17edo: Difference between revisions
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ET parameter name, cleanup |
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{{Infobox ET | {{Infobox ET | ||
| Step size = 70.588¢ | | Step size = 70.588¢ | ||
| Fifth | | Fifth = 10\17 = 705.88¢ | ||
| Major 2nd = 3\17 = 212¢ | | Major 2nd = 3\17 = 212¢ | ||
| Minor 2nd = 1\17 = 71¢ | | Minor 2nd = 1\17 = 71¢ | ||
| Line 17: | Line 17: | ||
== Theory == | == Theory == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! colspan="2" | | ! colspan="2" | <!-- empty cell --> | ||
! prime 2 | ! prime 2 | ||
! prime 3 | ! prime 3 | ||
| Line 24: | Line 24: | ||
! prime 11 | ! prime 11 | ||
! prime 13 | ! prime 13 | ||
!prime 17 | ! prime 17 | ||
!prime 19 | ! prime 19 | ||
!prime 23 | ! prime 23 | ||
|- | |- | ||
! rowspan="2" | Error | ! rowspan="2" | Error | ||
! absolute ([[cent|¢]]) | ! absolute ([[cent|¢]]) | ||
| 0 | | 0.0 | ||
| | | +3.9 | ||
| | | -33.4 | ||
| | | +19.4 | ||
| | | +13.4 | ||
| | | +6.5 | ||
| | | -34.3 | ||
| | | -15.2 | ||
| | | +7.0 | ||
|- | |- | ||
![[Relative error|relative]] (%) | ! [[Relative error|relative]] (%) | ||
| 0 | | 0 | ||
| | | +6 | ||
| | | -47 | ||
| | | +27 | ||
| | | +19 | ||
| | | +9 | ||
| | | -49 | ||
| | | -21 | ||
| | | +10 | ||
|- | |- | ||
! colspan="2" |[[nearest edomapping]] | ! colspan="2" | [[nearest edomapping]] | ||
|17 | | 17 | ||
|10 | | 10 | ||
|5 | | 5 | ||
|14 | | 14 | ||
|8 | | 8 | ||
|12 | | 12 | ||
|1 | | 1 | ||
|4 | | 4 | ||
|9 | | 9 | ||
|- | |- | ||
! colspan="2" |[[fifthspan]] | ! colspan="2" | [[fifthspan]] | ||
| 0 | | 0 | ||
| | | +1 | ||
| | | -8 | ||
| | | -2 | ||
| | | -6 | ||
| | | +8 | ||
| | | -5 | ||
| | | -3 | ||
| | | +6 | ||
|}17-EDO can plausibly be treated as a 2.3.25.7.11.13.23 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers). Because the 3, 7, 11, and 13 are all sharp, it adapts well to octave shrinking; [[27edt]] (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is [[44ed6]]. | |}17-EDO can plausibly be treated as a 2.3.25.7.11.13.23 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers). Because the 3, 7, 11, and 13 are all sharp, it adapts well to octave shrinking; [[27edt]] (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is [[44ed6]]. | ||