677edo: Difference between revisions
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Tristanbay (talk | contribs) Created page for 677edo Tags: Visual edit Mobile edit Mobile web edit |
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{{Infobox ET|677edo}} | |||
'''677 equal divisions of the octave''' (677edo) is a tuning system with notes that are about 1.77¢ apart. While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep. | '''677 equal divisions of the octave''' (677edo) is a tuning system with notes that are about 1.77¢ apart. While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep. | ||
{{Harmonics in equal | |||
| steps = 677 | |||
| num = 2 | |||
| denom = 1 | |||
| columns = 9 | |||
| start = 1 | |||
| prec = 2 | |||
| title = Approximation of prime harmonics in 677edo | |||
| intervals = prime | |||
}} | |||
Revision as of 09:36, 15 November 2023
| ← 676edo | 677edo | 678edo → |
677 equal divisions of the octave (677edo) is a tuning system with notes that are about 1.77¢ apart. While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several metallic ratios. Among those, it tunes acoustic phi (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.03 | +0.10 | +0.75 | -0.06 | -0.35 | -0.38 | +0.27 | -0.80 |
| Relative (%) | +0.0 | -2.0 | +5.5 | +42.1 | -3.5 | -19.8 | -21.2 | +15.3 | -45.1 | |
| Steps (reduced) |
677 (0) |
1073 (396) |
1572 (218) |
1901 (547) |
2342 (311) |
2505 (474) |
2767 (59) |
2876 (168) |
3062 (354) | |