17edo: Difference between revisions
→Theory: request clarification |
m →Regular temperament properties: style and comma names |
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{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 415: | Line 415: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 27 -17 }} | | {{monzo| 27 -17 }} | ||
| | | {{mapping| 17 27 }} | ||
| −1.24 | | −1.24 | ||
| 1.24 | | 1.24 | ||
| Line 422: | Line 422: | ||
| 2.3.7 | | 2.3.7 | ||
| 64/63, 17496/16807 | | 64/63, 17496/16807 | ||
| | | {{mapping| 17 27 48 }} | ||
| −3.13 | | −3.13 | ||
| 2.85 | | 2.85 | ||
| Line 429: | Line 429: | ||
| 2.3.7.11 | | 2.3.7.11 | ||
| 64/63, 99/98, 243/242 | | 64/63, 99/98, 243/242 | ||
| | | {{mapping| 17 27 48 59 }} | ||
| −3.31 | | −3.31 | ||
| 2.49 | | 2.49 | ||
| Line 436: | Line 436: | ||
| 2.3.7.11.13 | | 2.3.7.11.13 | ||
| 64/63, 78/77, 99/98, 144/143 | | 64/63, 78/77, 99/98, 144/143 | ||
| | | {{mapping| 17 27 48 59 63 }} | ||
| −3.00 | | −3.00 | ||
| 2.31 | | 2.31 | ||
| 3.28 | | 3.28 | ||
|} | |} | ||
* 17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next equal temperaments doing better in these subgroups are [[41edo|41]] and [[207edo|207]], respectively. | |||
17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next equal temperaments doing better in these subgroups are [[41edo|41]] and [[207edo|207]], respectively. | |||
=== Uniform maps === | === Uniform maps === | ||
| Line 452: | Line 451: | ||
{| class="commatable wikitable center-all left-3 right-4 left-6" | {| class="commatable wikitable center-all left-3 right-4 left-6" | ||
|- | |- | ||
! [[Harmonic limit|Prime<br | ! [[Harmonic limit|Prime<br>limit]] | ||
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
| Line 527: | Line 526: | ||
| 9.6880 | | 9.6880 | ||
| Saluzo | | Saluzo | ||
| Pentacircle | | Pentacircle comma | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 575: | Line 574: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator | ! Generator | ||
! Cents | ! Cents | ||
! Associated<br | ! Associated<br>ratio | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| Line 603: | Line 602: | ||
| 352.94 | | 352.94 | ||
| 11/9 | | 11/9 | ||
| [[Suhajira]] / [[neutrominant]] (17c) / [[beatles]] (17c) / [[dicotic]] (17) <br | | [[Suhajira]] / [[neutrominant]] (17c) / [[beatles]] (17c) / [[dicotic]] (17) <br>[[Hemif]] / [[mohamaq]] (17c) / [[salsa]] (17) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 621: | Line 620: | ||
| 564.71 | | 564.71 | ||
| 7/5 | | 7/5 | ||
| [[Lee]] / [[liese]] (17c) / [[pycnic]] (17)<br | | [[Lee]] / [[liese]] (17c) / [[pycnic]] (17)<br>[[Progress]] (17c) | ||
|} | |} | ||
{{todo|complete table|comment=add warts for every temperament|inline=1}} | {{todo|complete table|comment=add warts for every temperament|inline=1}} | ||