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]] | ||
Revision as of 11:03, 21 February 2024
| ← 306edo | 307edo | 308edo → |
Theory
307edo is consistent to the 7-odd-limit, but harmonic 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.
Using the full 7-limit patent val nonetheless, the equal temperament 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
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.63 | +0.66 | +0.56 | -0.65 | -0.18 | -0.14 | -1.62 | +0.58 | -0.44 | -1.73 | +1.04 |
| Relative (%) | +41.7 | +16.8 | +14.2 | -16.7 | -4.6 | -3.5 | -41.5 | +14.9 | -11.4 | -44.1 | +26.6 | |
| Steps (reduced) |
487 (180) |
713 (99) |
862 (248) |
973 (52) |
1062 (141) |
1136 (215) |
1199 (278) |
1255 (27) |
1304 (76) |
1348 (120) |
1389 (161) | |
Subsets and supersets
307edo is the 63rd prime edo. 614edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-973 307⟩ | [⟨307 973]] | +0.1029 | 0.1030 | 2.64 |
| 2.9.5 | 32805/32768, [2 47 -65⟩ | [⟨307 973 713]] | -0.0257 | 0.2004 | 5.13 |
| 2.9.5.7 | 32805/32768, 118098/117649, 589824/588245 | [⟨307 973 713 862]] | -0.0687 | 0.1889 | 4.87 |
| 2.9.5.7.11 | 5632/5625, 8019/8000, 32805/32768, 46656/46585 | [⟨307 973 713 862 1062]] | -0.0447 | 0.1756 | 4.49 |
| 2.9.5.7.11.13 | 729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647 | [⟨307 973 713 862 1062 1136]] | -0.0311 | 0.1632 | 4.18 |
| 2.9.5.7.11.13.17 | 729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735 | [⟨307 973 713 862 1062 1136 1255]] | -0.0470 | 0.1560 | 3.99 |