For those of you interested, it can be helpful to look at a graphical representation of the temperaments, when choosing which one to set on an instrument. Jason Kanter has done a great service to our community by transferring the published offsets of both historical temperaments and modern creations of alternate temperaments. These can be found at: www.rollingball.com In these graphs you can find the width of the major thirds, minor thirds and 5ths, arranged in circle of fifths order. Also documented is predicted beat rates, as well as the EDT offsets. When tuning, I like to look at three numbers: 1. the maximum offset from ET 2. the width of the smallest third 3. the width of the largest third Once you have those numbers, the shape of the graph gives you an idea of how many thirds are purer than ET and how many are less pure than ET. Remember that modern ears will start noticing that something is amiss once the major thirds cross the 17-18 cent width. With that in mind, all of the "biggies" (Vallotti, Young, etc.) with their 21+ cent thirds will be a big change from ET. The Maximum offset number may help explain why the Vallotti might have been a problem for the string players. Even though the Vallotti and the Young graphs appear similar, the maximum offset for the Young is around 6 cents, while the Vallotti pushes up somewhere around 8 cents from ET. I'd really recommend starting with the milder modern creations that have been formulated with an eye to beat-rate progressions and checking the Minor 3rd/Major 3rd ratios. Ron Koval Concordia University _________________________________________________________________ STOP MORE SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail
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