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Brouncker's golden temperament?

🔗genewardsmith <genewardsmith@juno.com>

2/24/2002 11:38:58 PM

Isacoff claims Brouncker came up with a temperament based on the golden ratio which was "absolutely unusable". Does anyone know what he is talking about? If he means 2^phi in place of 3, that's nearly 40 cents *sharp*, and hardly seems like something someone would suggest to temper 12 tones to the octave.

🔗manuel.op.de.coul@eon-benelux.com

2/25/2002 7:27:39 AM

Yes Brouncker proposed 17-tET (Joe please note). See
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Brouncker.html

From this page:
"These studies were mathematics and music, two topics which
Brouncker loved. It was during this time that he worked on a
publication which would in fact be his only book. Descartes had
written a paper on music in 1618 but it had never been published.
Only after Descartes' death in 1650 did a Dutch publisher print
it as a 58 page pamphlet with the title Renati Descartes Musicae
Compendium. In 1653 Brouncker published his English translation
of Descartes' work but he added notes of his own which doubled
the size of the work. Mersenne had proposed a scale of 12 equal
semitones after Descartes' manuscript had been written and in
his notes Brouncker proposed a variation of Mersenne's ideas but
he divided the scale into 17 equal semitones. One should not be
surprised that all these mathematicians were contributing to
musical theory and indeed Brouncker's notes are highly
mathematical using algebra and logarithms. One might wonder why
Brouncker chose 17 equal semitones and again the reason was a
mathematical one for he derived this from taking ratios based on
the golden section."

Manuel