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The
hand written text and the drawn spirals
in the figure above,
come from the score of "Das wohltemperirte Clavier" by J. S. Bach. The above figure with spirals, could contain indications from J. S. Bach, on how to tune a keyboard, according a hypothesis formulated by Jobin, A slightly differing interpretation of the above "Bach spirals" can be worked out, based on equal beating characteristics of fifths and major thirds of C-major, rather than the equal ratio of fifths leading to pure thirds, such as assumed by Jobin. Jobin: see https://www.clavecin-en-france.org/spip.php?article52 A text discussing the
calculated alternatives based on interval beat calculations, for
sure clear to any musicologist, possibly assisted by some
mathematician, is published in the december 2020 edition of the
PIANISTIKjournal (https://europianofrance.org/).It became clear that an assumption leading to of perfect equal
beating and five fifths, meets the assumed characteristics of
spirals very well. An almost identical hypothesis, includes three
major thirds of almost
equal beating and six fifths..three
major thirdsA new (English) version of the above referred Pianistik text can be downloaded. A video esplaining the temperament is available at This text should be accessible for comprehensive reading by anyone interested. This text includes supplements: brief history of musical temperaments, mathematical, acoustic and physical sciences, some basic music theory, and sufficiently extensive calculations of all the models studied, to allow for their verification,. Calvet believes a beat rate approach can make sense. http://andrecalvet.com/v3/index.php (diapason: Key
resultsA4 = 440)5 fifths and 3 major thirds, with
perfectly equal beat
Broekaert Johan 2021-01-05
broekaert.devriendt@gmail.com
Most recent version of the papers : |
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Very sincere thanks to: Prof. E. Amiot, A. Calvet, E. Jobin, T. Paintoux: they were kindly open for communications and interchanges of ideas, leading to this disclosure. G. Baroin: for the compilation of a magnificent video dealing with the subject My daughter Hilde: she drew my attention to investigate on what musicians want (diatonic interval purity) and not on what might be someone's preferred musical temperament. |