230edt: Difference between revisions
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== Harmonics == | 230edt is related to [[145edo]], but with the [[3/1|perfect twelfth]] instead of the [[2/1|octave]] tuned just. It is [[consistent]] to the [[integer limit|13-integer-limit]]. In comparison, 145edo is only consistent to the 12-integer-limit. | ||
{{Harmonics in equal | |||
| | === Harmonics === | ||
| | {{Harmonics in equal|230|3|1|intervals=integer|columns=11}} | ||
| | {{Harmonics in equal|230|3|1|intervals=integer|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 230edt (continued)}} | ||
}} | |||
{{Harmonics in equal | === Subsets and supersets === | ||
| | Since 230 factors into primes as {{nowrap| 2 × 5 × 23 }}, 230edt contains subset edts {{EDs|equave=t| 2, 5, 10, 23, 46, and 115 }}. | ||
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| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 13:26, 24 March 2025
| ← 229edt | 230edt | 231edt → |
230 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 230edt or 230ed3), is a nonoctave tuning system that divides the interval of 3/1 into 230 equal parts of about 8.27 ¢ each. Each step represents a frequency ratio of 31/230, or the 230th root of 3.
230edt is related to 145edo, but with the perfect twelfth instead of the octave tuned just. It is consistent to the 13-integer-limit. In comparison, 145edo is only consistent to the 12-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.94 | +0.00 | -1.88 | +0.46 | -0.94 | -3.19 | -2.82 | +0.00 | -0.48 | -0.09 | -1.88 |
| Relative (%) | -11.4 | +0.0 | -22.8 | +5.6 | -11.4 | -38.6 | -34.2 | +0.0 | -5.8 | -1.1 | -22.8 | |
| Steps (reduced) |
145 (145) |
230 (0) |
290 (60) |
337 (107) |
375 (145) |
407 (177) |
435 (205) |
460 (0) |
482 (22) |
502 (42) |
520 (60) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.12 | -4.13 | +0.46 | -3.77 | -1.22 | -0.94 | -3.58 | -1.42 | -3.19 | -1.04 | -3.57 | -2.82 |
| Relative (%) | +1.5 | -50.0 | +5.6 | -45.5 | -14.7 | -11.4 | -43.3 | -17.2 | -38.6 | -12.5 | -43.1 | -34.2 | |
| Steps (reduced) |
537 (77) |
552 (92) |
567 (107) |
580 (120) |
593 (133) |
605 (145) |
616 (156) |
627 (167) |
637 (177) |
647 (187) |
656 (196) |
665 (205) | |
Subsets and supersets
Since 230 factors into primes as 2 × 5 × 23, 230edt contains subset edts 2, 5, 10, 23, 46, and 115.