1429edo: Difference between revisions
ArrowHead294 (talk | contribs) m Partial undo |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 5: | Line 5: | ||
1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight. | 1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight. | ||
It [[tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament. | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 28: | Line 28: | ||
| {{monzo| 2265 -1429 }} | | {{monzo| 2265 -1429 }} | ||
| {{mapping| 1429 2265 }} | | {{mapping| 1429 2265 }} | ||
| | | −0.0235 | ||
| 0.0234 | | 0.0234 | ||
| 2.80 | | 2.80 | ||
| Line 35: | Line 35: | ||
| {{monzo| 39 -29 3 }}, {{monzo| -66 -36 53 }} | | {{monzo| 39 -29 3 }}, {{monzo| -66 -36 53 }} | ||
| {{mapping| 1429 2265 3318 }} | | {{mapping| 1429 2265 3318 }} | ||
| | | −0.0114 | ||
| 0.0257 | | 0.0257 | ||
| 3.06 | | 3.06 | ||
| Line 42: | Line 42: | ||
| 4375/4374, {{monzo| 26 4 -3 -14 }}, {{monzo| 40 -22 -1 -1 }} | | 4375/4374, {{monzo| 26 4 -3 -14 }}, {{monzo| 40 -22 -1 -1 }} | ||
| {{mapping| 1429 2265 3318 4012 }} | | {{mapping| 1429 2265 3318 4012 }} | ||
| | | −0.0302 | ||
| 0.0395 | | 0.0395 | ||
| 4.70 | | 4.70 | ||
| Line 49: | Line 49: | ||
| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172 | | 4375/4374, 131072/130977, 759375/758912, 3294225/3294172 | ||
| {{mapping| 1429 2265 3318 4012 4944 }} | | {{mapping| 1429 2265 3318 4012 4944 }} | ||
| | | −0.0471 | ||
| 0.0488 | | 0.0488 | ||
| 5.81 | | 5.81 | ||
| Line 56: | Line 56: | ||
| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172 | | 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172 | ||
| {{mapping| 1429 2265 3318 4012 4944 5288 }} | | {{mapping| 1429 2265 3318 4012 4944 5288 }} | ||
| | | −0.0420 | ||
| 0.0460 | | 0.0460 | ||
| 5.48 | | 5.48 | ||
| Line 63: | Line 63: | ||
| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045 | | 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045 | ||
| {{mapping| 1429 2265 3318 4012 4944 5288 5841 }} | | {{mapping| 1429 2265 3318 4012 4944 5288 5841 }} | ||
| | | −0.0364 | ||
| 0.0447 | | 0.0447 | ||
| 5.32 | | 5.32 | ||
| Line 90: | Line 90: | ||
| [[Trillium]] | | [[Trillium]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
| Line 97: | Line 97: | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] | [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] | [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] | * "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] | [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] | [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning | ||
[[Category:Listen]] | [[Category:Listen]] | ||