On Mar 23, 2009, at 10:42 AM, Sloane, Benjamin (sloaneba) wrote: > “Would the bps of all four at some location in the keyboard equally > tempered coincide? The greatest specificity for my question is > eliminated when I am forced to use certain notes to explain my > question. I use a minor 6th above the fundamental to check both the > 8:4 octave and the 8:6 fourth Practically speaking, I think these tests of coincidences of partials above the 6th partial are of little use. First of all, the partials tend to be weak (the 8th tends to be one of the weakest), so they are hard to hear. But more importantly, issues of inharmonicity come to the fore, especially in the midrange area, where the lower tenor notes (lowest plain strings) are highest in inharmonicity, and there tends not to be a good match of partial ladders (the low tenor, high inharmonicity notes have ladders that rapidly ascend, compared to the highest wound strings and the higher plain strings). In my experience, 3:2 5ths are far more useful than 6:4, and 4:3 4ths more than 8:6. For example, often you find that a 6:4 5th in the temperament octave that is "appropriately narrow" will mean a widened 3:2 5th (thinking of Acrosonics, Kimballs, and Wurlitzers as common examples). Where it is useful to listen to higher coincidences is in knowing why that 5th sounds the way it does, where those strange beats are located and why they are there. If you are "listening to the whole sound" of a 5th, you can become hopelessly confused. (On larger, more evenly scaled instruments, this is not so much of an issue). Regards, Fred Sturm University of New Mexico fssturm at unm.edu -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut_ptg.org/attachments/20090323/816750bf/attachment.html>
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