Playⓘ Each step represents a frequency ratio of 21/41, or 29.27 cents (Playⓘ), an interval close in size to the septimal comma.
It is the second smallest equal temperament, after 29-ET, whose perfect fifth is closer to just intonation than that of 12-ET.
Although 41-ET has not seen as wide use as other temperaments such as 19-ET or 31-ET [citation needed], pianist and engineer Paul von Janko built a piano using this tuning, which is on display at the Gemeentemuseum in The Hague.
[4] Thus, any two adjacent strings together contain all the pitch classes of the full 41-ET system.
The Kite Guitar's main tuning uses 13 steps of 41-ET (which approximates a 5/4 ratio) between strings.
With that tuning, all simple ratios of odd limit 9 or less are available at spans at most only 4 frets.
41-ET is also a subset of 205-ET, for which the keyboard layout of the Tonal Plexus is designed.
Here are the sizes of some common intervals (shaded rows mark relatively poor matches): As the table above shows, the 41-ET both distinguishes between and closely matches all intervals involving the ratios in the harmonic series up to and including the 10th overtone.
41-ET also closely matches a number of other intervals involving higher harmonics.
It distinguishes between and closely matches all intervals involving up through the 12th overtones, with the exception of the greater undecimal neutral second (11:10).
Using extended pythagorean notation results in double and even triple sharps and flats.
[5] The up and down arrows are written as a caret or a lower-case "v", usually in a sans-serif font.