1559edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|1559}} == Theory == 1559edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 43046721/43025920, 78125000/781218..." |
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== Theory == | == Theory == | ||
1559edo is [[consistent]] to the [[9-odd-limit]]. Using the patent val, it tempers out [[43046721/43025920]], [[78125000/78121827]] and {{monzo|32 1 -6 -7}} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit | 1559edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out|tempers out]] {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| 71 -99 37 }} (raider comma) in the 5-limit; [[43046721/43025920]], [[78125000/78121827]] and {{monzo| 32 1 -6 -7 }} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1559edo is the 246th [[prime | 1559edo is the 246th [[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|2471 -1559}} | | {{monzo| 2471 -1559 }} | ||
| {{mapping|1559 2471}} | | {{mapping| 1559 2471 }} | ||
| -0.0106 | | -0.0106 | ||
| 0.0106 | | 0.0106 | ||
| Line 30: | Line 30: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo|38 -2 -15}}, {{monzo|71 -99 37}} | | {{monzo| 38 -2 -15 }}, {{monzo| 71 -99 37 }} | ||
| {{mapping|1559 2471 3620}} | | {{mapping| 1559 2471 3620 }} | ||
| -0.0196 | | -0.0196 | ||
| 0.0155 | | 0.0155 | ||
| Line 38: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | | 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | ||
| {{mapping|1559 2471 3620 4377}} | | {{mapping| 1559 2471 3620 4377 }} | ||
| -0.0376 | | -0.0376 | ||
| 0.0339 | | 0.0339 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | | 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | ||
| {{mapping|1559 2471 3620 4377 5393}} | | {{mapping| 1559 2471 3620 4377 5393 }} | ||
| -0.0188 | | -0.0188 | ||
| 0.0483 | | 0.0483 | ||
| Line 51: | Line 51: | ||
|- | |- | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024 | | 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250 | ||
| {{mapping|1559 2471 3620 4377 5393 5769}} | | {{mapping| 1559 2471 3620 4377 5393 5769 }} | ||
| -0.0162 | | -0.0162 | ||
| 0.0445 | | 0.0445 | ||
| Line 79: | Line 79: | ||
| [[Raider]] | | [[Raider]] | ||
|} | |} | ||
<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 | ||