-16 35 -17&gt;.
+factors as 2^3 * 3 * 7 * 11. It is a superabundant number in the no-fives subgroup, that is if only numbers not divisible by 5 are counted. Its divisors are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 231, 264, 308, 462, 616, 924.