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'''Error''' (also '''mistuning'''<ref>[[Erlich, Paul]]. "[[:File:MiddlePath2015.pdf|A Middle Path: Between Just Intonation and the Equal Temperaments, Part 1]] | '''Error''' (also '''mistuning'''<ref>[[Erlich, Paul]]. "[[:File:MiddlePath2015.pdf|A Middle Path: Between Just Intonation and the Equal Temperaments, Part 1]]." ''Xenharmonikôn, An Informal Journal of Experimental Music'' 18 (2006): 159-199.</ref>) is a measurement of the deviation of an [[interval]] from another interval that it is approximating. The {{w|retronym}} ''absolute error'' is sometimes used to contrast it with [[relative error]]. Error is usually signed, with a positive value indicating an overshoot of the target, and a negative value indicating an undershoot. The {{w|absolute value}} of error is called ''unsigned error''. | ||
For example, the [[regular temperament|tempered]] ~3/2 of [[quarter-comma meantone]] is 696.578{{c}}, while a [[JI|just]] 3/2 is 701.955{{c}}, so the error of this ~3/2 is {{nowrap|696.578{{c}} − 701.955{{c}} {{=}} −5.377{{c}}}}. | For example, the [[regular temperament|tempered]] ~3/2 of [[quarter-comma meantone]] is 696.578{{c}}, while a [[JI|just]] 3/2 is 701.955{{c}}, so the error of this ~3/2 is {{nowrap|696.578{{c}} − 701.955{{c}} {{=}} −5.377{{c}}}}. | ||
Latest revision as of 15:42, 12 August 2026
Error (also mistuning[1]) is a measurement of the deviation of an interval from another interval that it is approximating. The retronym absolute error is sometimes used to contrast it with relative error. Error is usually signed, with a positive value indicating an overshoot of the target, and a negative value indicating an undershoot. The absolute value of error is called unsigned error.
For example, the tempered ~3/2 of quarter-comma meantone is 696.578 ¢, while a just 3/2 is 701.955 ¢, so the error of this ~3/2 is 696.578 ¢ − 701.955 ¢ = −5.377 ¢.
See also
- Damage, a measurement of how much an interval deviates from another interval it is approximating: the absolute value of error that has possibly been weighted over complexity
- Dave Keenan & Douglas Blumeyer's guide to RTT/Tuning fundamentals #Damage, error, and weight: for a discussion of error with respect to damage and weight
- Error map
- TE error
References
- ↑ Erlich, Paul. "A Middle Path: Between Just Intonation and the Equal Temperaments, Part 1." Xenharmonikôn, An Informal Journal of Experimental Music 18 (2006): 159-199.