1889edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1889edo is strong in the [[23-limit]], though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament. | 1889edo is strong in the [[23-limit]], though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament. | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.3 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|2994 -1889}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|1889 2994}} | ! rowspan="2" | [[Mapping]] | ||
| | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo|2994 -1889}} | |||
| {{mapping|1889 2994}} | |||
| −0.0012 | |||
| 0.0012 | | 0.0012 | ||
| 0.19 | | 0.19 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|54 -37 2}}, {{monzo|-66 -36 53}} | | {{monzo|54 -37 2}}, {{monzo|-66 -36 53}} | ||
|{{mapping|1889 2994 4386}} | | {{mapping|1889 2994 4386}} | ||
| +0.0104 | | +0.0104 | ||
| 0.0163 | | 0.0163 | ||
| 2.57 | | 2.57 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 3955078125/3954653486, {{monzo|-57 16 10 3}} | | 4375/4374, 3955078125/3954653486, {{monzo|-57 16 10 3}} | ||
|{{mapping|1889 2994 4386 5303}} | | {{mapping|1889 2994 4386 5303}} | ||
| +0.0131 | | +0.0131 | ||
| 0.0149 | | 0.0149 | ||
| 2.35 | | 2.35 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|4375/4374, 151263/151250, 820125/819896, 1879453125/1879048192 | | 4375/4374, 151263/151250, 820125/819896, 1879453125/1879048192 | ||
|{{mapping|1889 2994 4386 5303 6535}} | | {{mapping|1889 2994 4386 5303 6535}} | ||
| +0.0055 | | +0.0055 | ||
| 0.0201 | | 0.0201 | ||
| 3.16 | | 3.16 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|4375/4374, 4225/4224, 6656/6655, 4100625/4100096, 151263/151250 | | 4375/4374, 4225/4224, 6656/6655, 4100625/4100096, 151263/151250 | ||
|{{mapping|1889 2994 4386 5303 6535 6990}} | | {{mapping|1889 2994 4386 5303 6535 6990}} | ||
| +0.0084 | | +0.0084 | ||
| 0.0194 | | 0.0194 | ||
| 3.05 | | 3.05 | ||
|- | |- | ||
|2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
|4375/4374, 12376/12375, 4225/4224, 14400/14399, 14875/14872, 194481/194480 | | 4375/4374, 12376/12375, 4225/4224, 14400/14399, 14875/14872, 194481/194480 | ||
|{{mapping|1889 2994 4386 5303 6535 6990 7721}} | | {{mapping|1889 2994 4386 5303 6535 6990 7721}} | ||
| +0.0120 | | +0.0120 | ||
| 0.0200 | | 0.0200 | ||
| 3.15 | | 3.15 | ||
|- | |- | ||
|2.3.5.7.11.13.17.19 | | 2.3.5.7.11.13.17.19 | ||
|4375/4374, 12376/12375, 5985/5984, 4225/4224, 14400/14399, 6175/6174, 61965/61952 | | 4375/4374, 12376/12375, 5985/5984, 4225/4224, 14400/14399, 6175/6174, 61965/61952 | ||
|{{mapping|1889 2994 4386 5303 6535 6990 7721 8024}} | | {{mapping|1889 2994 4386 5303 6535 6990 7721 8024}} | ||
| +0.0167 | | +0.0167 | ||
| 0.0226 | | 0.0226 | ||
| Line 73: | Line 74: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Generator | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br> | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|392\1889 | | 392\1889 | ||
|249.021 | | 249.021 | ||
|{{monzo|-26 18 1}} | | {{monzo|-26 18 1}} | ||
|[[Monzismic]] | | [[Monzismic]] | ||
|- | |- | ||
|1 | | 1 | ||
|707\1889 | | 707\1889 | ||
|449.127 | | 449.127 | ||
|35/27 | | 35/27 | ||
|[[Semidimi]] | | [[Semidimi]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||