1193edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|1193}} == Theory == 1193et tempers out 2401/2400 in the 7-limit; 117440512/117406179, 26214400/26198073, 151263/151250, 369140625/369098752,..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1193}} | {{EDO intro|1193}} | ||
== Theory == | == Theory == | ||
1193et tempers out [[2401/2400]] in the 7-limit; [[117440512/117406179]], 26214400/26198073, 151263/151250, 369140625/369098752, 537109375/536870912, [[3025/3024]], [[41503/41472]] and 781258401/781250000 in the 11-limit. It | 1193et tempers out [[2401/2400]] in the 7-limit; [[117440512/117406179]], 26214400/26198073, 151263/151250, 369140625/369098752, 537109375/536870912, [[3025/3024]], [[41503/41472]] and 781258401/781250000 in the 11-limit. It supports the [[gross]] temperament. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|1193}} | |||
=== Subsets and supersets === | |||
1193edo is the 196th [[prime edo]]. | 1193edo is the 196th [[prime edo]]. | ||
==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|1891 -1193}} | | {{monzo| 1891 -1193 }} | ||
|{{val|1193 1891}} | | {{val| 1193 1891 }} | ||
| -0.0443 | | -0.0443 | ||
| 0.0443 | | 0.0443 | ||
| 4.40 | | 4.40 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|10 -40 -23}}, {{monzo|77 -31 -12}} | | {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }} | ||
|{{val|1193 1891 2770}} | | {{val| 1193 1891 2770 }} | ||
| -0.0209 | | -0.0209 | ||
| 0.0491 | | 0.0491 | ||
| 4.88 | | 4.88 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, {{monzo|-13 -12 15 -1}}, {{monzo|-18 -13 13 3}}, {{monzo|36 -16 -7 2}} | | 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| -18 -13 13 3 }}, {{monzo| 36 -16 -7 2 }} | ||
|{{val|1193 1891 2770 3349}} | | {{val|1193 1891 2770 3349}} | ||
| -0.000028 | | -0.000028 | ||
| 0.0558 | | 0.0558 | ||
| 5.55 | | 5.55 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|2401/2400, 3025/3024, 41503/41472, 151263/151250, 26214400/26198073 | | 2401/2400, 3025/3024, 41503/41472, 151263/151250, 26214400/26198073 | ||
|{{val|1193 1891 2770 3349 4127}} | | {{val| 1193 1891 2770 3349 4127 }} | ||
| +0.0059 | | +0.0059 | ||
| 0.0513 | | 0.0513 | ||
| 5.10 | | 5.10 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|2401/2400, 3025/3024, 154880/154791, 1071875/1070784, 1960000/1957527, 5175625/5174928 | | 2401/2400, 3025/3024, 154880/154791, 1071875/1070784, 1960000/1957527, 5175625/5174928 | ||
|{{val|1193 1891 2770 3349 4127 4415}} | | {{val| 1193 1891 2770 3349 4127 4415 }} | ||
| -0.0121 | | -0.0121 | ||
| 0.0617 | | 0.0617 | ||
| 6.13 | | 6.13 | ||
|- | |- | ||
|2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
|2401/2400, 2431/2430, 2601/2600, 3025/3024, 8624/8619, 12376/12375, 37180/37179, 42500/42471, 47432/47385, 122825/122694, 154880/154791 | | 2401/2400, 2431/2430, 2601/2600, 3025/3024, 8624/8619, 12376/12375, 37180/37179, 42500/42471, 47432/47385, 122825/122694, 154880/154791 | ||
|{{val|1193 1891 2770 3349 4127 4415 4876}} | | {{val|1193 1891 2770 3349 4127 4415 4876}} | ||
| +0.0017 | | +0.0017 | ||
| 0.0664 | | 0.0664 | ||
| Line 64: | Line 69: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator<br>( | ! Generator<br>(Reduced) | ||
! Cents<br>( | ! Cents<br>(Reduced) | ||
! Associated<br> | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|91\1193 | | 91\1193 | ||
|91.533948 | | 91.533948 | ||
|{{monzo|144 -22 -47}} | | {{monzo|144 -22 -47}} | ||
|Gross | | Gross | ||
|} | |} | ||