159edo: Difference between revisions

Mappings and JI approximation quality: re-evaluate the 19-limit and higher-limit interpretation. Linking; style
Regular temperament properties: as is discussed in the theory section, there's no other reasonable mappings other than the patent val
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=== Commas ===
=== Commas ===
Assuming the [[val]] {{val|159 252 369 446 550 588 650 }}, 159tet [[tempers out]] the following [[comma]]s in the 17-limit.
Assuming the patent val {{val| 159 252 369 446 550 588 650 675 719 }}, 159tet [[tempers out]] the following [[comma]]s in the 23-limit.


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
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| Sululuruyoyo
| Sululuruyoyo
| [[Sparkisma]]
| [[Sparkisma]]
|-
| 19
| 343/342
| {{monzo| -1 -2 0 3 0 0 0 -1 }}
| 5.0547
|
|
|-
| 19
| 361/360
| {{monzo| -3 -2 -1 0 0 0 0 2 }}
| 4.8023
|
|
|-
|-
|}  
|}  


In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas.  In the 23-limit, with the 19-limit skipped, this system is known to temper out 392/391, 460/459, 507/506, 529/528, 897/896, 1105/1104, 1288/1287, 2024/2023, 2025/2024, and 2646/2645 among others.
In the 23-limit, with the 19-limit skipped, this system is known to temper out 392/391, 460/459, 507/506, 529/528, 897/896, 1105/1104, 1288/1287, 2024/2023, 2025/2024, and 2646/2645 among others.


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===