1848edo: Difference between revisions
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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 2^3 * 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}}. | ||
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[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] | ||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per Octave | |||
!Generator | |||
(Reduced) | |||
!Cents | |||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperaments | |||
|- | |||
|3 | |||
|281\1848 | |||
|182.467 | |||
|10/9 | |||
|[[Domain]] | |||
|- | |||
|12 | |||
|3\1848 | |||
|1.948 | |||
|32805/32768 | |||
|[[Atomic]] | |||
|- | |||
|21 | |||
|901\1848 | |||
(21\1848) | |||
|585.065 | |||
(13.636) | |||
|91875/65536 | |||
(126/125) | |||
|[[Akjayland]] | |||
|- | |||
|56 | |||
|767\1848 | |||
(21\1848) | |||
|498.052 | |||
(13.636) | |||
|4/3 | |||
(126/125) | |||
|[[Barium]] | |||
|}<!-- 4-digit number --> | |||
[[Category:Akjayland]] | [[Category:Akjayland]] | ||
[[Category:Atomic]] | [[Category:Atomic]] | ||
Revision as of 18:46, 21 September 2022
Theory
It is a super strong 11-limit division, having the lowest 11-limit relative error than any division until 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>.
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 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
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.007 | +0.050 | +0.005 | -0.019 | -0.268 | +0.239 | -0.110 | +0.297 | +0.293 | -0.230 |
| Relative (%) | +0.0 | -1.1 | +7.7 | +0.8 | -3.0 | -41.3 | +36.9 | -17.0 | +45.8 | +45.1 | -35.5 | |
| Steps (reduced) |
1848 (0) |
2929 (1081) |
4291 (595) |
5188 (1492) |
6393 (849) |
6838 (1294) |
7554 (162) |
7850 (458) |
8360 (968) |
8978 (1586) |
9155 (1763) | |
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2929, 1848⟩ | [⟨1848 2929]] | 0.002192 | 0.002192 | 0.338 |
| 2.3.5 | [-16, 35, -17⟩, [129, -14, -46⟩ | [⟨1848 2929 4291]] | -0.005705 | 0.011311 | 1.742 |
| 2.3.5.7 | 250047/250000, 645700815/645657712, [43, -1, -13, -4⟩ | [⟨1848 2929 4291 5188]] | -0.004748 | 0.009935 | 1.530 |
| 2.3.5.7.11 | 9801/9800, 250047/250000, 14348907/14348180, 67110351/67108864 | [⟨1848 2929 4291 5188 6393]] | -0.002686 | 0.009797 | 1.509 |
Rank-2 temperaments
| Periods
per Octave |
Generator
(Reduced) |
Cents
(Reduced) |
Associated
Ratio |
Temperaments |
|---|---|---|---|---|
| 3 | 281\1848 | 182.467 | 10/9 | Domain |
| 12 | 3\1848 | 1.948 | 32805/32768 | Atomic |
| 21 | 901\1848
(21\1848) |
585.065
(13.636) |
91875/65536
(126/125) |
Akjayland |
| 56 | 767\1848
(21\1848) |
498.052
(13.636) |
4/3
(126/125) |
Barium |