1395edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1395}} | {{EDO intro|1395}} | ||
== Theory == | == Theory == | ||
1395edo is a strong higher-limit system, being a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, peak integer, integral and gap edo]]. The patent val is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only consistent through the 21-odd-limit, due to 23 being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {2058/2057, [[2401/2400]], 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}. | 1395edo is a strong higher-limit system, being a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only [[consistent]] through the 21-odd-limit, due to 23 being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {2058/2057, [[2401/2400]], 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1395|columns=15}} | {{Harmonics in equal|1395|columns=15}} | ||
=== Subsets and supersets === | |||
Since 1395 factors into 3<sup>2</sup> × 5 × 31, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465. | |||
Revision as of 13:22, 10 February 2023
| ← 1394edo | 1395edo | 1396edo → |
Theory
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, though it is only consistent through the 21-odd-limit, due to 23 being all of 0.3 cents flat. A comma basis for the 19-limit is {2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.020 | -0.077 | -0.224 | +0.080 | -0.098 | -0.009 | +0.121 | -0.317 | +0.100 | -0.089 | -0.161 | +0.185 | +0.310 | +0.300 |
| Relative (%) | +0.0 | -2.3 | -9.0 | -26.0 | +9.3 | -11.3 | -1.1 | +14.1 | -36.9 | +11.7 | -10.4 | -18.7 | +21.5 | +36.1 | +34.9 | |
| Steps (reduced) |
1395 (0) |
2211 (816) |
3239 (449) |
3916 (1126) |
4826 (641) |
5162 (977) |
5702 (122) |
5926 (346) |
6310 (730) |
6777 (1197) |
6911 (1331) |
7267 (292) |
7474 (499) |
7570 (595) |
7749 (774) | |
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.