Precision limits - FloraCanou/temperament_evaluator GitHub Wiki

Since v1.9.0, we switched to the COBYQA method for our main optimizer. This has massively improved the accuracy. Beware however, that it still has limits, with constrained tunings of particular concern.

For most of such tunings, it is safe to assume a tolerance of a fraction of a microcent. In other words, the first 6 decimal places should be accurate. However, this figure tends to scale with the inaccuracy of the temperament itself, with the tunings of exotemperaments such as father erring by as much as several microcents. Make sure to double check the figures if you're documenting them on the Xenharmonic Wiki, for example, even though the accuracy is more than enough for any sane musical purposes.

Tuning	Computed value (¢)	True value (¢)	Unsigned error (¢)
Father, 5-limit CTE	1937.468685902	1937.468684899	~ 1.0e-6
Father, 5-limit CEE	1957.820644501	1957.820643500	~ 1.0e-6
Father, 5-limit CBE	1931.530934208	1931.530929309	~ 4.9e-6
Blackwood, 7-limit CTE	2786.313713870	2786.313713865	~ 5e-9
Meantone, 7-limit CTE	1896.952137737	1897.952137737	< 1e-9
Meantone, 7-limit CWE	1896.656198703	1896.656198703	< 1e-9
Meantone, 7-limit CEE	1896.884349733	1896.884349752	~ 1.9e-8
Meantone, 7-limit CBE	1897.014734962	1897.014734962	< 1e-9
Meantone, 7-limit CTOP	1897.645846133	1897.645846857	~ 7.2e-7
Meantone, 7-limit CTC	1896.882590845	1896.882590647	~ 2.0e-7
BPS, 3.5.7-subgroup CTE	441.143147022	441.143147023	~ 1e-9