1553edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608. | 1553edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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1553edo is the 245th [[prime edo]]. 3106edo, which doubles it, provides a good correction to the harmonic 3. | 1553edo is the 245th [[prime edo]]. 3106edo, which doubles it, provides 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]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 23: | Line 25: | ||
| 2.9 | | 2.9 | ||
| {{monzo| 4923 -1553 }} | | {{monzo| 4923 -1553 }} | ||
| {{ | | {{mapping| 1553 4923 }} | ||
| | | −0.0130 | ||
| 0.0130 | | 0.0130 | ||
| 1.68 | | 1.68 | ||
| Line 30: | Line 32: | ||
| 2.9.5 | | 2.9.5 | ||
| {{monzo| 93 -33 5 }}, {{monzo| -36 -26 51 }} | | {{monzo| 93 -33 5 }}, {{monzo| -36 -26 51 }} | ||
| {{ | | {{mapping| 1553 4923 3606 }} | ||
| | | −0.0137 | ||
| 0.0106 | | 0.0106 | ||
| 1.38 | | 1.38 | ||
| Line 37: | Line 39: | ||
| 2.9.5.7 | | 2.9.5.7 | ||
| {{monzo| -5 5 5 -8 }}, {{monzo| 2 -10 14 -1 }}, {{monzo| 37 1 -4 -11 }} | | {{monzo| -5 5 5 -8 }}, {{monzo| 2 -10 14 -1 }}, {{monzo| 37 1 -4 -11 }} | ||
| {{ | | {{mapping| 1553 4923 3606 4360 }} | ||
| | | −0.0225 | ||
| 0.0178 | | 0.0178 | ||
| 2.31 | | 2.31 | ||
| Line 44: | Line 46: | ||
| 2.9.5.7.13 | | 2.9.5.7.13 | ||
| 4096/4095, 140625/140608, 28829034/28824005, {{monzo| 4 10 -9 0 -4 }} | | 4096/4095, 140625/140608, 28829034/28824005, {{monzo| 4 10 -9 0 -4 }} | ||
| {{ | | {{mapping| 1553 4923 3606 4360 5372 }} | ||
| | | −0.0271 | ||
| 0.0184 | | 0.0184 | ||
| 2.38 | | 2.38 | ||
|} | |} | ||
==Music== | |||
* [https://www.youtube.com/watch?v=gdxwRJSLyvw Stumbling Over Mystery] | == Music == | ||
; [[Francium]] | |||
* [https://www.youtube.com/watch?v=gdxwRJSLyvw ''Stumbling Over Mystery''] (2023) | |||
[[Category:Listen]] | |||