1600edo: Difference between revisions
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added some more RTPs, 32nd octave temperaments. |
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== Theory == | == Theory == | ||
{{Harmonics in equal|1600}} | {{Harmonics in equal|1600}} | ||
1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything else with this property until [[4501edo|4501]]. It is also the first division past [[311edo|311]] with a lower 43-limit relative error. One step of it is the [[relative cent]] for [[16edo|16]]. | 1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything else with this property until [[4501edo|4501]]. It is also the first division past [[311edo|311]] with a lower 43-limit relative error. One step of it is the [[relative cent]] for [[16edo|16]]. It's high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. | ||
1600's divisors are {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800}}. | 1600's divisors are {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800}}. | ||
In the 5-limit, it supports [[kwazy]]. | In the 5-limit, it supports [[kwazy]]. | ||
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| -0.015742 | | -0.015742 | ||
|0.033217 | |0.033217 | ||
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|- | |||
|2.3.5.7.11 | |||
|3025/3024, 4375/4374, 184549376/184528125, 7680000000/7672950131 | |||
|[{{val|1600 2536 3715 4492 5535}}] | |||
|? | |||
|? | |||
| | |||
|- | |||
|2.3.5.7.11.13 | |||
|3025/3024, 4096/4095, 4375/4374, 91125/91091, 14236560/14235529 | |||
|[{{val|1600 2536 3715 4492 5535 5921}}] | |||
|? | |||
|? | |||
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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 | |||
! Cents | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|2 | |||
|217\1600 | |||
|162.75 | |||
|1125/1024 | |||
|[[Kwazy]] | |||
|- | |||
|32 | |||
|121\1600 | |||
(21/1600) | |||
|90.75 | |||
(15.75) | |||
|48828125/46294416 | |||
(?) | |||
|[[Windrose]] | |||
|- | |||
|32 | |||
|357\1600 | |||
(7\1600) | |||
|267.75 | |||
(5.25) | |||
|245/143 | |||
(?) | |||
|[[Germanium]] | |||
|- | |||
|32 | |||
|23\1600 | |||
|17.25 | |||
|? | |||
|[[Dike]] | |||
|- | |||
|80 | |||
|629\1600 | |||
(9\1600) | |||
|471.75 | |||
(6.75) | |||
| 130/99 | |||
(?) | |||
|[[Mercury]] | |||
|}<!-- 4-digit number --> | |||