424edo: Difference between revisions

424edo is [[consistent]] to the [[9-odd-limit]], but the [[harmonic]] [[5/1|5]] is about halfway between its steps. It is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as [[212edo]]. The approximation to [[11/1|11]], although closer to just than 212edo's, tends sharp, so its improvement is debatable. All things considered, a 2.3.13.17.19.23 [[subgroup]] interpretation with optional additions of 7, 11, or both, seems most reasonable.  

Since 424 factors into 2³ × 53, 424edo has subset edos {{EDOs| 2, 4, 8, 53, 106, and 212 }}. [[848edo]], which doubles it, gives a good correction to the harmonic 5.  

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br>8ve Stretch (¢)

! colspan="2" | Tuning Error

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

| 2.3.7.11

| 41503/41472, 117649/117128, {{monzo| -26 19 1 -2 }}

| {{mapping| 424 672 1190 1467 }}

| +0.0499

| 0.1747

| 6.17