1051edo: Difference between revisions
→Theory: plz note that subgroup is part of RTT perspective. |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup. | 1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup. | ||
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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" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 25: | Line 27: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 1666 -1051 }} | | {{monzo| 1666 -1051 }} | ||
| {{ | | {{mapping| 1051 1666 }} | ||
| | | −0.0736 | ||
| 0.0736 | | 0.0736 | ||
| 6.45 | | 6.45 | ||
| Line 32: | Line 34: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| -68 18 17 }}, {{monzo| -26 -29 31 }} | | {{monzo| -68 18 17 }}, {{monzo| -26 -29 31 }} | ||
| {{ | | {{mapping| 1051 1666 2440 }} (1051) | ||
| +0.0077 | | +0.0077 | ||
| 0.1298 | | 0.1298 | ||
| Line 39: | Line 41: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 40 7 -22 }}, {{monzo| 63 -50 7 }} | | {{monzo| 40 7 -22 }}, {{monzo| 63 -50 7 }} | ||
| {{ | | {{mapping| 1051 1666 2441 }} (1051c) | ||
| | | −0.1562 | ||
| 0.1313 | | 0.1313 | ||
| 11.5 | | 11.5 | ||
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=== 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 | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
--> | --> | ||
== | == Music == | ||
*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning | |||
[[Category:Listen]] | |||