400edo: Difference between revisions
m →Theory: such a giant EDO, if anyone is considering it seriously for general use, deserves analysis in higher limits, so that it should not be collapsed; however, for those interested ive collapsed prime tables > 101 |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 22: | Line 22: | ||
=== Selected intervals === | === Selected intervals === | ||
{| class="wikitable center-1" | {| class="wikitable center-1" | ||
| | |- | ||
! Step | ! Step | ||
! Eliora's Naming System | ! Eliora's Naming System | ||
| Line 81: | Line 81: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| -7 22 -12 }}, {{monzo| 47 -15 -10 }} | | {{monzo| -7 22 -12 }}, {{monzo| 47 -15 -10 }} | ||
| {{mapping| 400 634 929 }} | | {{mapping| 400 634 929 }} | ||
| | | −0.1080 | ||
| 0.1331 | | 0.1331 | ||
| 4.44 | | 4.44 | ||
| Line 101: | Line 93: | ||
| 2401/2400, 1959552/1953125, 14348907/14336000 | | 2401/2400, 1959552/1953125, 14348907/14336000 | ||
| {{mapping| 400 634 929 1123 }} | | {{mapping| 400 634 929 1123 }} | ||
| | | −0.0965 | ||
| 0.1170 | | 0.1170 | ||
| 3.90 | | 3.90 | ||
| Line 108: | Line 100: | ||
| 2401/2400, 5632/5625, 9801/9800, 46656/46585 | | 2401/2400, 5632/5625, 9801/9800, 46656/46585 | ||
| {{mapping| 400 634 929 1123 1384 }} | | {{mapping| 400 634 929 1123 1384 }} | ||
| | | −0.1166 | ||
| 0.1121 | | 0.1121 | ||
| 3.74 | | 3.74 | ||
| Line 115: | Line 107: | ||
| 676/675, 1001/1000, 1716/1715, 4096/4095, 39366/39325 | | 676/675, 1001/1000, 1716/1715, 4096/4095, 39366/39325 | ||
| {{mapping| 400 634 929 1123 1384 1480 }} | | {{mapping| 400 634 929 1123 1384 1480 }} | ||
| | | −0.0734 | ||
| 0.1407 | | 0.1407 | ||
| 4.69 | | 4.69 | ||
| Line 122: | Line 114: | ||
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 4096/4095 | | 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 4096/4095 | ||
| {{mapping| 400 634 929 1123 1384 1480 1635 }} | | {{mapping| 400 634 929 1123 1384 1480 1635 }} | ||
| | | −0.0645 | ||
| 0.1321 | | 0.1321 | ||
| 4.40 | | 4.40 | ||
| Line 129: | Line 121: | ||
| 676/675, 936/935, 969/968, 1001/1000, 1156/1155, 1216/1215, 1716/1715 | | 676/675, 936/935, 969/968, 1001/1000, 1156/1155, 1216/1215, 1716/1715 | ||
| {{mapping| 400 634 929 1123 1384 1480 1635 1699 }} | | {{mapping| 400 634 929 1123 1384 1480 1635 1699 }} | ||
| | | −0.0413 | ||
| 0.1380 | | 0.1380 | ||
| 4.60 | | 4.60 | ||
{{comma basis end}} | |||
* 400et has lower absolute errors than any previous equal temperaments in the 17- and 19-limit. It is the first to beat [[354edo|354]] in the 17-limit, and [[311edo|311]] in the 19-limit; it is bettered by [[422edo|422]] in either subgroup. | * 400et has lower absolute errors than any previous equal temperaments in the 17- and 19-limit. It is the first to beat [[354edo|354]] in the 17-limit, and [[311edo|311]] in the 19-limit; it is bettered by [[422edo|422]] in either subgroup. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 181: | Line 167: | ||
|- | |- | ||
| 5 | | 5 | ||
| 123\400<br>(37\400) | | 123\400<br />(37\400) | ||
| 369.00<br>(111.00) | | 369.00<br />(111.00) | ||
| 1024/891<br>(16/15) | | 1024/891<br />(16/15) | ||
| [[Quintosec]] | | [[Quintosec]] | ||
|- | |- | ||
| 10 | | 10 | ||
| 83\400<br>(3\400) | | 83\400<br />(3\400) | ||
| 249.00<br>(9.00) | | 249.00<br />(9.00) | ||
| 15/13<br>(176/175) | | 15/13<br />(176/175) | ||
| [[Decoid]] | | [[Decoid]] | ||
|- | |- | ||
| 80 | | 80 | ||
| 166\400<br>(1\400) | | 166\400<br />(1\400) | ||
| 498.00<br>(3.00) | | 498.00<br />(3.00) | ||
| 4/3<br>(245/243) | | 4/3<br />(245/243) | ||
| [[Octogintic]] | | [[Octogintic]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Scales == | == Scales == | ||