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Mathematical steps are developed to obtain optimised well tempered model"temperaments", based on a musical Well Temperament definition by H. Kelletat,that is derived from A. Werckmeister. This supports objective mathematicalranking of historical temperaments. Historical temperaments that fit best withmathematical models are often installed on organs. Musical appreciation andmathematical ranking of historical temperaments are in agreement. The diatonicC-major impurity of Well Temperaments lies between that of an elaboratedoptimal model and that of Equal Temperament. Historical Well Temperaments jointhese limits very closely and the list is amply filled in small rising steps.Hence, it achieves little to develop new Well Temperaments. The developed RMScomputing modules can also be used for precise and accurate recognition ofhistorical temperaments.

Well Temperaments based on the Werckmeister Definition From  Werckmeister, passing Vallotti, Bach and Kirnberger, to Equal Temperament  Inspired by Kelletat and Amiot