398edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|398}} == Theory == 398et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 1280000000/12759898..." |
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== Theory == | == Theory == | ||
398edo is only [[consistent]] to the [[5-odd-limit]], though it has a reasonable approximation to the full 13-limit using the [[patent val]], which [[tempering out|tempers out]] [[10976/10935]], [[65625/65536]], 1500625/1492992, 102760448/102515625, 102942875/102036672, and 200120949/200000000 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 59290/59049, 117649/117128, and [[131072/130977]] in the 11-limit; and [[625/624]], [[1575/1573]], [[2080/2079]], [[2200/2197]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It [[support]]s [[yarman I]], [[bisupermajor]] and [[semiquindromeda]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
398 factors into 2 × 199, | Since 398 factors into 2 × 199, 398edo has [[2edo]] and [[199edo]] as its subsets. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| 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|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|631 -398}} | | {{monzo| 631 -398 }} | ||
|{{mapping|398 631}} | | {{mapping| 398 631 }} | ||
| -0.1759 | | -0.1759 | ||
| 0.1759 | | 0.1759 | ||
| 5.83 | | 5.83 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|390625000/387420489, {{monzo|-53 10 16}} | | 390625000/387420489, {{monzo| -53 10 16 }} | ||
|{{mapping|398 631 924}} | | {{mapping| 398 631 924 }} | ||
| -0.0622 | | -0.0622 | ||
| 0.2157 | | 0.2157 | ||
| 7.15 | | 7.15 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|10976/10935, 65625/65536, | | 10976/10935, 65625/65536, 200120949/200000000 | ||
|{{mapping|398 631 924 1117}} | | {{mapping| 398 631 924 1117 }} | ||
| +0.0412 | | +0.0412 | ||
| 0.2588 | | 0.2588 | ||
| 8.58 | | 8.58 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|3025/3024, | | 3025/3024, 4000/3993, 10976/10935, 65625/65536 | ||
|{{mapping|398 631 924 1117 1377}} | | {{mapping| 398 631 924 1117 1377 }} | ||
| +0.0075 | | +0.0075 | ||
| 0.2411 | | 0.2411 | ||
| 8.00 | | 8.00 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| | | 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935 | ||
|{{mapping|398 631 924 1117 1377 1473}} | | {{mapping| 398 631 924 1117 1377 1473 }} | ||
| -0.0243 | | -0.0243 | ||
| 0.2313 | | 0.2313 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|5\398 | | 5\398 | ||
|15.08 | | 15.08 | ||
|126/125 | | 126/125 | ||
|[[Yarman]] | | [[Yarman I]] | ||
|- | |- | ||
|1 | | 1 | ||
|183\398 | | 183\398 | ||
|551.76 | | 551.76 | ||
|11/8 | | 11/8 | ||
| | | [[Emkay]] | ||
|- | |- | ||
|2 | | 2 | ||
|54\398 | | 54\398 | ||
|162.81 | | 162.81 | ||
|11/10 | | 11/10 | ||
| | | [[Bisupermajor]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||