1395edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
1395edo is a strong higher-limit system, being a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. However, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}. | |||
Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|1395|columns=11}} | |||
{{Harmonics in equal|1395|columns=11|start=12|title=Approximation of prime harmonics in 1395edo (continued)}} | |||
=== Subsets and supersets === | |||
Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}. | |||
Latest revision as of 07:55, 1 March 2026
| ← 1394edo | 1395edo | 1396edo → |
1395 equal divisions of the octave (abbreviated 1395edo or 1395ed2), also called 1395-tone equal temperament (1395tet) or 1395 equal temperament (1395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1395 equal parts of about 0.86 ¢ each. Each step represents a frequency ratio of 21/1395, or the 1395th root of 2.
1395edo is a strong higher-limit system, being a zeta peak, peak integer, integral and gap edo. The patent val is the first one after 311 with a lower 37-limit relative error. However, it is only consistent through the 21-odd-limit, due to harmonic 23 being all of 0.3 cents flat, causing 23/19 to become inconsistent, though it remains the only inconsistency up to the 39-odd-limit. A comma basis for the 19-limit is {2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.
Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.020 | -0.077 | -0.224 | +0.080 | -0.098 | -0.009 | +0.121 | -0.317 | +0.100 | -0.089 |
| Relative (%) | +0.0 | -2.3 | -9.0 | -26.0 | +9.3 | -11.3 | -1.1 | +14.1 | -36.9 | +11.7 | -10.4 | |
| Steps (reduced) |
1395 (0) |
2211 (816) |
3239 (449) |
3916 (1126) |
4826 (641) |
5162 (977) |
5702 (122) |
5926 (346) |
6310 (730) |
6777 (1197) |
6911 (1331) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.161 | +0.185 | +0.310 | +0.300 | -0.386 | -0.247 | -0.326 | -0.167 | +0.088 | +0.168 | +0.194 |
| Relative (%) | -18.7 | +21.5 | +36.1 | +34.9 | -44.9 | -28.7 | -37.9 | -19.4 | +10.3 | +19.5 | +22.6 | |
| Steps (reduced) |
7267 (292) |
7474 (499) |
7570 (595) |
7749 (774) |
7990 (1015) |
8206 (1231) |
8273 (1298) |
8462 (92) |
8579 (209) |
8635 (265) |
8794 (424) | |
Subsets and supersets
Since 1395 factors into 32 × 5 × 31, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.