User:Francium/1301edo
| ← 1300edo | 1301edo | 1302edo → |
1301 equal divisions of the octave (abbreviated 1301edo or 1301ed2), also called 1301-tone equal temperament (1301tet) or 1301 equal temperament (1301et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1301 equal parts of about 0.922 ¢ each. Each step represents a frequency ratio of 21/1301, or the 1301st root of 2.
Theory
1301edo is consistent to the 5-limit, tempering out [61 4 -29⟩ and [-69 45 -1⟩. It is strong in the 2.3.5.23 subgroup, tempering out 48892572/48828125, 199344128/199290375 and 144115188075855872/144102261572578125.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.033 | +0.158 | -0.340 | +0.258 | -0.251 | +0.194 | +0.412 | -0.142 | -0.215 | -0.378 |
| Relative (%) | +0.0 | -3.6 | +17.2 | -36.9 | +27.9 | -27.2 | +21.1 | +44.6 | -15.4 | -23.3 | -40.9 | |
| Steps (reduced) |
1301 (0) |
2062 (761) |
3021 (419) |
3652 (1050) |
4501 (598) |
4814 (911) |
5318 (114) |
5527 (323) |
5885 (681) |
6320 (1116) |
6445 (1241) | |
Subsets and supersets
1301edo is the 212th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2062 1301⟩ | [⟨1301 2062]] | +0.0105 | 0.0105 | 1.14 |
| 2.3.5 | [61 4 -29⟩, [-69 45 -1⟩ | [⟨1301 2062 3021]] | −0.0157 | 0.0381 | 4.13 |
| 2.3.5.7 | 420175/419904, 1640558367/1638400000, 152946081792/152587890625 | [⟨1301 2062 3021 3652]] | +0.0185 | 0.0678 | 7.35 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 430\1301 | 396.6180 | 98304/78125 | Squarschmidt |
| 1 | 540\1301 | 498.0784 | 4/3 | Counterschismic |