  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 mathematical
ranking of historical temperaments. Historical temperaments that fit best with
mathematical models are often installed on organs. Musical appreciation and
mathematical ranking of historical temperaments are in agreement. The diatonic
C-major impurity of Well Temperaments lies between that of an elaborated
optimal model and that of Equal Temperament. Historical Well Temperaments join
these limits very closely and the list is amply filled in small rising steps.
Hence, it achieves little to develop new Well Temperaments. The developed RMS
computing modules can also be used for precise and accurate recognition of
historical temperaments.
