307edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|307}} | {{EDO intro|307}} | ||
== Theory == | == Theory == | ||
307edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. It can be considered in either the 2.9.5.7 [[subgroup]] or the 2.9.15.21 subgroup, but the former is more flexible as it lends itself to an [[extension]] to the 2.9.5.7.11.13.17.19.23. | |||
===Odd harmonics=== | |||
Using the full 7-limit [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit, and in the 11-limit extension, [[3388/3375]], [[6250/6237]], 15488/15435, [[16384/16335]], and 43923/43904. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|307}} | {{Harmonics in equal|307}} | ||
===Subsets and supersets=== | |||
=== Subsets and supersets === | |||
307edo is the 63rd [[prime edo]]. [[614edo]], which doubles it, gives a good correction to the harmonic 3. | 307edo is the 63rd [[prime edo]]. [[614edo]], which doubles it, gives a good correction to the harmonic 3. | ||
==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]] | ||
| Line 15: | Line 21: | ||
! colspan="2" |Tuning Error | ! colspan="2" |Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.9 | | 2.9 | ||
|{{monzo|-973 307}} | | {{monzo| -973 307 }} | ||
|{{ | | {{mapping| 307 973 }} | ||
| +0.1029 | | +0.1029 | ||
| 0.1030 | | 0.1030 | ||
| 2.64 | | 2.64 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|32805/32768, {{monzo|2 47 -65}} | | 32805/32768, {{monzo| 2 47 -65 }} | ||
|{{ | | {{mapping|307 973 713 }} | ||
| -0.0257 | | -0.0257 | ||
| 0.2004 | | 0.2004 | ||
| 5.13 | | 5.13 | ||
|- | |- | ||
|2.9.5.7 | | 2.9.5.7 | ||
|32805/32768, 118098/117649, 589824/588245 | | 32805/32768, 118098/117649, 589824/588245 | ||
|{{ | | {{mapping| 307 973 713 862 }} | ||
| -0.0687 | | -0.0687 | ||
| 0.1889 | | 0.1889 | ||
| 4.87 | | 4.87 | ||
|- | |- | ||
|2.9.5.7.11 | | 2.9.5.7.11 | ||
|5632/5625, 8019/8000, 32805/32768, 46656/46585 | | 5632/5625, 8019/8000, 32805/32768, 46656/46585 | ||
|{{ | | {{mapping| 307 973 713 862 1062 }} | ||
| -0.0447 | | -0.0447 | ||
| 0.1756 | | 0.1756 | ||
| 4.49 | | 4.49 | ||
|- | |- | ||
|2.9.5.7.11.13 | | 2.9.5.7.11.13 | ||
|729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647 | | 729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647 | ||
|{{ | | {{mapping| 307 973 713 862 1062 1136 }} | ||
| -0.0311 | | -0.0311 | ||
| 0.1632 | | 0.1632 | ||
| 4.18 | | 4.18 | ||
|- | |- | ||
|2.9.5.7.11.13.17 | | 2.9.5.7.11.13.17 | ||
|729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735 | | 729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735 | ||
|{{ | | {{mapping| 307 973 713 862 1062 1136 1255 }} | ||
| -0.0470 | | -0.0470 | ||
| 0.1560 | | 0.1560 | ||
| Line 63: | Line 69: | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Broken Music From A Broken Mind" from ''Melancholie'' (2023) [https://open.spotify.com/track/3FBm2hcuQwuH5rNjQ9IOZ9 Spotify] | [https://francium223.bandcamp.com/track/broken-music-from-a-broken-mind Bandcamp] | [https://www.youtube.com/watch?v=CKq9y6qk10g YouTube] | * "Broken Music From A Broken Mind" from ''Melancholie'' (2023) – [https://open.spotify.com/track/3FBm2hcuQwuH5rNjQ9IOZ9 Spotify] | [https://francium223.bandcamp.com/track/broken-music-from-a-broken-mind Bandcamp] | [https://www.youtube.com/watch?v=CKq9y6qk10g YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||