Improved and supplemented
edition.
From Werckmeister, passing Bach and Kirnberger to Vallotti. Inspired by Kelletat or go to (1.5 MB) Summary of content: Graphic display of some interval
characteristics of widespread Well Temperaments:
Abstract :
Based on the definition of well temperaments, elaborated by Kelletat
H., but derived from Werckmeister, a number of logic mathematical steps
are developed, in order to obtain mathematically optimised well
tempered model-“temperaments”. This leads to an objective mathematical
classification of historical temperaments. Historical temperaments that
fit best with the well tempered models are the same as those that are
very often installed on organs, with highest established musical
appreciations and notoriety. The elaborated mathematical appreciation
and the musical appreciation of historical temperaments are thus in
good accordance. All Well Temperaments lie qualitatively between the
elaborated optimum and the Equal Temperament. They join these limits
very closely and the list is well filled in small rising steps. Hence,
it makes no sense to develop new well temperaments further on. Temperament Recognition:
Download file Characterisation_of_Temperaments.xls Kelletat Definition,
based on Werckmeister publications: Well
temperament means a mathematical-acoustic and musical-practical
organisation of
the tone system within the twelve steps of an octave, so that
impeccable performance
in all tonalities is enabled, .keep the diatonic intervals as
pure as possibleThis
temperament acts, while tied to given pitch ratios, as a thriftily
tempered
smoothing and and
as(equally beating) equal ”..temperamentOriginal German text: “Wohltemperierung heißt mathematisch-akustische und
praktisch-musikalischen
Einrichtung von Tonmaterial innerhalb der zwölfstufigen Oktavskala
zum einwandfreien
Gebrauch in allen Tonarten auf der Grundlage des
natürlich-harmonischen Systems
mit Bestreben möglichster Reinerhaltung der diatonische Intervalle. Sie tritt auf als proportionsgebundene, sparsam temperierende Lockerung und Dehnung des mitteltönigen Systems, als ungleichschwebende Semitonik und als gleichschwebende Temperatur.” (Orgelprobe, 1681). |