271edt: Difference between revisions
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271edt acts as a stretched version of [[171edo]], with the same val and commas up to the [[19-limit]], but with [[3/1]] instead of [[2/1]] just. The octave is stretched by about 0.13 cents, which brings harmonics [[5/1|5]] and [[7/1|7]] much closer to just, though harmonics [[11/1|11]], [[13/1|13]], and [[17/1|17]] become worse. | 271edt acts as a stretched version of [[171edo]], with the same val and commas up to the [[19-limit]], but with [[3/1]] instead of [[2/1]] just. The octave is stretched by about 0.13 cents, which brings harmonics [[5/1|5]] and [[7/1|7]] much closer to just, though harmonics [[11/1|11]], [[13/1|13]], and [[17/1|17]] become worse. | ||
Considered as a no-twos system, 271edt does very well in the [[3.5.7 subgroup|3.5.7- | Considered as a no-twos system, 271edt does very well in the [[3.5.7 subgroup|3.5.7-subgroup]]. Harmonic [[11/1|11]] is almost exactly halfway between its steps, suggesting the use of [[542edt]] in the [[3.5.7.11 subgroup|3.5.7.11-subgroup]]. | ||
{{Harmonics in equal|271|3|intervals=prime}} | {{Harmonics in equal|271|3|intervals=prime}} | ||
Latest revision as of 22:44, 8 April 2026
| ← 270edt | 271edt | 272edt → |
271 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 271edt or 271ed3), is a nonoctave tuning system that divides the interval of 3/1 into 271 equal parts of about 7.02 ¢ each. Each step represents a frequency ratio of 31/271, or the 271st root of 3.
Theory
271edt acts as a stretched version of 171edo, with the same val and commas up to the 19-limit, but with 3/1 instead of 2/1 just. The octave is stretched by about 0.13 cents, which brings harmonics 5 and 7 much closer to just, though harmonics 11, 13, and 17 become worse.
Considered as a no-twos system, 271edt does very well in the 3.5.7-subgroup. Harmonic 11 is almost exactly halfway between its steps, suggesting the use of 542edt in the 3.5.7.11-subgroup.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.13 | +0.00 | -0.05 | -0.05 | +3.51 | +2.05 | +0.83 | -2.24 | -3.14 | +2.62 | -0.55 |
| Relative (%) | +1.8 | +0.0 | -0.8 | -0.7 | +50.0 | +29.2 | +11.8 | -31.9 | -44.8 | +37.3 | -7.8 | |
| Steps (reduced) |
171 (171) |
271 (0) |
397 (126) |
480 (209) |
592 (50) |
633 (91) |
699 (157) |
726 (184) |
773 (231) |
831 (18) |
847 (34) | |