719edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|719}} == Theory == 719edo is only consistent to the 3-odd-limit and the error of its harmonic 3 is quite large. Its harmonics [..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
719edo is only [[consistent]] to the [[3-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Its harmonics [[5/1|5]] and [[7/1|7]] are also about halfway its steps. | 719edo is only [[consistent]] to the [[3-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Its harmonics [[5/1|5]] and [[7/1|7]] are also about halfway between its steps. Its distinction, however, is that it is the largest EDO to temper out the [[15625/15552|kleisma (15625/15552)]] and therefore [[support]] [[hanson]] in its patent val; it also supports the extension [[marfifths]] that tempers out the hemimage comma, [[10976/10935]] in addition, and in fact is the [[optimal patent val]] for marfifths. For other purposes than tempering out the kleisma, it can be used in the 2.9.15.21.11.17.19.23.29 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[3025/3024]], [[2376/2375]], 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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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" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.9 | | 2.9 | ||
| {{monzo|-2279 719}} | | {{monzo|-2279 719}} | ||
| {{mapping|719 2279}} | | {{mapping|719 2279}} | ||
| 0.0464 | | +0.0464 | ||
| 0.0464 | | 0.0464 | ||
| 2.78 | | 2.78 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "Mar-A-Lago & FBI-Raid" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3NhTTk12RA51RgPqtZ70lc Spotify] | [https://francium223.bandcamp.com/track/mar-a-lago-fbi-raid Bandcamp] | [https://www.youtube.com/watch?v=nE16ZpLWUqo YouTube] – in Marfifths, 719edo tuning | |||
{{todo|inline=1|explain its xenharmonic value}} | |||