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== Theory ==
== 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>.
1848edo 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. In the 5-limit it is an atomic system, tempering out the [[atom]], {{monzo| 161 -84 -12 }} and also the minortone comma, {{monzo| -16 35 -17 }}. It also tempers out the 7-limit [[landscape comma]], 250047/250000. It is distinctly consistent through the 15-odd-limit, and tempers out the 13-limit commas [[4225/4224]] and [[6656/6655]].  


In the 7-limit, it supports [[domain]] and [[akjayland]].
In the 7-limit, it supports [[domain]] and [[akjayland]].


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 {{EDOs|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}}.
1848 factors as 2<sup>3</sup> × 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 {{EDOs| 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 }}.


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|1848}}
{{Harmonics in equal|1848|columns=11}}


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |Subgroup
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal  
! rowspan="2" | Optimal<br>8ve Stretch (¢)
8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" |Tuning error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{Monzo|-2929, 1848}}
| {{monzo| -2929 1848 }}
|[{{val|1848 2929}}]
| [{{val| 1848 2929 }}]
|0.002192
| 0.002192
|0.002192
| 0.002192
|0.338
| 0.338
|-
|-
|2.3.5
| 2.3.5
|{{Monzo|-16, 35, -17}}, {{Monzo|129, -14, -46}}
| {{monzo| -16 35 -17 }}, {{monzo| 129 -14 -46 }}
|[{{val|1848 2929 4291}}]
| [{{val| 1848 2929 4291 }}]
|<nowiki>-0.005705</nowiki>
| -0.005705
|0.011311
| 0.011311
|1.742
| 1.742
|-
|-
|2.3.5.7
| 2.3.5.7
|250047/250000, 645700815/645657712, {{Monzo|43, -1, -13, -4}}
| 250047/250000, 645700815/645657712, {{monzo| 43 -1 -13 -4 }}
|[{{val|1848 2929 4291 5188}}]
| [{{val| 1848 2929 4291 5188 }}]
| -0.004748
| -0.004748
|0.009935
| 0.009935
|1.530
| 1.530
|-
|-
|2.3.5.7.11
|2.3.5.7.11
|9801/9800, 250047/250000, 14348907/14348180, 67110351/67108864
| 9801/9800, 250047/250000, 14348907/14348180, 67110351/67108864
|[{{val|1848 2929 4291 5188 6393}}]
| [{{val|1848 2929 4291 5188 6393}}]
|<nowiki>-0.002686</nowiki>
| -0.002686
|0.009797
| 0.009797
|1.509
| 1.509
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|4225/4224, 9801/9800, 67392/67375, 250047/250000, 4429568/4428675
| 4225/4224, 9801/9800, 67392/67375, 250047/250000, 4429568/4428675
|[{{val|1848 2929 4291 5188 6393 6838}}]
| [{{val|1848 2929 4291 5188 6393 6838}}]
|0.009828
| 0.009828
|0.029378
| 0.029378
|4.524
| 4.524
|}
|}
[[Category:Equal divisions of the octave|####]]


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
!Periods
! Periods<br>per 8ve
per Octave
! Generator<br>(Reduced)
!Generator
! Cents<br>(Reduced)
(Reduced)
! Associated<br>Ratio
!Cents
! Temperaments
(Reduced)
!Associated
Ratio
!Temperaments
|-
|-
|3
| 3
|281\1848
| 281\1848
|182.467
| 182.467
|10/9
| 10/9
|[[Domain]]
| [[Domain]]
|-
|-
|12
| 12
|3\1848
| 3\1848
|1.948
| 1.948
|32805/32768
| 32805/32768
|[[Atomic]]
| [[Atomic]]
|-
|-
|21
| 21
|901\1848<br>(21\1848)
| 901\1848<br>(21\1848)
|585.065<br>(13.636)
| 585.065<br>(13.636)
|91875/65536<br>(126/125)
| 91875/65536<br>(126/125)
|[[Akjayland]]
| [[Akjayland]]
|-
|-
|44
|44
|767\1848<br>(11\1848)
| 767\1848<br>(11\1848)
|498.052<br>(7.143)
| 498.052<br>(7.143)
|4/3<br>(?)
| 4/3<br>(?)
|[[Ruthenium]]
| [[Ruthenium]]
|-
|-
|56
| 56
|767\1848<br>(21\1848)
| 767\1848<br>(21\1848)
|498.052<br>(13.636)
| 498.052<br>(13.636)
|4/3<br>(126/125)
| 4/3<br>(126/125)
|[[Barium]]
| [[Barium]]
|}<!-- 4-digit number -->
|}
 
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
[[Category:Akjayland]]
[[Category:Akjayland]]
[[Category:Atomic]]
[[Category:Atomic]]
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