2019edo: Difference between revisions
Jump to navigation
Jump to search
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
+subsets and supersets |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|2019}} | {{EDO intro|2019}} | ||
== Theory == | == Theory == | ||
2019edo is excellent in the | 2019edo is excellent in the 7-limit, and with such small errors it supports a noticeable amount of [[very high accuracy temperaments]]. While it is [[consistent]] in the [[11-odd-limit]], there is a large relative error on the representation of the [[11/1|11th harmonic]]. | ||
In higher limits, it tunes [[23/16]] and [[59/32]] with the comparable relative accuracy to the 2.3.5.7 subgroup (less than 7% error). A comma basis for the 2.3.5.7.23.59 subgroup is {14337/14336, 25921/25920, 250047/250000, 48234496/48234375, 843396867/843308032}. | In higher limits, it tunes [[23/16]] and [[59/32]] with the comparable relative accuracy to the 2.3.5.7 subgroup (less than 7% error). A comma basis for the 2.3.5.7.23.59 subgroup is {14337/14336, 25921/25920, 250047/250000, 48234496/48234375, 843396867/843308032}. | ||
| Line 8: | Line 9: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2019}} | {{Harmonics in equal|2019}} | ||
=== Subsets and supersets === | |||
Since 2019 factors into {{factorization|2019}}, 2019 contains [[3edo]] and 673edo as subsets. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 15: | Line 19: | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
Revision as of 12:05, 30 October 2023
| ← 2018edo | 2019edo | 2020edo → |
Theory
2019edo is excellent in the 7-limit, and with such small errors it supports a noticeable amount of very high accuracy temperaments. While it is consistent in the 11-odd-limit, there is a large relative error on the representation of the 11th harmonic.
In higher limits, it tunes 23/16 and 59/32 with the comparable relative accuracy to the 2.3.5.7 subgroup (less than 7% error). A comma basis for the 2.3.5.7.23.59 subgroup is {14337/14336, 25921/25920, 250047/250000, 48234496/48234375, 843396867/843308032}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.023 | +0.016 | -0.029 | +0.242 | -0.112 | +0.245 | +0.258 | -0.043 | -0.157 | +0.284 |
| Relative (%) | +0.0 | -3.9 | +2.7 | -5.0 | +40.8 | -18.8 | +41.3 | +43.4 | -7.2 | -26.4 | +47.8 | |
| Steps (reduced) |
2019 (0) |
3200 (1181) |
4688 (650) |
5668 (1630) |
6985 (928) |
7471 (1414) |
8253 (177) |
8577 (501) |
9133 (1057) |
9808 (1732) |
10003 (1927) | |
Subsets and supersets
Since 2019 factors into 3 × 673, 2019 contains 3edo and 673edo as subsets.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 154\2019 | 91.530 | [46 -7 -15⟩ | Gross |
| 1 | 307\2019 | 182.467 | 10/9 | Minortone |
| 3 | 307\2019 | 182.467 | 10/9 | Domain |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct