29edo: Difference between revisions
→Modern renderings: Erroll Garner's ''Misty'' (1954) – microtonal cover in 29edo by Bryan Deister (2026) |
Septischisma |
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== Approximation to JI == | == Approximation to JI == | ||
[[File:29ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.| | === Selected 13-limit intervals === | ||
[[File:29ed2-002.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|29edo’s strengths in the 13-limit, using an odd-limit of 45 and a 5.7-cent error threshold. Pythagorean thirds and 5-odd-limit intervals are also included for reference, even where they exceed this threshold.]] | |||
=== Interval mappings === | === Interval mappings === | ||
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* 29et (29g val) has a lower relative error than any previous equal temperament in the [[23-limit]]. The next equal temperament doing better in this subgroup is [[46edo|46]]. | * 29et (29g val) has a lower relative error than any previous equal temperament in the [[23-limit]]. The next equal temperament doing better in this subgroup is [[46edo|46]]. | ||
* 29et does well in the no-17 [[19-limit]] and no-17 23-limit, being consistent to the no-17 [[23-odd-limit]]. However, [[15edo]] is lower in relative error in both these subgroups than 29. | * 29et does relatively well in the no-17 [[19-limit]] and no-17 23-limit, being consistent to the no-17 [[23-odd-limit]]. However, [[15edo]] is lower in relative error in both these subgroups than 29. | ||
=== Commas === | === Commas === | ||
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| 7.71 | | 7.71 | ||
| Ruyoyo | | Ruyoyo | ||
| Marvel comma | | Marvel comma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 5.76 | | 5.76 | ||
| Saruyo | | Saruyo | ||
| | | Aberschisma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 3.80 | | 3.80 | ||
| Sasaru | | Sasaru | ||
| [[ | | [[Septischisma]] | ||
|- | |- | ||
| 11 | | 11 | ||
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* [[Blackville]] / [[Marvel dipentatonic]]: 2 3 4 3 2 3 4 3 2 3] | * [[Blackville]] / [[Marvel dipentatonic]]: 2 3 4 3 2 3 4 3 2 3] | ||
* Baobab{{idio}} (approximated from [[30afdo]]): 8 4 5 4 4 4 | * Baobab{{idio}} (approximated from [[30afdo]]): 8 4 5 4 4 4 | ||
== Chords == | |||
29edo offers an excellent approximation of the 10:11:13:14:15 chord, whose intervals above the root are 11/10, 13/10, 7/5, and 3/2. Mapped to 0–4–11–14–17, this chord can be repeated indefinitely at successive fifths. Its utonal counterpart, 1/(15:14:13:11:10), has intervals of 15/14, 15/13, 15/11, and 3/2 above the root and is mapped to 0–3–6–13–17. | |||
The [[12L 5s]] MOS scale, in the rotation 2 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1, provides a useful framework for exploring this chord though successive transpositions by a fifth. It accommodates four successive statements of the 10:11:13:14 core, each transposed up a tempered fifth (3/2) from the preceding one. | |||
== Instruments == | == Instruments == | ||