53edo: Difference between revisions
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ArrowHead294 (talk | contribs) Comma list |
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53et is lower in relative error than any previous equal temperaments in the 3-, 5-, and 13-limit. The next equal temperaments doing better in these subgroups are 306, 118, and 58, respectively. It is even more prominent in the 2.3.5.7.13.19 and 2.3.5.7.13.19.23 subgroups, and the next equal temperament doing better in either subgroup is 130. | 53et is lower in relative error than any previous equal temperaments in the 3-, 5-, and 13-limit. The next equal temperaments doing better in these subgroups are 306, 118, and 58, respectively. It is even more prominent in the 2.3.5.7.13.19 and 2.3.5.7.13.19.23 subgroups, and the next equal temperament doing better in either subgroup is 130. | ||
=== Commas === | |||
Commas that 53edo tempers out using its patent val, {{val| 53 84 123 149 183 196 225 }}, include: | |||
{| class="commatable wikitable center-1 center-2 right-4 center-5" | |||
|- | |||
! [[Harmonic limit|Prime<br>Limit]] | |||
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | |||
! [[Monzo]] | |||
! [[Cent]]s | |||
! [[Color name]] | |||
! Name(s) | |||
|- | |||
| 3 | |||
| <abbr title="19383245667680019896796723/19342813113834066795298816">(52 digits)</abbr> | |||
| {{monzo| -84 53 }} | |||
| 3.62 | |||
| Tribilawa | |||
| 53-comma, [[Mercator's comma]] | |||
|- | |||
|} | |||
=== Linear temperaments === | === Linear temperaments === | ||