473edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
473edo is in[[consistent]] to the [[5-odd-limit]] with large errors on both [[harmonic]]s [[3/1|3]] and [[5/1|5]]. It is most notable for [[tempering out]] the kleisma, [[15625/15552]], in the 5-limit and [[5120/5103]] in the 7-limit, providing the [[optimal patent val]] for the 7-limit [[countercata]] temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|473}} | |||
=== Subsets and supersets === | |||
Since 473 factors into {{factorization|473}}, 473edo contains [[11edo]] and [[43edo]] as subsets. | |||
[[Category:Countercata]] | [[Category:Countercata]] | ||
[[Category: | [[Category:Kleismic]] | ||
Latest revision as of 15:00, 20 February 2025
| ← 472edo | 473edo | 474edo → |
473 equal divisions of the octave (abbreviated 473edo or 473ed2), also called 473-tone equal temperament (473tet) or 473 equal temperament (473et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 473 equal parts of about 2.54 ¢ each. Each step represents a frequency ratio of 21/473, or the 473rd root of 2.
473edo is inconsistent to the 5-odd-limit with large errors on both harmonics 3 and 5. It is most notable for tempering out the kleisma, 15625/15552, in the 5-limit and 5120/5103 in the 7-limit, providing the optimal patent val for the 7-limit countercata temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.79 | -0.69 | +0.31 | -0.95 | -0.79 | -0.78 | +0.10 | -0.94 | -0.68 | +1.10 | +0.90 |
| Relative (%) | +31.3 | -27.2 | +12.1 | -37.5 | -31.1 | -30.8 | +4.1 | -37.0 | -27.0 | +43.4 | +35.5 | |
| Steps (reduced) |
750 (277) |
1098 (152) |
1328 (382) |
1499 (80) |
1636 (217) |
1750 (331) |
1848 (429) |
1933 (41) |
2009 (117) |
2078 (186) |
2140 (248) | |
Subsets and supersets
Since 473 factors into 11 × 43, 473edo contains 11edo and 43edo as subsets.