601edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 25: | Line 26: | ||
| {{monzo| -1905 601 }} | | {{monzo| -1905 601 }} | ||
| {{mapping| 601 1905 }} | | {{mapping| 601 1905 }} | ||
| 0.0393 | | +0.0393 | ||
| 0.0393 | | 0.0393 | ||
| 1.97 | | 1.97 | ||
| Line 32: | Line 33: | ||
| 32805/32768, {{monzo| -105 -65 134 }} | | 32805/32768, {{monzo| -105 -65 134 }} | ||
| {{mapping| 601 1905 1395 }} | | {{mapping| 601 1905 1395 }} | ||
| 0.1635 | | +0.1635 | ||
| 0.1785 | | 0.1785 | ||
| 8.94 | | 8.94 | ||
| Line 39: | Line 40: | ||
| 32805/32768, 68359375/68024448, {{monzo| -16 -5 -2 13 }} | | 32805/32768, 68359375/68024448, {{monzo| -16 -5 -2 13 }} | ||
| {{mapping| 601 1905 1395 1687 }} | | {{mapping| 601 1905 1395 1687 }} | ||
| 0.1618 | | +0.1618 | ||
| 0.1546 | | 0.1546 | ||
| 7.74 | | 7.74 | ||
| Line 46: | Line 47: | ||
| 6250/6237, 41503/41472, 32805/32768, 3294225/3294172 | | 6250/6237, 41503/41472, 32805/32768, 3294225/3294172 | ||
| {{mapping| 601 1905 1395 1687 2079 }} | | {{mapping| 601 1905 1395 1687 2079 }} | ||
| 0.1431 | | +0.1431 | ||
| 0.1432 | | 0.1432 | ||
| 7.17 | | 7.17 | ||
| Line 53: | Line 54: | ||
| 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 | | 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 | ||
| {{mapping| 601 1905 1395 1687 2079 2224 }} | | {{mapping| 601 1905 1395 1687 2079 2224 }} | ||
| 0.1160 | | +0.1160 | ||
| 0.1441 | | 0.1441 | ||
| 7.22 | | 7.22 | ||
Latest revision as of 13:04, 21 February 2025
| ← 600edo | 601edo | 602edo → |
601 equal divisions of the octave (abbreviated 601edo or 601ed2), also called 601-tone equal temperament (601tet) or 601 equal temperament (601et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 601 equal parts of about 2 ¢ each. Each step represents a frequency ratio of 21/601, or the 601st root of 2.
Theory
601edo is inconsistent to the 5-odd-limit and both harmonics 3 and 5 are about halfway between its steps. It can be used in the 2.9.15.7.11.13.19 subgroup, tempering out 41503/41472, 104272/104247, 10648/10647, 388962/388531 and 10097379/10092544.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.874 | -0.956 | -0.440 | -0.249 | -0.236 | +0.071 | -0.082 | +0.868 | -0.009 | +0.434 | +0.677 |
| Relative (%) | +43.8 | -47.9 | -22.0 | -12.5 | -11.8 | +3.6 | -4.1 | +43.5 | -0.4 | +21.7 | +33.9 | |
| Steps (reduced) |
953 (352) |
1395 (193) |
1687 (485) |
1905 (102) |
2079 (276) |
2224 (421) |
2348 (545) |
2457 (53) |
2553 (149) |
2640 (236) |
2719 (315) | |
Subsets and supersets
601edo is the 110th prime edo. 1202edo, which doubles it, gives a good correction to the harmonics 3 and 5.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-1905 601⟩ | [⟨601 1905]] | +0.0393 | 0.0393 | 1.97 |
| 2.9.5 | 32805/32768, [-105 -65 134⟩ | [⟨601 1905 1395]] | +0.1635 | 0.1785 | 8.94 |
| 2.9.5.7 | 32805/32768, 68359375/68024448, [-16 -5 -2 13⟩ | [⟨601 1905 1395 1687]] | +0.1618 | 0.1546 | 7.74 |
| 2.9.5.7.11 | 6250/6237, 41503/41472, 32805/32768, 3294225/3294172 | [⟨601 1905 1395 1687 2079]] | +0.1431 | 0.1432 | 7.17 |
| 2.9.5.7.11.13 | 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 | [⟨601 1905 1395 1687 2079 2224]] | +0.1160 | 0.1441 | 7.22 |